Answers
Answer:
View Image
Step-by-step explanation:
Solve for y.
You have a ≥ so it's a solid line and you shade above that line.
Related Questions
Analytic function on unit disk with power series has pole on unit circle, then power series diverges on unit circle.
Answers
Answer:
The function
{\ displaystyle f (z) = {\ frac {z} {1- | z | ^ {2}}}} {\ displaystyle f (z) = {\ frac {z} {1- | z | 2}
It is an example of real and bijective analytical function from the open drive disk to the Euclidean plane, its inverse is also an analytical function. Considered as a real two-dimensional analytical variety, the open drive disk is therefore isomorphic to the complete plane. In particular, the open drive disk is homeomorphic to the complete plan.
However, there is no bijective compliant application between the drive disk and the plane. Considered as the Riemann surface, the drive disk is therefore different from the complex plane.
There are bijective conforming applications between the open disk drive and the upper semiplane and therefore determined as Riemann surfaces, are isomorphic (in fact "biholomorphic" or "conformingly equivalent"). Much more in general, Riemann's theorem on applications states that the entire open set and simply connection of the complex plane that is different from the whole complex plane admits a bijective compliant application with the open drive disk. A bijective compliant application between the drive disk and the upper half plane is the Möbius transformation:
{\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}} {\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}}
which is the inverse of the transformation of Cayley.
if an analytic function on the unit disk has a pole on the unit circle, its power series representation diverges on the unit circle, as the singularity prevents the power series from converging outside the disk of convergence.
To understand why a power series diverges on the unit circle when the analytic function it represents has a pole on the unit circle, we can use the concept of analytic continuation and the properties of poles and singularities.
Here's a step-by-step explanation:
1.Analytic function on the unit disk: Let's consider an analytic function defined on the open unit disk, denoted by[tex]\(D = \{z \in \mathbb{C} : |z| < 1\}\)[/tex]. This means the function is holomorphic (complex differentiable) at every point within this disk.
2.Power series representation: Since the function is analytic on[tex]\(D\)[/tex], it can be represented by a power series expansion around any point [tex]\(z_0\) in \(D\)[/tex]. Let's denote this function by[tex]\(f(z)\)[/tex], and its power series representation centered at[tex]\(z_0\) by \(\sum_{n=0}^{\infty} a_n (z - z_0)^n\)[/tex].
3.Pole on the unit circle: Suppose[tex]\(f(z)\)[/tex] has a pole (a point where the function becomes unbounded) on the unit circle[tex]\(|z| = 1\)[/tex], i.e., there exists a point [tex]\(z_1\)[/tex] on the unit circle such that [tex]\(f(z_1)\)[/tex] is infinite. Without loss of generality, let's assume [tex]\(z_1 = 1\)[/tex] (since the unit circle is symmetric about the origin).
4.Behavior near the pole: Near the pole at [tex]\(z = 1\)[/tex], the function[tex]\(f(z)\)[/tex]can be expanded in a Laurent series, which includes negative powers of [tex]\((z - 1)\)[/tex]. This expansion will have infinitely many terms with negative powers, indicating the singularity at [tex]\(z = 1\)[/tex].
5.Radius of convergence: The radius of convergence of the power series representation of [tex]\(f(z)\)[/tex]is at least the distance from the center of convergence to the nearest singularity. In this case, since the singularity (pole) is on the unit circle, the radius of convergence of the power series cannot exceed 1.
6.Divergence on the unit circle: Since the radius of convergence of the power series representation of [tex]\(f(z)\)[/tex] is at most 1, the power series diverges at every point on the unit circle (except possibly at the point of singularity itself, where it may converge by definition). This divergence occurs because the function has a singularity (pole) on the unit circle.
Therefore, if an analytic function on the unit disk has a pole on the unit circle, its power series representation diverges on the unit circle, as the singularity prevents the power series from converging outside the disk of convergence.
If $-5\leq a \leq -1$ and $1 \leq b \leq 3$, what is the least possible value of $\displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) $
Answers
Answer:
The least possible value is -2, obtained for a = -1 and b = 1.
Step-by-step explanation:
We want the minimum of [tex] \displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) [/tex] , where
[tex] -5 \leq a \leq -1 [/tex][tex] 1 \leq b \leq 3 [/tex]First, lets simplify the expression given, we use common denominator on the second part, using ab as the common denominator. We obtain
[tex] \frac{1}{b} - \frac{1}{a} = \frac{a-b}{ab} [/tex]
As a result
[tex] \displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) = \frac{a-b}{(ab)^2} [/tex]
we need the minimum of the function
[tex] f(a,b) = \frac{a-b}{(ab)^2} [/tex]
with the restrictions [tex] -5 \leq a \ -1, 1 \leq b \leq 3 [/tex]
First, we calculate the gradient of f and find where it takes the zero value.
