Cylindrical coordinates? Hi,
I am having problems with a homework question,
I am asked to sketch the solid by the given inequalities.
0 <= theta <= pi/2 and r <= z <= 2
How do I find r?
If possible please guide me to the answer instead of giving it to me. I need to know this stuff.
Thanks in advance for any help.
Answers
Recalling that in cylindrical coordinates, [tex]r^2=x^2+y^2\implies r=\sqrt{x^2+y^2}[/tex], we then know that [tex]0\le\sqrt{x^2+y^2}\le z[/tex], and so we're confined to the first octant (where each of [tex]x,y,z[/tex] are non-negative).
The upper limit of [tex]z\le2[/tex] tells us that the region is bounded above by the plane [tex]z=2[/tex], which is parallel to the [tex]x[/tex]-[tex]y[/tex] plane.
Meanwhile, the lower limit of [tex]z=r=\sqrt{x^2+y^2}[/tex] can be visualized by first squaring both sides:
[tex]z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2[/tex]
If you're not already familiar with what this equation represents, we can approach it piecemeal. At one extreme, when [tex]x=y=0[/tex], we have [tex]z=\sqrt{0^2+0^2}=0[/tex], so the region has a "vertex" at the origin.
When [tex]z=2[/tex], we have the Cartesian equation [tex]4=x^2+y^2[/tex], which corresponds to a circle of radius 2. Similarly, if we consider values of [tex]z[/tex] between 0 and 2, we end up with circles of increasing radii. Stacking these circles onto one another, we get a cone.
More specifically, the region is the part of the cone between the [tex]x[/tex]-[tex]y[/tex] plane and the plane [tex]z=2[/tex] restricted to the first octant.
(Image of region attached)
Related Questions
Mr. Thompson borrowed $3,000. He repaid the loan with an interest charge of $500 in 36 equal monthly payments. What approximate annual percentage rate did he pay? Find the answer to the nearest tenth of a percent.
Answers
APR=(2 × n × I) / [P × (N + 1)]
APR=(2×12×500)÷(3,000×(36+1))
APR=(2×12×500)÷(3,000×37)
APR=0.1081×100
APR=10.81%
people who are physically active should increase the daily amount of water they drink to 2/3 ounces per pound of body weight. how much should a 245 pound football player drink per day?
A 1,470 ounces of water
B 163 ounces of water
C 163 1/3 ounces of water
D no water, football players only drink gatorade
Answers
245*2/3=
245*2 =490/3 =163.33 = 163 1/3 ounces
Given the arithmetic sequence an = −1 + 7(n − 1), what is the domain for n?
All integers
All integers where n ≥ 0
All integers where n ≥ 1
All integers where n > 1
Answers
The domain for n in the arithmetic sequence is all integers where n ≥ 1.
Explanation:The domain for n in the arithmetic sequence is all integers where n ≥ 1. In this sequence, the value of n represents the position of the term in the sequence. Since the first term of the sequence is represented by n=1, n can't be less than 1 because there is no zeroth term in the sequence. Therefore, the domain for n is all integers where n ≥ 1.
B is between a and c ac=15.8 and ab=9.9. find bc
Answers
Answer:
The value of bc is 5.9 units.
Step-by-step explanation:
Given information: b is between a and c, ac=15.8 and ab=9.9.
We need to find the measure of bc.
Since b is between a and c, therefore the segment ac is the sum of two segments ab and bc.
[tex]ac=ab+bc[/tex]
Substitute ac=15.8 and ab=9.9 in the above equation.
[tex]15.8=9.9+bc[/tex]
Subtract 9.9 from both sides.
[tex]15.8-9.9=9.9+bc-9.9[/tex]
[tex]5.9=bc[/tex]
Therefore the value of bc is 5.9 units.
If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].
Reminder - Given that statement seems to be incomplete, we assume that we are talking about Line Segments and that Segments AC and BC may be Collinear.
By Geometry and, being more specific, by definition of Triangles, if we assume that all segment are not necessarily Collinear, then a Triangle may exist and can be modelled by the Law of Cosine:
[tex]BC = \sqrt{AC^{2}+AB^{2}-2\cdot AC\cdot AB\cdot \cos \beta}[/tex] (2)
Where [tex]\beta[/tex] is the angle at point B, in sexagesimal degrees and is between 0° and 180°.
If we know that [tex]AC = 15.8[/tex] and [tex]AB = 9.9[/tex], then the expression for the length of BC is:
[tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex]
If assumption of Collinearity is not for granted, then the length of Segment BC is defined by [tex]BC = \sqrt{347.65 -312.84\cdot \cos \beta}[/tex], for [tex]\beta \in [0^{\circ}, 180^{\circ}][/tex].
