As near as I can tell, you're given the vector field
[tex]\vec F(x,y,z)=\langle y,-x,14\rangle[/tex]
and that [tex]S[/tex] is the part of the upper half of the sphere with equation
[tex]x^2+y^2+z^2=4[/tex]
with boundary [tex]C[/tex] the circle in the plane [tex]z=0[/tex].
Line integral:Parameterize [tex]C[/tex] by
[tex]\vec r(t)=\langle2\cos t,2\sin t,0\rangle[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\vec F(x,y,z)[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_C\vec F(x,y,z)\cdot\mathrm d\vec r=\int_0^{2\pi}\langle2\sin t,-2\cos t,14\rangle\cdot\langle-2\sin t,2\cos t,0\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle-4\int_0^{2\pi}(\sin^2t+\cos^2t)\,\mathrm dt=\boxed{-8\pi}[/tex]
Surface integral:Parameterize [tex]S[/tex] by
[tex]\vec s(u,v)=\langle2\cos u\sin v,2\sin u\sin v,2\cos v\rangle[/tex]
with [tex]0\le u\le2\pi[/tex] and [tex]0\le v\le\dfrac\pi2[/tex]. We have
[tex]\nabla\times\vec F(x,y,z)=\langle0,0,-2\rangle[/tex]
Take the normal vector to [tex]S[/tex] to be
[tex]\vec s_v\times\vec s_u=\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle[/tex]
Then the surface integral of the curl of [tex]\vec F(x,y,z)[/tex] across [tex]S[/tex] is
[tex]\displaystyle\iint_S(\nabla\times\vec F(x,y,z))\cdot\mathrm d\vec S=\iint_S(\nabla\times\vec F(x(u,v),y(u,v),z(u,v)))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}\langle0,0,-2\rangle\cdot\langle4\cos u\sin^2v,4\sin u\sin^2v,2\sin2v\rangle\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle-4\int_0^{\pi/2}\int_0^{2\pi}\sin2v\,\mathrm du\,\mathrm dv=\boxed{-8\pi}[/tex]
Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).
Answer:
f(x) = 9(x -1/3)^2 -3
Step-by-step explanation:
In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...
y = a(x -h)^2 +k
To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":
1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given
1 = (4/9)a -3 . . . . simplify
4 = (4/9)a . . . . . . add 3
9 = a . . . . . . . . . . multiply by 9/4
The quadratic function you desire is ...
f(x) = 9(x -1/3)^2 -3
A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the wall of the barn, so one side of the rectangle won’t need a fence. What dimensions will maximize the area of the pen?
Answer:
20 ft out from the wall by 40 ft parallel to the wall
Step-by-step explanation:
Let x represent the length of fence in the direction parallel to the wall. Then the other dimension of the rectangular pen is (80 -x)/2. The area is the product of these dimensions:
area = x(80 -x)/2
This function describes a downward-opening parabola with zeros at x=0 and x=80. The vertex (maximum) is halfway between the zeros, at x=40.
The dimensions are 40 ft parallel to the wall and 20 ft out from the wall.
Length l=40 and Breadth b=20 will maximize the area of the pen.
let us take 'l' as the length of the rectangular pen.
'b' as the width of the rectangular pen.
let us assume that the barn will be built opposite to length.
so, according to the given condition
l +b+b=80
l+2b=80......(1)
area of the rectangular pen = lb= (80-2b)b
f(b)= (80-2b)b.......(2)
How to check the local maxima?to get local maxima, differentiate the function and equate to zero, get the point say it 'x'
again check double derivative if its value is negative the point 'x' will give the maximum value of the function.
to maximize the area
let us derivate the f(b)= (80-2b)b
f'(b)= 80-4b=0
b=20
f"(b)= -4(-ve)
means we will have local maxima at b=20
it means at b=20, we will get maximum area.
l = 80-2b=80-2*20=40
therefore, l=40 and b=20 will maximize the area of the pen.
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What is the value of x?
