Find the volume of the solid obtained by rotating the region bounded by y = 8 x 2 , x = 1 , and y = 0 , about the x -axis.

1 answer:

6 0

A cross-section is a disc with radius $8x^2$

$V = \int_0^1 A(x)\, dx = \int_0^1 \pi\left(8x^2\right)^2 dx = \int_0^1 64 \pi x^4 = \left[\frac{64\pi}{5} x^5\right]_0^1 \\
\\
= \frac{64\pi}{5}$

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Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(

oee [108]

The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

<h3>What is polynomial equation?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

$2x^3 +18x^2 - 18x - 162$

The factor of the polynomial equation are given as,

$2(x+ k)(x - k)(x +9)$

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,

$2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)$

Take out the highest common factor to make the groups as,

$2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)$

Use the property of difference of the square for the (x²-3²) term as,

$2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)$

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

Learn more about factor of polynomial here;

brainly.com/question/24380382

7 0

2 years ago

Select all that apply:

avanturin [10]

Answer: (-6,-4) (-2,-2) (-1,0) (2,6)

Step-by-step explanation:

We can see that points (2,0) and (4,1) isn't plotted on the line