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What's the answer help me out please ?
Answers
whats the answer to >> 3/10 + 2/11 and find the sum
Answers
33/110 + 20/110 =
53/110 <==
1. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.
2. What is the sum of the measures of the exterior angles in a heptagon? Explain.
3. Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work.
a. Decagon
b. Pentagon
c. Dodecagon
d. 16-gon
e. 25-gon
Answers
let
"a" be the number of angles (or sides)
"t" be the number of triangular regions, that the diagonals drawn from one angle divide the regular polygon into.
it is clear that for a polygon of n-sides, there are n-2 triangular regions, each of which has a total measure of angles equal to 180°.
so the sum of the interior angles of a n-gon is (n-2)180°.
In a regular polygon, the measure of each interior angle is equal, so:
the measure of each interior angle of a regular n-gon is: [tex] \frac{(n-2)180}{n} [/tex]
apply the formula to each angle.
a. n=10, [tex]\frac{(n-2)180}{n}=\frac{(10-2)180}{10}[/tex]=(8*180)/10=144
b. n=5, [tex]\frac{(n-2)180}{n}=\frac{(5-2)180}{5}[/tex]=(3*180)/5=108
c. n=12, [tex]\frac{(n-2)180}{n}=\frac{(12-2)180}{12}[/tex]=(10*180)/12=150
d. n=16, [tex]\frac{(n-2)180}{n}=\frac{(16-2)180}{16}[/tex]=(14*180)/16=157.5
e. n=25, [tex]\frac{(n-2)180}{n}=\frac{(25-2)180}{25}[/tex]=(23*180)/25=165.5
2.
the sum of the interior angles of a heptagon is (7-2)180°=5*180°=900°
let the measures of the interior angles be a,b,c,d,e,f and g.
so a+b+c+d+e+f+g=900°
the exterior angle measures are 180-a, 180-b, 180-c, 180-d, 180-e, 180-f, 180-g,
so the sum of the measure angles of the exterior angles is
(180°-a)+(180°-b) +(180°-c)+(180°-d)+(180°-e)+(180°-f)+(180°-g)
= 180°*7-(a+b+c+d+e+f+g)=1260°-900°=360°.
In fact, the sum of the measures of the exterior angles of any polygon is 360°.
1. Let the length of the second base be x
then
[tex] \frac{x+24}{2}=19 [/tex]
x+24=38
x=38-24=14 units
Scientists studied two animal populations. Function f(x) = 830(0.8)^x models a bear population in a given region x years after the study began. The table models the cougar population in the same region.
Year after study began: 0, 1, 2, 6, 15
Cougar population: 790, 735, 683, 511, 266
In the year the study began, how many more bears than cougars were in the given region.
Answers
830-790=40
Answer:
There were 40 more bears than cougars when the study started.Step-by-step explanation:
Givens:
[tex]f(x)=830(0.8)^{x}[/tex]; where [tex]x[/tex] refers to years after the study began, about bear population.Table given is for cougar population.So, the problem is asking how many more bears than cougars were in the given region. From the table, we know that there where 790 cougar when the study started.
Now, we have to calculate the initial condition of the function, because it's modelling bear population. Initial condition means when the study started, which is when [tex]x=0[/tex].
So, we have:
[tex]f(0)=830(0.8)^{0}=830(1)=830[/tex]
So, there were 830 bears when the study started.
If we compare, we find that there were 40 more bears than cougars when the study started, because 830-790 = 40.
The next three terms of the sequence 20, 40, 80, 160,… are 320, 640, and 1280.
Answers
Its a geometric sequence with common ratio 2.
Factor completely then place the answer in the proper location on the grid. Write the answer in descending powers if x
6x^4+15x^3y^2+3x^2y^3
Answers
3x^2 (2x^2 + 5xy^2 + y^3) <==
Describe how to determine if two polygons have the same size and shape.
Answers
Answer:
Prove that their corresponsing sides are all congruentsStep-by-step explanation:
Remember that if two figures have corresponding angles congruent, but proportional sides, then those figures are similar.
However, if those figures have corresponding angles and sides congruent, then they are congruent.
Therefore, to determine if two polygons are congruent, that is, in size and shape, we need to prove that their corresponsing sides are all congruents, that way, we'll be able to demonstrate their absolute congruence.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
Answers
Question a)
Let C represents the five-star recruit who chooses one of the best three conferences
Let S represents the scholarship offer
P(C∩S) = 0.75×0.93 = 0.6975
Question b)
P(C'∩S) = 0.75×0.07 = 0.0525
Question c)
The two events are independent because it is possible for the events to happen in any order and one event's outcome does not affect the other event's.