Find the ratio of the bases: 15 in / 5 in = 3
The triangle on the right side is 3 times larger.
X = 8 * 3
x = 24 inches.
what are the coefficients in the polynomial 5x^2+2x-4
A. 5, 2
B. -5, -2
C. 5, 2, -4
D. 5, -2, -4
Answer:
A. 5,2
Step-by-step explanation:
Coefficients are numbers with a variable next to it (ex. 5 in 5x^2).
–4y=10 in standard form
Answer:
Already in standard form
Step-by-step explanation:
-4y=10
-4y= by
10= c
And in this case ax=0x, so it will not show up in the equation
0x-4y=10, which is already in standward form
-4y=10 divide both sides by -2, so 2y=5 subtract 5 from both sides,
2y-5=0
I need the solution and the work for it... for each of the multiple choices.
For this case we have the following equation:
[tex]x ^ 3 = 375[/tex]
We must find the value of "x":
We apply cube root on both sides of the equation to eliminate the exponent:
[tex]x = \sqrt [3] {375}[/tex]
We can write 375 as [tex]5 ^ 3 * 3[/tex]
So:
[tex]x = \sqrt [3] {5 ^ 3 * 3}\\x = 5 \sqrt [3] {3}[/tex]
Then, the correct options are:
[tex]x = \sqrt [3] {375}\\x = 5 \sqrt [3] {3}[/tex]
Answer:
Option A and B
need help with this one
Answer:
68
Step-by-step explanation:
∠DPG and ∠EPF are vertical angles, so they are equal.
7x = 4x + 48
3x = 48
x = 16
So ∠DPG is:
∠DPG = 7x
∠DPG = 112
∠DPE and ∠DPG are supplementary, so they add up to 180:
∠DPE + ∠DPG = 180
∠DPE + 112 = 180
∠DPE = 68
Bob and Fred together make $20.00 a week less than double John. John makes $110.00 a week and Bob makes $140.00 a week. How much does Fred make? answer
If both Bob and Fred make $20 less a week than twice John's weekly salary, then
[tex]B+F+20 = 2*J[/tex],
where B, F, and J are Bob's, Fred's, and John's salaries, respectively.
We want to find F, Fred's salary. Plugging in Bob's and John's salaries, we obtain
[tex]140+F+20 = 2*110[/tex]
[tex]F+160 = 220[/tex]
[tex]F = 60[/tex]
So Fred makes $60 a week.
Answer:
Fred makes $60/week.
Step-by-step explanation:
Fred makes f dollars per week, john j dollars and bob b dollars.
Then b = $140/week; j = $110/week; and b + f = 2j - 20.
Substitute $140/week for b in this equation; also substitute $110/week for j. Then:
$140/week + f = 2($110) - $20. There's only one variable here, f, so we're ready to solve for f:
$140/week + f = $220/week - $20/week, or:
$140/week + f = $200/week
Subtract $140 from both sides, obtaining:
f = $60
Fred makes $60/week.
Doreen Schmidt is a chemist. She needs to prepare 24 ounces of a 9% hydrochloric acid solution. Find the amount of 12% solution and the amount of 6% solution she should mix to get this solution.
PLEASE HELP ME
Answer:
Step-by-step explanation:
So we need to balance two things here. The overall volume, and the amount of hydrochloric acid.
Let's say x is the volume of the 12% solution and y is the volume of the 6% solution.
The sum of the volumes equals the total volume:
x + y = 24
And the sum of the amounts is the total amount:
0.12 x + 0.06 y = 0.09 (24)
We now have two equations and two variables. We can solve this system of equations with either substitution or elimination. Using substitution:
x = 24 - y
0.12 (24 - y) + 0.06 y = 0.09 (24)
2.88 - 0.12 y + 0.06 y = 2.16
0.72 = 0.06 y
y = 12
x = 24 - 12 = 12
So she needs to mix 12 ounces of 12% solution with 12 ounces of 6% solution to get 24 ounces of 9% solution.
The amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount of 12% solution needed to be mixed be represented by x, while the amount of 6% solution needed to be mixed be represented by y.
