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2 years ago

What happens to the value?

Mathematics

1 answer:

Fiesta28 [93]2 years ago

4 0

Answer:

D.) c is multiplied by 4

Step-by-step explanation:

$c = \dfrac{8a^3}{b}$

If a is doubled, it becomes 2a. If b is doubled, it becomes 2b. Now we replace a with 2a and b with 2b and simplify.

$c = \dfrac{8(2a)^3}{2b}$

$c = \dfrac{8 \times 8a^3}{2b}$

$c = \dfrac{4 \times 8a^3}{b}$

$c = 4 \times \dfrac{8a^3}{b}$

Answer: D.) c is multiplied by 4

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2 years ago

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Find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)

timama [110]

<h3>Answer: c = 7/4</h3>

================================================

Work Shown:

Compute the function value at the endpoints

$f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\$

With a = -5 and b = 4, we have

$f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\$

So,

$f(x) = \sqrt{4-x}\\\\f'(x) = -\frac{1}{2\sqrt{4-x}}\\\\f'(c) = -\frac{1}{3}\\\\-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\$

Use algebra to solve for c

$-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\\frac{1}{2\sqrt{4-c}} = \frac{1}{3}\\\\3 = 2\sqrt{4-c}\\\\2\sqrt{4-c} = 3\\\\\sqrt{4-c} = \frac{3}{2}\\\\4-c = \frac{9}{4}\\\\c = 4-\frac{9}{4}\\\\c = \frac{16-9}{4}\\\\c = \frac{7}{4}\\\\$

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3 years ago

If x+y = -1, and xy= -12, what is the value of (x+3) (y+3) ?

9966 [12]

Answer:

Here are my hints. You can solve it yourself

1/ xy = -12 --> x = -12/y

2/ (-12/y) + y = -1 --> -(12/y) + (y²/y) = -1 --> -12 + y² = -y --> y²+y-12=0

3/ From y²+y-12=0 we can find y then use y to find x and then do your

(x+3) * (y+3)

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3 years ago