[tex]\nabla{f} = (f_a,f_b) [/tex]
with
[tex]f_a = \frac{(ab)^2 - (a-b) 2ab^2}{(ab)^2} = -1 + 2 \frac{b}{a}[/tex]
Since it has the reversed sign, we get
[tex]f_b = - (-1 + 2 \frac{a}{b}) =1 - 2 \frac{a}{b}[/tex]
In order for [tex] \nabla{f} [/tex] to be zero, we need both [tex] f_a [/tex] and [tex] f_b [/tex] to be zero, observe that
[tex]f_b = 0 \, \rightarrow 1 -2\frac{a}{b} = 0 \, \rightarrow 1 = 2 \frac{a}{b} \, \rightarrow b = 2a [/tex]
Which is impossible with the given restrictions. Hence, the minimum is realized in the border.
If we fix a value a₀ for a, with a₀ between -5 and -1 the function g(b) = f(a₀,b) wont have a minimum for b in [1,3] because the partial derivate of f over b didnt reach the value 0 in the restrictions given. On the other hand. by making a similar computation that before, we can obtain that the partial derivate of f over the variable a doesnt reach the value 0 either. This means that f doesnt reach the minimum on the sides. As a consecuence, it reach a minimum on the corners.
The 4 possible corner values are (-5,1), (-5,3), (-1,1) and (-1,3)
[tex] f(-5,1) = \frac{-6}{25} = -0.24 [/tex]
[tex] f(-5,3) = \frac{-8}{225} = -0.0355 [/tex]
[tex] f(-1,1) = \frac{-2}{1} = -2 [/tex]
[tex] f(-1,3) = \frac{-4}{9} = -0.444 [/tex]
Clearly the least possible value between the four corners is -2.
Consider the vector field ????(x,y,z)=(5z+y)????+(4z+x)????+(4y+5x)????.
a. Find a function ???? such that ????=∇???? and ????(0,0,0)=0.
b. Suppose C is any curve from (0,0,0) to (1,1,1). Use part a. to compute the line integral ∫????????⋅????????.
Answers
Answer:
a) [tex]5xz + xy + 4yz[/tex]
b) 10
Step-by-step explanation:
a) Here [tex]F(x,y,z)=(5z+y)i+(4z+x)j+(4y+5x)k[/tex]
Since the case [tex]F[/tex] = ∇[tex]f[/tex] holds, then
∇[tex]f = f_xi+f_yj+f_zk[/tex] = [tex](5z+y)i+(4z+x)j+(4y+5x)k[/tex]
So, [tex]f_x = 5z + y[/tex]
If we integrate [tex]f_x[/tex] with respect to x, we will get an integration constant C which is also a function that depends to y and z.
Hence,
[tex]f = \int f_xdx = 5xz + xy + g(y,z)[/tex]
Now we need to find g(y,z).
So first let's take the derivative of g(y,z) with respect to y.
[tex]f_y = x + g_y(y,z) = 4z + x[/tex]
Hence, [tex]g_y(y,z) = 4z[/tex]
So now, if we integrate [tex]g_y[/tex] with respect to y to find g(y,z)
[tex]g = \int g_ydy = 4yz + C[/tex]
Thus,
[tex]f = 5xz + xy + g(y,z) = 5xz + xy + 4yz + C[/tex]
And since [tex]f(0,0,0)=0[/tex], then [tex]C=0[/tex]
Thus,
[tex]f = f(x,y,z) = 5xz + xy + 4yz[/tex]
b) By the Fundamental Theorem of Line Integrals, we know that
[tex]\int\limits^a_b F. dr = F[r(b)]-F[r(a)][/tex]
Hence,
[tex]\int\limits^a_b F. dr = F(1,1,1)-F(0,0,0) =[(5+1+4)-(0+0+0)]=10[/tex]
To find ????, solve the system of partial differential equations. Use the function ???? from part a to compute the line integral.
Explanation:To find a function ???? such that ????=∇???? and ????(0,0,0)=0, we can solve the system of partial differential equations. Let ????=????????+????????+????????, then compute the partial derivatives of ???? with respect to each variable. Equating these partial derivatives to the given vector field components, we can solve for the unknown function ???? and find its value at the point (0,0,0).
To compute the line integral ∫????????⋅????????, we can use the fundamental theorem of calculus for line integrals. Since ????(x,y,z) is the gradient of ????, the line integral is equal to the change in ???? along the curve C from (0,0,0) to (1,1,1). We can use the function ???? found in part a to evaluate this change in ????.
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The perimeter of a rectangle is 360m. If it's length is decreased by 20% and it's breadth is increased by 25%, we get the same perimeter. Find the dimensions of the rectangle.