Now, since the total amount of solution needed to be made is 24 ounces, therefore, an equation can be formed as,
x+y=24
Solve the equation of x,
x=24 - y
Also, the total concentration of the combined should be 9%, therefore, we can write,
(12% of x) + (6% of y) = 9% of 24
0.12x + 0.06y = (0.09×24)
Substitute the value of x,
0.12(24-y) + 0.06y = 2.16
2.88 - 0.12y + 0.06y = 2.16
y = 12 ounces
substitute the value of y in the equation of x,
x = 24 - y
x = 24 - 12
x = 12
Hence, the amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.
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Find the distance on the coordinate system from the point (-3,4)to the point (8,-7)Find
To find the distance between two points on a coordinate system, we can use the distance formula, which is derived from the Pythagorean theorem.
Explanation:To find the distance between two points on a coordinate system, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (-3,4) and (8,-7), we can plug in the coordinates into the formula:
d = sqrt((8 - (-3))^2 + (-7 - 4)^2)
Simplifying the equation, we get:
d = sqrt(11^2 + (-11)^2)
Finally, calculating the square root, we find that the distance between the two points is sqrt(242), which is approximately 15.56 units.
Thus, the distance on the coordinate system from the point (-3,4)to the point (8,-7) is fond to be 15.56 units.
A physician prescribes alprazolam for a patient on an as needed basis. The patient can take up to 2.25mg per day in divided does. If alprazolam comes in .25 mg tablets, how many tablets can the patient take throughout the day?
Answer:
9
Step-by-step explanation:
If n is the number of tablets, the maximum value it can have is given by ...
0.25n = 2.25
Dividing by the coefficient of n gives ...
n = 2.25/0.25 = 9
The patient can take a total of 9 tablets through the day.
Answer:
The answer is 2:9
Step-by-step explanation:
On plato
Prove that for all whole values of n the value of the expression:
n(n+2)–(n–7)(n–5) is divisible by 7.
Explanation:
Multiply it out, collect terms, and look for a factor of 7:
n(n +2) -(n -7)(n -5) = n² +2n -(n² -12n +35)
= 14n -35
= 7(2n -5)
The expression has a factor of 7, so is divisible by 7 with a resulting quotient of 2n-5.
Gertrude took out a 30-year loan for $95,000 at 8.4% interest, compounded monthly. If her monthly payment on the loan is $723.75, how much of her first payment went toward note reduction?
Answer:
$58.75
Step-by-step explanation:
The monthly interest rate is 8.4%/12 = 0.7%, so the first month's interest is ...
$95,000×0.007 = $665
The amount of the first payment that goes to note reduction is the part that does not go for paying interest. That difference is ...
$723.75 - 665.00 = $58.75
Answer:$58.75
Step-by-step explanation:
i planted 12 flower bulbs. this is 60% i purchased. how many total bulbs did i purchase?.
let's say "x" is the whole lot and thus the 100%.
we know 12 is 60%, how much is "x" or 100%?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 12&60 \end{array}\implies \cfrac{x}{12}=\cfrac{100}{60}\implies \cfrac{x}{12}=\cfrac{5}{3} \\\\\\ 3x=60\implies x=\cfrac{60}{3}\implies x=20[/tex]
Which statement describes what these four powers have in common?
Answer:
b
Step-by-step explanation:
Rhonda completed the right column of the table to help her find the sum of 1/2 and 1/3 in which Step did her first error occur
Step 4
The numerator of this fraction is right because there are 5 shaded sections, but the denominator is incorrect because there are 6 total boxes, not 5.
Hope this helps!!
Answer:
the answer is C step 3
Step-by-step explanation:
because out side the box said 1/2 when its 3/6 and the question sais
In which step did her first error occur? so thats the firt the second one
its 1/3 when its 2/6. Hope it helps :)
Write the equation for the parabola that has x− intercepts (−4,0) and (1.5,0) and
y-intercept (0,−15).
