Answer:
YES
Step-by-step explanation:
cause 12.6 / 4.5 = 2.8
and 4.2 / 1.5 = 2.8
Step by step:A prediction is basically an educated guess and if you are looking for the exact word to describe that you would find that hypothesis is the correct way to tell what is a prediction.
Answer:B
Step-by-step explanation:
ok so just take 4×10=40
-6^40=20
Answer:
<em>The largest rectangle of perimeter 182 is a square of side 45.5</em>
Step-by-step explanation:
<u>Maximization Using Derivatives</u>
The procedure consists in finding an appropriate function that depends on only one variable. Then, the first derivative of the function will be found, equated to 0 and find the maximum or minimum values.
Suppose we have a rectangle of dimensions x and y. The area of that rectangle is:

And the perimeter is

We know the perimeter is 182, thus

Simplifying

Solving for y

The area is

Taking the derivative:

Equating to 0

Solving

Finding y

The largest rectangle of perimeter 182 is a square of side 45.5
We draw region ABC. Lines that connect y = 0 and y = x³ are vertical so:
(i) prependicular to the axis x - disc method;
(ii) parallel to the axis y - shell method;
(iii) parallel to the line x = 18 - shell method.
Limits of integration for x are easy x₁ = 0 and x₂ = 9.
Now, we have all information, so we could calculate volume.
(i)

![V=\pi\cdot\int\limits_0^9(x^3)^2\, dx=\pi\cdot\int\limits_0^9x^6\, dx=\pi\cdot\left[\dfrac{x^7}{7}\right]_0^9=\pi\cdot\left(\dfrac{9^7}{7}-\dfrac{0^7}{7}\right)=\dfrac{9^7}{7}\pi=\\\\\\=\boxed{\dfrac{4782969}{7}\pi}](https://tex.z-dn.net/?f=V%3D%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%28x%5E3%29%5E2%5C%2C%20dx%3D%5Cpi%5Ccdot%5Cint%5Climits_0%5E9x%5E6%5C%2C%20dx%3D%5Cpi%5Ccdot%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%5Cright%5D_0%5E9%3D%5Cpi%5Ccdot%5Cleft%28%5Cdfrac%7B9%5E7%7D%7B7%7D-%5Cdfrac%7B0%5E7%7D%7B7%7D%5Cright%29%3D%5Cdfrac%7B9%5E7%7D%7B7%7D%5Cpi%3D%5C%5C%5C%5C%5C%5C%3D%5Cboxed%7B%5Cdfrac%7B4782969%7D%7B7%7D%5Cpi%7D)
Answer B. or D.
(ii)

![V=2\pi\cdot\int\limits_0^{9}(x\cdot x^3)\, dx=2\pi\cdot\int\limits_0^{9}x^4\, dx= 2\pi\cdot\left[\dfrac{x^5}{5}\right]_0^9=2\pi\cdot\left(\dfrac{9^5}{5}-\dfrac{0^5}{5}\right)=\\\\\\=2\pi\cdot\dfrac{9^5}{5}=\boxed{\dfrac{118098}{5}\pi}](https://tex.z-dn.net/?f=V%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E%7B9%7D%28x%5Ccdot%20x%5E3%29%5C%2C%20dx%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E%7B9%7Dx%5E4%5C%2C%20dx%3D%0A2%5Cpi%5Ccdot%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E9%3D2%5Cpi%5Ccdot%5Cleft%28%5Cdfrac%7B9%5E5%7D%7B5%7D-%5Cdfrac%7B0%5E5%7D%7B5%7D%5Cright%29%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cdfrac%7B9%5E5%7D%7B5%7D%3D%5Cboxed%7B%5Cdfrac%7B118098%7D%7B5%7D%5Cpi%7D)
So we know that the correct answer is D.
(iii)
Line x = h

![V=2\pi\cdot\int\limits_0^9\big((18-x)\cdot x^3\big)\, dx=2\pi\cdot\int\limits_0^9(18x^3-x^4)\, dx=\\\\\\=2\pi\cdot\left(\int\limits_0^918x^3\, dx-\int\limits_0^9x^4\, dx\right)=2\pi\cdot\left(18\int\limits_0^9x^3\, dx-\int\limits_0^9x^4\, dx\right)=\\\\\\=2\pi\cdot\left(18\left[\dfrac{x^4}{4}\right]_0^9-\left[\dfrac{x^5}{5}\right]_0^9\right)=2\pi\cdot\Biggl(18\biggl(\dfrac{9^4}{4}-\dfrac{0^4}{4}\biggr)-\biggl(\dfrac{9^5}{5}-\dfrac{0^5}{5}\biggr)\Biggr)=\\\\\\](https://tex.z-dn.net/?f=V%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%5Cbig%28%2818-x%29%5Ccdot%20x%5E3%5Cbig%29%5C%2C%20dx%3D2%5Cpi%5Ccdot%5Cint%5Climits_0%5E9%2818x%5E3-x%5E4%29%5C%2C%20dx%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cleft%28%5Cint%5Climits_0%5E918x%5E3%5C%2C%20dx-%5Cint%5Climits_0%5E9x%5E4%5C%2C%20dx%5Cright%29%3D2%5Cpi%5Ccdot%5Cleft%2818%5Cint%5Climits_0%5E9x%5E3%5C%2C%20dx-%5Cint%5Climits_0%5E9x%5E4%5C%2C%20dx%5Cright%29%3D%5C%5C%5C%5C%5C%5C%3D2%5Cpi%5Ccdot%5Cleft%2818%5Cleft%5B%5Cdfrac%7Bx%5E4%7D%7B4%7D%5Cright%5D_0%5E9-%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D_0%5E9%5Cright%29%3D2%5Cpi%5Ccdot%5CBiggl%2818%5Cbiggl%28%5Cdfrac%7B9%5E4%7D%7B4%7D-%5Cdfrac%7B0%5E4%7D%7B4%7D%5Cbiggr%29-%5Cbiggl%28%5Cdfrac%7B9%5E5%7D%7B5%7D-%5Cdfrac%7B0%5E5%7D%7B5%7D%5Cbiggr%29%5CBiggr%29%3D%5C%5C%5C%5C%5C%5C)

Answer D. just as before.