Answers
Answer:the length of the rectangle is 100m
the width of the rectangle is 80m
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + B)
The perimeter of a rectangle is 360m. This means that
2(L + B) = 360
L + B = 180 - - - - - - - - - -1
If it's length is decreased by 20%, its new length would be
L - 0.2L = 0.8L
it's breadth is increased by 25%, it means that the new breadth
B + 0.25B = 1.25B
Since the perimeter remains the same,
2(0.8L + 1.25B) = 360
0.8L + 1.25B = 180 - - - - - - - - -2
Substituting L = 180 - B into equation 2, it becomes
0.8(180 - B) + 1.25B = 180
144 - 0.8B + 1.25B = 180
- 0.8B + 1.25B = 180 - 144
0.45B = 36
B = 36/0.45 = 80
L = 180 - B = 180 - 80
L = 100
Which equilibrium at one atmosphere pressure is correctly associated with Kelvin temperature at which it occur?a. ice-water equilibrium at 0 K
b. ice-water equilibrium at 32 K
c. steam-water equilibrium at 212 K
d. steam-water equilibrium at 373 K
Answers
The correct equilibrium at one atmosphere pressure associated with its Kelvin temperature is the steam-water equilibrium at 373 K.
Explanation:The equilibrium at one atmosphere pressure that is correctly associated with the Kelvin temperature at which it occurs is option d. steam-water equilibrium at 373 K. To explain, in the Kelvin temperature scale, the freezing point of water is 273.15 K and the boiling point is 373.15 K, both under standard atmospheric conditions (1 atmosphere pressure). So, at 373 K, the situation would be a steam-water equilibrium, not an ice-water equilibrium as in options a and b. The Kelvin temperature for ice-water equilibrium is 273.15 K and not 0 K and 32 K as stated in options a or b. Similarly, steam-water equilibrium does not occur at 212 K as suggested in option c.
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Option d. steam-water equilibrium at 373 K. The steam-water equilibrium at one atmosphere pressure occurs at 373 K.
The correct answer is:
Steam-water equilibrium at 373 KLet's break down the reasons:
Ice-water equilibrium: This occurs at 0°C, which is 273.15 K, not 0 K or 32 K.Steam-water equilibrium: The boiling point of water is 100°C, which is 373.15 K. At one atmosphere of pressure, water and steam are in equilibrium at this temperature.Thus, the correct association is the steam-water equilibrium occurring at 373 K at 1 atmosphere pressure.
James and Lucas competed in climbing a mountain and coming back. James climbed at an average rate of 3 mph and ran back at 4 mph. Lucas climbed at an average rate of 2 mph and ran back at 5 mph. If the path from the bottom to the top of the mountain was 2 miles, how much time did each take to finish and who was faster? Answer:
Answers
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Step-by-step explanation:
Given,
Climbing rate of James = 3 mph
Running back rate of James = 4 mph
Climbing rate of Lucas = 2 mph
Running back rate = 5 mph
Total distance = 2 miles
We know that;
Distance = Speed * Time
As we have to find, we will rearrange the formula in terms of time
[tex]Time=\frac{Distance}{Speed}[/tex]
Time took by James for climbing = [tex]\frac{2}{3}\ hours[/tex]
Time took for running back = [tex]\frac{2}{4}\ hours[/tex]
Total time = [tex]\frac{2}{3}+\frac{2}{4}=\frac{8+6}{12}=\frac{14}{12}[/tex]
Total time taken by James = [tex]\frac{7}{6}\ hours[/tex]
1 hour = 60
Total time taken by James = [tex]\frac{7}{6}*60=70\ minutes[/tex]
Time took by Lucas for climbing = [tex]\frac{2}{2}=\ 1\ hour[/tex]
Time took by Lucas for climbing = 60 minutes
Time took on return = [tex]\frac{2}{5} of\ an\ hour=\frac{2}{5}*60=24\ minutes[/tex]
Total time taken by Lucas = 60+24 = 84 minutes
Therefore,
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Keywords: distance, speed
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Answer:
Step-by-step explanation:
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Step-by-step explanation:
Given,
Climbing rate of James = 3 mph
Running back rate of James = 4 mph
Climbing rate of Lucas = 2 mph
Running back rate = 5 mph
Total distance = 2 miles
We know that;
Distance = Speed * Time
As we have to find, we will rearrange the formula in terms of time
Time took by James for climbing =
Time took for running back =
Total time =
Total time taken by James =
1 hour = 60
Total time taken by James =
Time took by Lucas for climbing =
Time took by Lucas for climbing = 60 minutes
Time took on return =
Total time taken by Lucas = 60+24 = 84 minutes
Therefore,
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.®
What is the common difference of an AP which has its first term as 100 and the sum of its first 6 terms = 5 times the sum of its next six terms Pick one of the choices 1. 10 2. -10 3. 12 4. 15
Answers
Answer:
The common difference of given AP is Option 2) -10.
Step-by-step explanation:
We are given the following information in the question:
First term of AP, a = 100
The sum of its first 6 terms = 5(the sum of its next six terms)
We have to find the common difference of AP.