Answer:
y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15
Step-by-step explanation:
Each given zero corresponds to a factor that is zero at that point. Those factors are (x +4) and (x -1.5).
The y-intercept tells us the scale factor, the multiplier that is needed to make the function value be -15 at x=0.
y = a(x +4)(x -1.5) = a(0 +4)(0-1.5) = -6a
-15 = -6a
-15/-6 = a = 2.5
So, the quadratic is ...
y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15
___
"The equation" can be written in many different forms. The simplest, given the information here, is the factored form (also called "intercept form"). We have also shown "standard form" (US version). The "standard form" (UK version) is also known as vertex form:
y = 2.5(x +1.25)^2 -18.90625
Plz help ASAP!! Explain your answer! I will mark at brainliest!!! And don’t copy anybody else’s answer
Answer:
No. Anna is incorrect.
Step-by-step explanation:
In order to find if the answer is right, just find the diagonals using the pythogorean theorem.
a² + b² = c²
For the rectangle, the base is 14 and the height is 7. We will have to find the hypotenuse.
14² + 7² = c²
196 + 49 = c²
245 = c²
c = √245
c = √49 × √5
c = 7√5
For the square, the base is 7 and the height is 7. We will have to find the hypotenuse.
7² + 7² = c²
49 + 49 = c²
98 = c²
c = √98
c = √49 × √2
c = 7√2
Now compare :
7√5 and 7√2
Clearly, 7√5 is not the double of 7√2
Please help me out guys. The photo will show you what to do. 50 points cause I need it done fast
Answer:
a) starting height: 5.5 ft
b) hang time: 5.562 seconds
c) maximum height: 126.5 ft
d) time to maximum height: 2.75 seconds
Step-by-step explanation:
a) The starting height is the height at t=0.
h(0) = -16·0 +88·0 +5.5
h(0) = 5.5
The starting height is 5.5 feet.
__
b) The ball is in the air between t=0 and the non-zero time when h(t) = 0. We can find the latter by solving ...
-16t^2 + 8t +5.5 = 0
t^2 -(11/2)t = 5.5/16 . . . . . subtract 5.5, then divide by -16
t^2 -(11/2)t +(11/4)^2 = (5.5/16) +(11/4)^2 . . . . complete the square
(t -11/4)^2 = 126.5/16 . . . . . . . . . . . . . . . . . . . . call this [eq1] for later use
t -11/4 = √7.90625
t = 2.75 +√7.90625 ≈ 5.562
The ball will be in the air about 5.562 seconds.
__
c) If we multiply [eq1] above by -16 and add the constant on the right, we get the vertex form of the height equation:
h(t) = -16(t -11/4) +126.5
The vertex at (2.75, 126.5) tells us ...
The maximum height of the ball is 126.5 feet.
__
d) That same vertex point tells us ...
The maximum height will be reached at t = 2.75 seconds.
_____
If you really need answers fast, a graphing calculator can give them to you in very short order (less than a minute).
55) Louis started a simple interest savings account with $1500 that earned 3.5% interest. He left the account untouched until some
55) Louis started a simi
time later when he withdrew all the money in that account, which totaled $1683.75. How long did Louis leave his money in the
account? years
Answer:
3.5 years
Step-by-step explanation:
Each year, Louis earned
$1500×0.035 = $52.50
in interest.
The amount of interest that had been credited to his account at the time of withdrawal was ...
$1683.75 -1500.00 = $183.75
Then the length of time the money had been in the account was ...
$183.75/($52.50/yr) = 3.5 yr
_____
Comment on the problem
We have assumed the account earned simple interest. Given the neatness of the answer, we believe that to be a correct assumption.
The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, October 24, 2012). Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 61 86 74 72 73 20 57 80 79 83 74 a. Develop a point estimate of mean fan rating for the population of NFL games. b. Develop a point estimate of the standard deviation for the population of NFL games.
The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.
What is a point Estimate?
A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.
