<img src="https://tex.z-dn.net/?f=6%285-8v%29%2B12%3D-54" id="TexFormula1" title="6(5-8v)+12=-54" alt="6(5-8v)+12=-54" align="ab

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Elenna [48]

2 years ago

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Mathematics

2 answers:

spayn [35]2 years ago

7 0

Answer:

v = 2

Step-by-step explanation:

Given

6(5 - 8v) + 12 = - 54 ← distribute and simplify left side

30 - 48v + 12 = - 54

42 - 48v = - 54 ( subtract 42 from both sides )

- 48v = - 96 ( divide both sides by - 48 )

v = 2

Lena [83]2 years ago

3 0

Answer:

$v = 2$

Step-by-step explanation:

$6(5-8v)+12=-54 \\ 30 - 48v + 12 = - 54 \\ 42 - 48v = - 54 \\ - 48v = - 54 - 42 \\ - 48v = - 96 \\ \\ v = \frac{( - 96)}{( - 48)} \\ \\ v = \frac{96}{48} \\ \\ v = 2$

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Which function has the greatest rate of change on the interval from x = 3 pi over 2 to x = 2π?

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$\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }$

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(1) the first function f
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∴ The average rate of f = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}$

(2) the second function g(x)
from the graph g(3π/2) = -2   and   g(2π) = 0
∴ The average rate of g = $\frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ 
\frac{\pi}{2} } = \frac{4}{\pi}$

(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
   h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
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By comparing the results, The <span>function which has the greatest rate of change is h(x)
</span>

So, the correct answer is option <span>C) h(x)</span>

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