The sum of n terms of AP is given by:
[tex]S_n = \dfrac{n}{2}\big(2a + (n-1)d\big)[/tex]
where a is the first term and d is the common difference.
Thus, we can write:
[tex]S_6 = 5 (S_{12}-S_6)\\\dfrac{6}{2}\big(200 + (6-1)d\big) = 5\bigg(\dfrac{12}{2}\big(200 + (12-1)d\big)-\dfrac{6}{2}\big(200 + (6-1)d\big)\bigg)\\\\600 + 15d =5(1200+66d-600-15d)\\600+15d=3000+255d\\2400 = -240d\\d = -10[/tex]
Thus, the common difference of given AP is -10.
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
Answers
Answer:
There were 22 men in the sight-seeing tour
Step-by-step explanation:
If the number f women on the sight-seeing tour was less than 30, the closest number that can be divided by 5 is 25, so we suppose that there were 25 women, so with the ratio women(5): children(2) we can apply a rule of three, so we multiply 25*2 divided by 2, now we know that there were 10 children, now with the ratio of men(11): children(5) we apply another rule of three, and multiply 10*11 and then divide it by 5, and now we know that there were 22 men in the sight-seeing tour.
A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just when the balloon is 65 feet above the ground, a bicycle passes under it, going 17 ft/sec. How fast is the distance between and bicycle and the balloon changing 3 seconds later?
Answers
To calculate the rate at which the distance between the bicycle and the balloon is changing, take into account the speeds of the balloon and bicycle and use Pythagoras's theorem and the formula dd/dt = sqrt((dx/dt)^2 + (dy/dt)^2). This calculates out to approximately 17.03 ft/sec.
Explanation:This problem can be solved using the concepts of relative velocity and Pythagoras' theorem. It's a classic problem of a balloon moving vertically upwards at a speed of 1 ft/sec and a bicycle moving horizontally at a speed of 17 ft/sec.
After 3 seconds, the balloon would have ascended an additional 3 feet (because it's rising at 1 foot per second), so it will be at a height of 68 feet. Meanwhile, in those same 3 seconds, the bicycle will have travelled 51 feet (because it's going at 17 feet per second).
At this point, you can use Pythagoras's theorem to find the distance (d) between the bicycle and the balloon. The distance d is the hypotenuse of a right triangle where one side (the vertical side) is 68 feet and the other side (the horizontal side) is 51 feet. Using Pythagoras' theorem, d² = 68² + 51². So, d = sqrt(68^2+51^2) = 85 feet.
Then, find the change in d, known as dd/dt, which tells us how fast the distance between the balloon and the bicycle is changing. Given the constant velocities of the balloon and the bicycle, dd/dt is also a constant. You can use the formula dd/dt = sqrt((dx/dt)^2 + (dy/dt)^2), where dx/dt = 17 ft/sec (the speed of the bicycle), and dy/dt = 1 ft/sec (the speed of the balloon). So, dd/dt = sqrt(1^2 + 17^2) = sqrt(290) = approximately 17.03 ft/sec. So, the distance between the balloon and the bicycle is increasing at a rate of 17.03 ft/sec after 3 seconds.
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The distance between the bicycle and the balloon is changing at a rate of approximately 11 ft/sec, 3 seconds after the bicycle has passed under the balloon.
We need to determine how fast the distance between the bicycle and the balloon is changing 3 seconds after the bicycle passes under the balloon.
Let's denote:
y as the height of the balloon above the groundx as the horizontal distance between the bicycle and the point directly beneath the balloonz as the distance between the bicycle and the balloonWe are given:
Balloon’s rise rate: 1 ft/secBicycle’s speed: 17 ft/secInitial height of the balloon: 65 feetAfter 3 seconds:
Balloon’s height: y = 65 + 3 × 1 = 68 ftHorizontal distance travelled by bicycle: x = 3 × 17 = 51 ftApply the Pythagorean theorem to find z:
z = √(x² + y²)
z = √(51² + 68²)
z = √(2601 + 4624)
z = √7225
z = 85 ft
To find the rate of change of the distance z, we differentiate with respect to time (t):
2z (dz/dt) = 2x (dx/dt) + 2y (dy/dt)
Continue with substituting the known values:
85 (dz/dt) = 51 (17) + 68 (1)
85 (dz/dt) = 867 + 68
dz/dt = 935 / 85
dz/dt ≈ 11 ft/sec
Thus, the distance between the bicycle and the balloon is changing at a rate of approximately 11 ft/sec after 3 seconds.
You interview four people. You find that person A is a married 24-year-old white female with 2 pets and whose college GPA was 2.4. Person B is a single 44-year-old Asian female with 5 pets and whose college GPA was 2.5. Person C is a single 35-year-old Hispanic male with 4 pets and whose college GPA was 2.2. Person D is a single 48-year-old Asian male with 3 pets and whose college GPA was 3.8. Construct a data file for the characteristics number of pets and ethnic group for this sample.