Here,
∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74
= 816
n = 12 numbers
Thus;
Mean = ∑x/n
= 816/12
Mean = 68
B) In order to find the estimate of the standard deviation, we have the formula;
s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]
∑x² = 57² + 61² + 86² + ... + 74²
= 59,010
s = √[ (12*(59,010) - (816)²)/(12)(11)]
s = 17.6
Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.
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....Help Please.......
Answer:
y = 2x+3
Step-by-step explanation:
The slope is "what happens to the graph when you move one unit to the right in x-direction". As you can check, if you move 1 to the right, the y value increases by 2. Therefore the slope is 2.
The intercept is the graph's y value when x=0, ie., when it passes the y axis. This is at y=3.
Now we have our two ingredients, so y = slope * x + intercept, so 2x+3
Find the solution set for the equation, given the replacement set.
y = –5x + 8; {(6, –11), (4, –12), (5, –9), (3, –14)}
a.
{(6, –11)}
c.
{(4, –12)}
b.
{(3, –14)}
d.
{(5, –9)}
Answer:
c. {(4, -12)}
Step-by-step explanation:
It is convenient to rearrange the equation to standard form:
5x +y = 8
Then check the offered points.
(6, -11): 5·6 -11 = 19 ≠ 8
(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set
(5, -9): 5·5 -9 = 16 ≠ 8
(3, -14): 5·3 -14 = 1 ≠ 8
To find the solution set, substitute the x and y values into the equation and check if it is true.
Explanation:To find the solution set for the equation, we need to check which coordinates from the replacement set satisfy the equation y = -5x + 8.
For (6, -11): Substituting x = 6 and y = -11 into the equation, we get -11 = -5(6) + 8, which simplifies to -11 = -30 + 8. This is not true, so (6, -11) is not a solution.For (4, -12): Substituting x = 4 and y = -12 into the equation, we get -12 = -5(4) + 8, which simplifies to -12 = -20 + 8. This is not true, so (4, -12) is not a solution.For (5, -9): Substituting x = 5 and y = -9 into the equation, we get -9 = -5(5) + 8, which simplifies to -9 = -25 + 8. This is not true, so (5, -9) is not a solution.For (3, -14): Substituting x = 3 and y = -14 into the equation, we get -14 = -5(3) + 8, which simplifies to -14 = -15 + 8. This is true, so (3, -14) is a solution.The solution set for the equation, given the replacement set, is {(3, -14)}.
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Which statement is best represented by the inequality d>11?
A. Mo worked more than 11 hours this week.
B. Mo worked 11 more hours than Quinn worked this week.
C. Mo worked less than 11 hours this week.
D. Mo worked 11 less hours than Quinn worked this week.
For this case we have the following inequality:[tex]d> 11[/tex]
Assuming that "d" is the variable that represents the number of hours worked by Mo during this week, we have that the hours were greater than 11, according to the inequality sign.
So, the correct option is:
Mo worked more than 11 hours this week.
Answer:
Option A
Answer: a
Step-by-step explanation:
The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? State the null hypothesis and the alternate hypothesis. State whether the decision rule is true or false: Reject H0 if z < −1.645. True False Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Do not reject H0 What is the p-value? (Round your answer to 4 decimal places.) Next Visit question mapQuestion 3 of 4 Total 3 of 4 Prev
The p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.
- Decision regarding H0: Reject H0
- p-value: 0.0768.
The null hypothesis (H0) states that the mean waiting time is 3 minutes or more, while the alternate hypothesis (H1) states that the mean waiting time is less than 3 minutes.
- Null hypothesis (H0): μ ≥ 3
- Alternate hypothesis (H1): μ < 3
The decision rule is to reject H0 if the test statistic (z-score) is less than -1.645.
