Which of the following phrases are inequalities? PLSSS HELP

Mathematics

1 answer:

Ymorist [56]2 years ago

3 0

Answer:

B, D, and E.

Inequalities are recognized from >, <, ≤, and ≥ signs.

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

vodka [1.7K]

The average rate of change for the function f(x) can be calculated from the following equation
$\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }$

By applying the last formula on the given equations
(1) the first function f
from the table f(3π/2) = -2   and   f(2π) = 0
∴ 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 = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{1-(-5)}{ \frac{\pi}{2} }= \frac{6}{ 
\frac{\pi}{2} } = \frac{12}{\pi}$

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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