Answers
Answer:
The data file is included in attached excel file.
Step-by-step explanation:
There are seven variables in the data file for four persons interviewed. Person type, marital status, ethnic group and gender are categorical variables while age, number of pets and GPA are quantitative variables. Person type is classified as A,B,C and D. Marital status consists of category married and single. Age of persons lies between 20-50. Ethic group has three categories that are white, Asian and Hispanic. Gender of persons has two categories male and female. Number of pets for the persons interviewed lies in the range of 2 to 5. Last GPA variable ranges from 2.2 to 3.8.
What is the probability of two consecutive ones in the string of 1s and 0s of length n?
Answers
The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated as (n-1) / (2n).
Explanation:The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated by considering the number of possible outcomes and the number of favorable outcomes.
Let's assume that the probability of getting a one is p and the probability of getting a zero is q. The favorable outcomes are when two consecutive ones occur, which can be represented as (1,1).
To calculate the probability, we need to determine the number of ways we can arrange the numbers in the string. Since we are only interested in the position of the ones, we can ignore the zeros.
Therefore, the number of favorable outcomes is n-1, because we have n-1 places where two consecutive ones can occur in a string of length n.
The number of possible outcomes is 2n, because each digit in the string can be either a one or a zero. Therefore, the probability of getting two consecutive ones is:
p = (n-1) / (2n)
How much of the sphere do you have to paint red so that no matter ow you put a cube in it, some corner touches red?
Answers
Explanation:
To achive that you have to piant a ring in red, which will have its big diameter equal to the sphere diameter and its small diameter equal to the cube diagonal.
The diagonal of the cube can be calculated using Pithagoras:
[tex]D^2=L^2+L^2[/tex]
Where D is the diagonal and L is the side of the cube
Josh has a rope that is 43 feet long. He cuts off a piece that is 10 feet long and gives it to his brother. He wants to cut the rest of the rope into pieces measuring exactly 5 feet each. How many pieces can he cut?
Answers
Answer:
6
Step-by-step explanation:
Answer:
Step-by-step explanation:
The initial length of Josh's rope was 43 feet. He cuts off a piece that is 10 feet long and gives it to his brother. This means that the length of the remaining rope would be
43 - 10 = 33 feet.
He wants to cut the rest of the rope into pieces measuring exactly 5 feet each. To determine the number of pieces that he can cut, it becomes
33/5 = 6.6
Therefore, only 6 pieces measuring exactly 5 feet each can be cut.
Two school buses leave the same school at the same time, but are headed in opposite directions. One bus traveled 45 miles per hour and the other bus traveled 40 miles per hour.
How long until the buses are 170 miles apart?
Answers
Answer:
2 hours
Step-by-step explanation:
45x + 40x = 170
85x = 170
x = 2
Answer:
40 mph: 4 hours 15 minutes
45 mph: 3 hours 46 minutes 40 seconds
Step-by-step explanation:
The rate of separation = 45 + 40 = 85 mph
speed = distance / time
85 = 170 / t
t= 170/85 hour
During a football game a concert in stenciled family three hamburgers and two white dogs for a total of $13 and another family two hamburgers and five hotdogs for a $ $16 what are the prices of a hamburger and a hotdog
Answers
Answer:
Price of hamburgers = $2
Price of white-dogs = $3
Step-by-step explanation:
Let
The number price of hamburgers be x
The number price of white-dogs be y
Then the first family buys 3 hamburgers and 2 white -dogs for $13
3x + 2y = 13-----------------------------(1)
Another first family buys 2 hamburgers and 5 white -dogs for $16
2x + 5y = 16----------------------------(2)
To solve let us multiply eq(1) by 2 and eq(2) by 3, we get
6x + 4y = 26-----------------------------(3)
6x + 15y = 48----------------------------(4)
subracting (3) from (4)
6x + 15y = 48
6x + 4y = 26
(-)
-------------------------
11y = 22
---------------------------
[tex]y =\frac{22}{11}[/tex]
y =2
Now substituting the value of y in eq(1),
3x + 2(2) = 13
3x + 4 = 13
3x = 13-4
3x = 9
x =[tex]\frac{9}{3}[/tex]
x =3
Not good at this need some help
Answers
Answer:
216 sq. units
Step-by-step explanation:
From the figure, we can see that only one pair of opposite angles are equal. So, the quadrilateral is a kite.
Formula to find the area of a kite:
Area, A = [tex]$ \frac{1}{2} \times d_1 \times d_2 $[/tex]
where, [tex]$ d_1 $[/tex] and [tex]$ d_2 $[/tex] are the lengths of the diagonals.
Here, [tex]$d_1 = 18 $[/tex] units.
And, [tex]$ d_2 = 24 $[/tex] units.
Therefore, the area A = [tex]$ \frac{1}{2} \times 18 \times 24 $[/tex]
= [tex]$ \frac{432}{2} $[/tex]
= 216 sq. units which is the required answer.
