3 years ago

Find the volume of the composite space figure to the nearest whole number.

1 answer:

8 0

B. 180cm3

You have to find length, width, and height of both objects.

For the first one multiply:
3 x 8 x 5 = 120

Then multiply:
2 x 5 x 6 = 60

Add them together:

120 + 60 = 180cm3

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2 years ago

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Nuetrik [128]

Answer:

$\displaystyle k = \frac{34}{3}$

Step-by-step explanation:

We are given the polynomial:

$\displaystyle P(x) = 3x^3 - kx^2 + 5x + k$

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Recall that the Factor Theorem states that a binomial (x - a) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (x - 2). Thus, a = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

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$\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k \end{aligned}$

This must equal zero. Hence:

$\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3} \end{aligned}$

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2 years ago

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