If we multiply every observation in a data set by 2, the mean will
Answers
In addition to the trigonometric ratios, what other methods can be used to solve a right triangle? Give situations for when you might want to use them
Answers
We shall discuss two methods for solving the right triangle.
Method 1. Use of trigonometric ratios
To use trigonometric ratios requires that either m∠A or m∠B is known and that one of the sides a, b, or c is known.
Example:
Assume that m∠A is known, then m∠B = 90° - m∠A.
Also, assume that b is known.
By definition,
tan A = a/b => a = b*tan A
cos A = b/c => c = b/cos A, or
sin A = a/c => c = a/sin A
Method 2. Algebraic method
When neither m∠A nor m∠B is known, then it is necessary to know the values of two sides: (a and b), (a and c), or (b and c).
The Pythagorean theorem states that
a² + b² = c²
(a) If a and b are known, then
c = √(a² + b²)
(b) If a and c are known, then
b = √(c² - a² )
(c) If b and c are known, then
a = √(c² - b²)
Once all sides are known, trigonometric ratios can be used t determine m∠A and m∠B.
Example:
Because a and c are known,
sin A = a/c
A = sin⁻¹ (a/c), which can be determined from the calculator.
If 9a+5b+5c=9 what is -10c-18a-10b?
Answers
Multiplying the whole equation by -2.
-18a - 10b - 10c = -18.
Hence, the answer is -18.
the quadratic equation whose roots are the am and hm between the roots of the equation 2x2 - 3x+5=0
Answers
The first thing to do is to find the roots.
The sum of the roots, x1 + x2 = -b / a
x1 + x2 = 3 / 2
The product of the roots, x1 * x2 = c / a
x1 * x2 = 5 / 2
The AM means arithmetic mean and is calculated using the formula:
AM = (x1 + x2) / 2
AM = (3 / 2) / 2
AM = 3 / 4 = y1
The HM means harmonic mean and is calculated using the formula:
2 / HM = 1 / x1 + 1 / x2
or
2 / HM = (x1 + x2) / x1 * x2
Rewriting in terms of HM alone on the left side:
HM = 2 x1*x2 / (x1 + x2)
HM = 2 (5 / 2) / (3 / 2)
HM = 10 / 3 = y2
Creating an equation from y1 and y2:
(y – ¾) (y – 10/3) = 0
y^2 – 10/3 y – ¾ y + 30/12 = 0
y^2 - 49/12 y + 30/12 = 0 (ANSWER)
or
y^2 – 4.083y + 2.5 = 0
Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?
18 + c
18 - c 1
8 ÷ c
18 c
Answers
Answer:
i think answer 1
Step-by-step explanation:
tell me i i am wrong
Which of the binomials below is a factor of this trinomial?
x² + 2x - 48
A. x + 8
B. x - 3
C. x - 8
D. x + 3
Answers
The complete factor of x² + 2x - 48 is (x-6)(x+8)
So, the correct option is A (x + 8)
I hope that helps!
how many foci does the graph of a hyperbola have
Answers
Answer:
A graph of a hyperbola have 2 foci.
Step-by-step explanation:
Foci of a Hyperbola-
The foci of a hyperbola are two fixed points located inside each curve of a hyperbola.
The foci is a plural of the word focus i.e. two focus of a hyperbola are combinely called foci.
Hence, a graph of a hyperbola have 2 foci.
for f(x)= 1/x^2-3 substitute 3 for x in the function to solve for f(3)
Answers
The value of the function f(x)= 1/x²-3 when x is 3, denoted as f(3), is -8/9.
Explanation:To solve for f(3) in the function "f(x)= 1/x²-3", you should substitute x = 3 into the function. By doing so, we have:
f(3) = 1/(3²) - 3 = 1/9 - 3 = -8/9
Therefore, f(3) for this function is -8/9.
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What's the mean of 0,1,3,2
Answers
☛ To find the mean, we add together all the numbers and then divide it by the amount of numbers there are.
0 + 1 + 3 + 2
= 6
= 6 / 4 = 1.5
Answer: 1.5
Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia
On her first stroke, Maria hit a golf ball 140 yards, 2 feet, 9 inch. On her second she hit it 170 yards, 1 foot, 6 inches. How far did the ball go all together
Answers
2 feet 9 inches + 1 foot 6 inches = 3 feet 15 inches
15 inches = 1 foot 3 inches
3 feet + 1 foot = 4 feet
2 ft 9 inches + 1 ft 6 inches = 4 ft 3 inches
1 yard = 3 feet
4feet 3 inches = 1 yard, 1 foot 3 inches
140+170 = 310 yards
310 + 1 = 311
so it traveled 311 yards 1 foot and 3 inches
Answer:
311 yards and 1 feet and 3 inches
Step-by-step explanation:
Find the probability that 3 randomly selected people all have the same birthday. ignore leap years. round to eight decimal places.\
Answers
The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.