Which of the following ordered pair could NOT be included in this set if it is a function? { (-4, 2), (3, 6), (4, 3), (x, y) }
(x, y) = (4, -3)
(x, y) = (3, 6)
(x, y) = (1, 2)
(x, y) = (-3, 6)
Answers
Why is this the answer?
The x value x = 4 shows up in the point (4, 3), which is in the given function set. Adding (4, -3) to this set will have x = 4 show up twice. We cannot have one x value pair up with more than one y value. In other words, any input cannot map to more than one output. Visually, the two points (4,3) and (4,-3) will fail the vertical line test, which means we wouldnt have a function.
What is the gross profit? A. $130,000 B. $120,000 C. $230,000 D. $300,000 Previous Next
Answers
Answer: check explanation
Step-by-step explanation:
The question is not complete but nonetheless, gross profit is easy to calculate. Let us start by the definition of gross profit, to how to calculate gross profit and, calculation of gross profit margin.
GROSS PROFIT: gross profit can be defined as the profit gained after subtracting the costs of making and selling the products. Gross profit is also known as gross margin.
HOW TO CALCULATE GROSS PROFIT: Gross profit can be calculated by subtracting the total revenue from the cost of goods sold. That is, gross profit= total revenue - cost of goods sold.
So, for example; Company A makes women handbags. Assuming the company made $10million in total revenue for the year and cost of goods sold is $5 million. We can use the formula above to find the company's gross profit margin.
Hence, company A's gross profit= total revenue($10,000,000) - cost of goods sold ($5,000,000).
= $5,000,000.
That is, the gross profit for company A= $5,000,000.
GROSS PROFIT MARGIN: This can be calculated using the formula below;
Gross profit margin= (total revenue - cost of goods)/ revenue.
Hence, from the example above;
Gross profit margin= $10,000,000 - $5,000,000) / $10,000,000.
= 50%
(NOTE: this symbol "*" will be used to express variables that go under the number, like a reverse exponent.)Find the 4th term in the sequence with the following definition:
a*1=2
a*n=(a*n-1)^2
Answers
Answer:
256
Step-by-step explanation:
a₁ = 2
aₙ = (aₙ₋₁)²
a₂ = (a₂₋₁)²
a₂ = (a₁)²
a₂ = (2)²
a₂ = 4
a₃ = (a₃₋₁)²
a₃ = (a₂)²
a₃ = (4)²
a₃ = 16
a₄ = (a₄₋₁)²
a₄ = (a₃)²
a₄ = (16)²
a₄ = 256
If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = 10x5 + 7x4 + 5
A) Degree: 10; leading coefficient: 5
B) Not a polynomial function
C) Degree: 9; leading coefficient: 10
D) Degree: 5; leading coefficient: 10
Answers
Answer:
It's D; degree- 5; leading coefficient-10 :)
Step-by-step explanation:
I just took the test and got it right
The given polynomial function f(x) = 10x⁵ + 7x⁴ + 5 has Degree: 5; leading coefficient: 10 which is the correct answer would be option (D).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The degree of a polynomial is the highest exponent of the variables in the polynomial. In this case, the highest exponent is 5, so the degree of the polynomial is 5.
The leading coefficient is the coefficient of the term with the highest degree.
In this case, the coefficient of the term with the highest degree (x⁵) is 10, so the leading coefficient is 10. Therefore, the correct answer is D).
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2. A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answers
Answer:
Step-by-step explanation:
Initial amount that was deposited into the savings account is $600 This means that the principal,
P = 600
The account earns 2.1 % interest compounded annually.. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
It was compounded for t years. So
t = t
a) The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 600 (1+0.021/1)^1×t
A = 600(1.021)^t
b)when A =$800, it becomes
800 = 600(1.021)^t
Dividing both sides by 600, it becomes
1.33 = (1.021)^t
Taking the tth root of both sides
t = 14 years
It will take 14 years
A baker uses 2 1/3 cups of cookie dough and 1/4 cup of chocolate chips to make 10 cookies. If the baker has 3 cups of chocolate chips, how much dough will he need
Answers
Answer: he will need 28 cups of dough for 3 cups of chocolate.
Step-by-step explanation:
The baker uses 2 1/3 cups of cookie dough and 1/4 cup of chocolate chips to make 10 cookies. Converting 2 1/3 cups of cookie dough into improper fraction, it becomes 7/3 cups of cookie dough.
It means that for every 1/4 cup of chocolate, 7/3 cups of cookie dough is needed.
Let x represent the amount of cookie dough needed for 3 cups of chocolate chips.
