Answer:
The graph of the equation is shown in the picture attached below.
We can see w = 12 corresponds to the global maximum of the function, and for any w greater than 12 the value of A(w) decreases.
This means that for any value of the width greater than 12, the function cannot model the situation.
Making the equation only valid for
w ∈ [0,12]
Answer:what grade are you in?
Step-by-step explanation:
Answer:
30 fruits
Step-by-step explanation:
Let
x ----> number of plums on the plate
y ----> number of apples on the plate
we know that
The ratio of the number of plums to the number of apples was 3:2
so

----> equation A
After Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples
so
----> equation B
substitute equation A in equation B

solve for y

Find the value of x

therefore
Mon put on the table

Answer: the 3
Step-by-step explanation:
It goes ones, tens, hundreds, thousands, etc. You round the 3 (down, less than 5) because that is in the hundreds place.
Answer:

or

Step-by-step explanation:
Given


![[a,b] = [0,2]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B0%2C2%5D)
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:

Integrate


Substitute values for a, b, f(x) and g(x)

Evaluate the exponents

Simplify like terms

Factor out 8

Integrate
![v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B2%2B1%7D%7D%7B2%2B1%7D%20-%20%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%20%5D%7C%5Climit%5E2_0)
![v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%20%5D%7C%5Climit%5E2_0)
Substitute 2 and 0 for x, respectively
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%20%5Cfrac%7B2%2A0%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B0%5E%7B4%7D%7D%7B4%7D%20%5D%29)
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%200%20-%200%5D%29)
![v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D)
![v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%7D%7B3%7D%20-%20%5Cfrac%7B16%7D%7B4%7D%20%5D)
Take LCM
![v = 8\pi [ \frac{16*4- 16 * 3}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%2A4-%2016%20%2A%203%7D%7B12%7D%5D)
![v = 8\pi [ \frac{64- 48}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B64-%2048%7D%7B12%7D%5D)

Simplify


or