Explanation:In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:
P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125
Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.
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PLEASE HELP!!! 9. Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
|4x + 3| = 9 + 2x
x = _____ or _____
Answers
[tex]4x+3=9+2x[/tex] and
[tex]4x+3=-(9+2x)[/tex]
The second one simplifies to
[tex]4x+3=-9-2x[/tex]
Now solve each for x:
[tex]4x+3=9+2x[/tex]
[tex]2x=6[/tex] and x=3
The second one:
[tex]4x+3=-9-2x[/tex]
[tex]6x=-12[/tex] and x=-2
If you check both of these solutions, they both work; neither are extraneous.
if a sprinkler waters 1/18 of a lawn in 1/3 hour, how much time will it take to water the entire lawn
Answers
3/3 would be 1 hour
3/18 of the lawn would be done in 1 hour
18/3=6
6*1 = 6
it would take 6 hours to do the whole lawn
It will take 360 minutes to water the entire lawn
What is cross multiplication?Cross multiply can be defined as the process of multiplying the numerator of the first fraction on one side of the equals to symbol, with the denominator of the second fraction on the other side of the equals to symbol.
1/18 lawn is watered in 1/3 of hour = 20 min
Whole lawn will be watered in 20 × 18 = 360 min
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What is the solution of \sqrt(2x+4)=16?
x = 6
x = 72
x = 126
no solution
Answers
2x+4=256 subtract 4 from both sides
2x=252 divide both sides by 2
x=126
The solution of the expression will be;
⇒ x = 126
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ √(2x + 4) = 16
Now,
Solve the expression as;
The expression is,
⇒ √(2x + 4) = 16
Square both side, we get;
⇒ 2x + 4 = 16²
⇒ 2x + 4 = 256
⇒ 2x = 256 - 4
⇒ 2x = 252
⇒ x = 126
Thus, The solution of the expression will be;
⇒ x = 126
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Interpret the average rate of change of –14/3 that you found previously. What does this mean in terms of the waterslide, from x = 0 to x = 15?
Answers
Solution: The average rate of change of [tex]\frac{-14}{3}[/tex] represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
Explanation:
The rate of change shows the change in first variable with respect to change in second variable.
If the rate of chang is given by [tex]\frac{-14}{3}[/tex] it means second variable is decrease by 14 if the first variable increase by 3.
In the context of water slide it shows that the vertical height of slide is decreased by 14 units as we cover the distance of 3 units.
If we cover the distance from x = 0 to x = 15, it means we cover the distance of 15 units.
Let the vertical height of the slide covered from x = 0 to x =15 be y.
It means when distance increased by 15 units the height of slide decreased by y units.
So rate of change = [tex]\frac{-y}{15}[/tex].
It is given that the rate of change is [tex]\frac{-14}{3}[/tex].
Equate both equations.
[tex]\frac{-y}{15}=\frac{-14}{3}[/tex]
[tex]y=15(\frac{14}{3} )[/tex]
[tex]y=5(14)[/tex]
[tex]y=70[/tex]
Therefore, the average rate of change of [tex]\frac{-14}{3}[/tex] represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
What this mean in terms of the waterslide, from x = 0 to x = 15 is:
The vertical height of slide is decreased at the rate of 4.66 per unit.The vertical height of the slide decreased by 70 units from x= 0 to x=15What is Rate of Change?This refers to how fast or slow a thing is required before it changes form from one form to another.
With this in mind, we can see that with the water slide, there exists the decrease of the vertical height by 14 units over a distance of 3 units.
Therefore, the rate of change is -y/15
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The center of a circle is A (-3,3), and B (1,6) is on the circle. Find the area of the circle in terms of pi.
Answers
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 3}})\quad % (c,d) &({{ 1}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[6-3]^2}\implies r=\sqrt{(1+3)^2+(6-3)^2} \\\\\\ r=\sqrt{4^2+3^2}\implies r=\sqrt{25}\implies \boxed{r=5}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad r=5\implies \boxed{A=25\pi }[/tex]
Is a triangle with sides of length 7 ft, 24 ft, and 25 ft a right triangle? Explain.
Answers
7^2 + 24^2 = 49+576 = 625
625 = 625
ANswer
Yes. It's right triangle
the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse....It's right triangle angle
What is 10 1/2 divided 2 1/4
Answers
(21/2) / (9/4) -- when dividing with fractions, flip what u r dividing by, then multiply
21/2 * 4/9 =
42/9 =
4 2/3 <===