4 p^2 without exponents

What is the mean of -9,-5,-4,-4,-2,0,1,2,3,5

IrinaK [193]

Answer: - 1.3

Step-by-step explanation: I believe that it's -1.3 if you're referring to the arithmetic mean.

(1) Take the sum of -9, -5, -4, -4, -2, 0, 1, 2, 3, 5 and simplify it to -13

(2) Count the number of terms in the data set.

{-9, -5, -4, -4, -2, 0, 1, 2, 3, 5}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - The number of terms in the data set is <u>10.</u>

(3) Divide the sum by the number of terms and simplify.

-13 / 10 = -1.3 (simplified)

8 0

3 years ago

Find the area of the circle. Leave your answer in terms of Pi. Diameter is 14 ft.

QveST [7]

Answer:

The area of the circle is $49\pi\ ft^{2}$

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^{2}$

we have

$r=14/2=7\ ft$ -----> the radius is half the diameter

substitute the value

$A=\pi (7)^{2}$

$A=49\pi\ ft^{2}$

7 0

3 years ago

Read 2 more answers

This is a "water tank" calculus problem that I've been working on and I would really appreciate it if someone could look at my w

Sedaia [141]

Part A

Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points.

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Part B

It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis.

dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)

Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 = (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0

Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)

Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)

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Part C

Your answer is correct.
Below is an alternative way to find the same answer

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Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet

Set up the radius r(t) function
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B

Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)]
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)

Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before

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Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)

8 0

3 years ago

The sum of 5 consecutive integers is 200. What is the fourth number in this sequence.

babunello [35]

STEP-BY-STEP SOLUTION:

Let the smallest integer of the five integers = x

x + x + 1 + x + 2 + x + 3 + x + 4 = 200

5x + 10 = 200

5x = 200 - 10

5x = 190

x = 190 / 5

x = 38

Therefore:

Number no. 4 = x + 3 = 38 + 3 = 41

FINAL ANSWER:

Hence, the fourth number in the sequence is 41.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3

7 0

4 years ago

The product of a number and 4 increased by 8 -36

Julli [10]

4x + 8 - 36 first subtract 36 from 8 to get the simplified equation 4x + (-28), or 4x - 28. As you cannot combine these terms, this is as far as you can go. Hope this helps! :)

8 0

3 years ago