To compute the test statistic (z-score), we use the formula:
[tex]\[ z = \frac{{\bar{x} - \mu}}{{\frac{\sigma}{\sqrt{n}}}} \][/tex]
Where:
- [tex]\(\bar{x}\)[/tex] is the sample mean waiting time (2.75 minutes)
- [tex]\(\mu\)[/tex] is the population mean waiting time (3 minutes)
- [tex]\(\sigma\)[/tex] is the population standard deviation (1 minute)
- [tex]\(n\)[/tex] is the sample size (50)
Substituting the given values:
[tex]\[ z = \frac{{2.75 - 3}}{{\frac{1}{\sqrt{50}}}} \][/tex]
[tex]\[ z = \frac{{-0.25}}{{0.1414}} \][/tex]
[tex]\[ z ≈ -1.768 \][/tex]
Since -1.768 is less than -1.645, we reject the null hypothesis.
To find the p-value, we look up the z-score (-1.768) in the standard normal distribution table. The corresponding area to the left of -1.768 is approximately 0.0384. Since this is a one-tailed test, we multiply by 2 to get the total probability of both tails:
[tex]\[ p-value ≈ 2 \times 0.0384 = 0.0768 \][/tex]
Thus, the p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.
Complete questions:
The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? State the null hypothesis and the alternate hypothesis. State whether the decision rule is true or false: Reject H0 if z < −1.645. True False Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Do not reject H0 What is the p-value? (Round your answer to 4 decimal places.)
Which could be the area of one face of the triangular prism? Check all that apply
Area of rectangles = Length x width.
Area of triangles = 1/2 x base x height.
1 face is 12 x 10 = 120 square units
1 face is 12 x 8 = 96 square units
1 face is 12 x 6 = 72 square units
And 2 faces are 1/2 x 8 x 6 = 24 square units
Answers are 24 , 72 and 96 square units.
Answer:
A.24 Square units
C.72 Square units
D.96 Square units
Step-by-step explanation:
I got it right edge 2020.
What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?
exponential graph passing through point negative 1, negative 2 and point 0, negative 1.
f(x) − 2
2 • f(x)
f(x) + 1
−1 • f(x)
Answer:
Last option
−1 • f(x)
Step-by-step explanation:
The function [tex]f(x) = (0.5) ^ x[/tex] passes through point (-1, 2) because:
[tex]f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2[/tex]
and also goes through the point (0, 1)
Because:
[tex]f(0) = (0.5)^0 = 1[/tex]
Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of [tex]f(x) = (0.5) ^ x[/tex] reflected on the axis x. This means that if the point [tex](x_0, y_0)[/tex] belongs to f(x), then the point [tex](x_0, -y_0)[/tex] belongs to the transformed function
The transformation that reflects the graph of a function on the x-axis is.
[tex]y = cf(x)[/tex]
Where c is a negative number. In this case [tex]c = -1[/tex]
Then the transformation is:
[tex]y = -1*f(x)[/tex]
and the transformed function is:
[tex]f (x) = - (0.5) ^ x[/tex]
Observe the attached image.Answer:
f(x) -2 is the correct answer.
Step-by-step explanation:
Just took the test!
12. Complete the property of exponents. (ab)n = _______
A. an + bn
B. anbn
C. abn
D. an – bn
Answer:
(B) is the homogeneous mixture
What are the values of x and y? [tex]-2x+3y=8\wedge2x-3y=10[/tex]
Answer:
no solutions
Step-by-step explanation:
-2x+3y=8
2x-3y=10
We can use elimination to solve for x and y
Add the two equations together
-2x+3y=8
2x-3y=10
---------------------
0 = 18
Since this is never true, there are no solutions to this system of equations
If P=(-2,5) and (x,-27), find all numbers x such that the vector represented by PQ has length -40
Answer:
x ∈ {-26, 22}
Step-by-step explanation:
A graph shows that the points (-26, -27) and (22, -27) lie on a circle of radius 40 centered at (-2, 5). That is, if Q is either one of these points, the vector PQ will have a length of 40:
√((-26-(-2))^2 +(-27-5)^2) = √((-24)^2 +(-32)^2) = √1600 = 40√((22 -(-2))^2 +(-27 -5)^2) = √(24^2 +(-32)^2) = √1600 = 40You can call it -40 if you like, but you have to define what negative length means when you do that.