If 7/3 dough = 1/4 cup of chocolate
x dough = 3 cups of chocolate
x × 1/4 =7/3 × 3
x/4 = 7
x = 7×4 = 28 cups of dough
Suppose that the current equilibrium price of silver is $34 per ounce. If silver is produced under conditions of perfect competition and the industry is in long-run equilibrium, the average total cost of producing silver: a. is less than $34 per ounce. b. is $34 per ounce. c. is indeterminate. d. exceeds $34 per ounce.
Answers
Answer:
b. is $34 per ounce
Step-by-step explanation:
If the production cost were less, a competitor would drive the price down. If the production cost were more, the supplier would go out of business.
Since we're at equilibrium, the production cost must be equal to $34 per ounce.
To fulfill the requirements for a certain degree, a student can choose to take any 7 out of a list of 20 courses, with the constraint that at least 1 of the 7 courses must be astatistics course. Suppose that 5 of the 20 courses are statistics courses.(a) How many choices are there for which 7 courses to take?(b) Explain intuitively why the answer to (a) is not
Answers
Complete answer:
Fulfill the requirements for a certain degree, a student can choose to take any 7 out of a list of 20 courses, with the constraint that at least 1 of the 7 courses must be a statistics course. Suppose that 5 of the 20 courses are statistics courses.
(a) How many choices are there for which 7 courses to take?
(b) Explain intuitively why the answer to (a) is not [tex] \binom{5}{1}\binom{19}{6} [/tex]
Answer:
a) 71085 choices
b) See below
Step-by-step explanation:
a) First we're going to calculate in how many ways you can take 7 courses from a list of 20 without the constraint that at least 1 of the 7 courses must be a statistics course, that's simply a combination of elements without repetition so it's: [tex]\binom{20}{7} [/tex], but now we should subtract from that all the possibilities when none of the courses chose are a statistic course, that's is [tex]\binom{15}{7} [/tex] because 15 courses are not statistics and 7 are the ways to arrange them. So finally, the choices for which 7 courses to take with the constraint that at least 1 of the 7 courses must be a statistics course are:
[tex]\binom{20}{7}-\binom{15}{7}=71085 [/tex]
b) It's important to note that the constraint at least 1 of the 7 courses must be a statistics course make the possible events dependent, we can not only fix an statistic course and choose the others willingly ( that is what [tex] \binom{5}{1}\binom{19}{6} [/tex] means) because the selection of one course affect the other choices.
In this exercise, we have to use our knowledge of statistics to calculate how many options can be chosen for a course, so we find that:
a) 169 choices
b) 1 of the 7 courses must be a statistics course, because the selection of one course affect the other choices.
So from the data reported in the exercise we can say that:
a) First we're going to calculate in how many ways you can take 7 courses from a list of 20 without the constraint that at least 1 of the 7 courses must be a statistics course, that's simply a combination of elements without repetition so it's. So we have that;
[tex]C=\frac{m!}{p!(m-p)!}\\C=\frac{20!}{7!(20-7)!}\\C=169[/tex]
b) It's influential to note that the restraint not completely 1 of the 7 courses must be a enumeration course form the attainable occurrence determined by, we can not only fix a statistic course and select the possible choice gladly because the preference from among choices of individual course influence the added selection.
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Which of the following must also be known in order to compute the standard deviation?A) ModeB) MeanC) RangeD) Median
Answers
Answer:
B) Mean
Step-by-step explanation:
Standard Deviation is the measure of the amount of variation or dispersion of a set of values. Standard Deviation is represented by lower case Greek alphabet sigma σ. Standard Deviation is the square root of variance. Variance is the average of the squared differences or variation or dispersion from the Mean. Therefore, to compute standard deviation, the mean of the given data must be known.
Standard Deviation, σ = [tex]\sqrt{Variance}[/tex]
σ = [tex]\sqrt({\frac{1}{N-1}}[/tex] ∑[tex]_{i = 1}^{N}(x_{i} - X)^{2})[/tex]
where
[tex]x_{1},x_{2},x_{3}, ...x_{N},[/tex] are the values of the sample observed,
X is the mean value of these observations, and
N is the number of observations in the sample.
State the vertical asymptote of the rational function. F(x)=(x-6)(x+6)/x^2-9.
X=6,x=-6
X=3,x=-3
X=-6,x=6
None
Answers
Answer:
x = 3, x = -3
Step-by-step explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
Solve : x² - 9 = 0 ⇒ x² = 9 ⇒ x = ± 3
The vertical asymptotes are x = - 3 and x = 3
The vertical asymptotes of the rational function F(x) = (x - 6)(x + 6)/(x^2 - 9) are x = -3 and x = 3.
Explanation:The rational function F(x) = (x - 6)(x + 6)/(x^2 - 9) has vertical asymptotes at x = -3 and x = 3.
To find the vertical asymptotes, we need to determine the values of x that make the denominator equal to zero. In this case, the denominator is x^2 - 9, which can be factored as (x - 3)(x + 3).
Therefore, the vertical asymptotes occur at x = -3 and x = 3, since these are the values that make the denominator zero.
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For a parade, a large spherical balloon is filled with a gas that weighs 200 grams per cubic meter. When filled with the gas, the balloon has a diameter of 9 meters. What is the total weight, in grams, of the gas in a filled balloon? Use 3.14 for π .
Answers
Answer:
76302 grams
Step-by-step explanation:
Diameter of the balloon = 9 m
Density of the gas (weight occupied per m³) = 200 g per m³
Volume of the spherical balloon = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here r = 4.5 m
Then V= [tex]\frac{4}{3}\times\ 3.14 \times (4.5)^{3}[/tex]
V = 381.51 m³
Total weight = Total volume occupied * Density
= 381.51*200 = 76302 grams.
Final answer:
The total weight of the gas in a filled balloon with a 9-meter diameter is 76,340.25 grams, calculated by first finding the volume of the balloon and then multiplying it by the weight of the gas per cubic meter.
Explanation:
To find the total weight of the gas in a filled spherical balloon, first, we need to find the volume of the balloon using the formula for the volume of a sphere, which is V = (4/3)πr³. The diameter of the balloon is given as 9 meters, so the radius r is 9/2 meters or 4.5 meters.
Calculating the volume of the balloon:
V = (4/3)π(4.5 m)³ = (4/3)π(4.5³) = (4/3) × 3.14 × (91.125) ≈ 381.70125 cubic metersNow, we'll multiply the volume of the balloon by the weight per cubic meter of the gas to get the total weight of the gas:
Total weight = Volume × Weight per cubic meter = 381.70125 m³ × 200 g/m³ = 76340.25 gramsTwo cars enter the Delaware turnpike at shoreline drive at 8 am, each heading for ocean city. One cars average speed is 10 mph faster than the other. The faster car arrives at ocean city at 11 am, a half hour before the slower car. What is the average speed of each car?
Answers
Average speed of slower car = 60 mph
Average speed of faster car = 70 mph
Solution:
Given that Two cars enter the Delaware turnpike at shoreline drive at 8 am, each heading for ocean city
Given that One cars average speed is 10 mph faster than the other
Let "x" be the average speed of slower car
Then x + 10 is the average speed of faster car
The faster car arrives at ocean city at 11 am, a half hour before the slower car
Time taken by faster car:
The faster car arrives at ocean city at 11 am but given that they start at 8 a.m
So time taken by faster car = 11 am - 8am = 3 hours
Time taken by slower car:
The faster car arrives at ocean city at 11 am, a half hour before the slower car
So slower car takes half an hour more than faster car
Time taken by slower car = 3 hour + half an hour = [tex]3\frac{1}{2} \text{ hour}[/tex]
Now the distance between Delaware turnpike at shoreline drive and ocean city will be same for both cars
Let us equate the distance and find value of "x"
The distance is given by formula:
[tex]distance = speed \times time[/tex]
Distance covered by faster car:
[tex]distance = (x + 10) \times 3 = 3x + 30[/tex]
Distance covered by slower car:
[tex]distance = x \times 3\frac{1}{2} = x \times \frac{7}{2} = 3.5x[/tex]
Equating both the distance,
3x + 30 = 3.5x
3x - 3.5x = -30
-0.5x = -30
x = 60
Thus average speed of slower car = 60 mph
Average speed of faster car = x + 10 = 60 + 10 = 70 mph
Jacob and Ayden work at a dry cleaners ironing shirts. Jacob can iron 25 shirts per hour, and Ayden can iron 35 shirts per hour. Ayden worked twice as many hours as Jacob and they ironed 380 shirts between them. Determine the number of hours Jacob worked and the number of hours Ayden worked.
Answers
Answer:
Step-by-step explanation:
Start with the unknown, which is the number of hours J worked and the number of hours A worked. If A worked twice as many hours as J, then J worked x hours and A worked 2x hours. If J can iron 25 shirts per hour, x, then the number of shirts he can iron in his shift is 25x. If A can iron 35 shirts per hour, x, then the number of shirts he can iron in his shift is 35(2x). The number of shirts they iron together in x hours is
25x + 35(2x) = 380 and
25x + 70x = 380 and
95x = 380 so
x = 4
This means that J worked 4 hours and A worked 8 hours.
I need help with this math question
Answers
Answer:
a.) y = 3/(2ˣ)
b.) y = 1/(2ˣ)
c.) y = (π^π)ˣ
d.) y = (1/27)(1/√(3))ˣ
e.) y = .002908/(.119025ˣ)
f.) y = .00000004808/(.0413ˣ)
Step-by-step explanation:
Concept need to know is:
a negative exponent will flip the numerator with the denominatora fraction as an exponent is just a root. so if the exponent is x^(1/2) then the root is 2 and x^(1/3) is a cube rootadding and subtracting exponent is the same thing as multiplying the same base. so x^(1+2) = (x^1)(x^2)and x^(1-2) = (x^1)(x^-2)