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3 years ago

Compare each of the functions shown below:

Mathematics

1 answer:

Marina86 [1]3 years ago

7 0

Answer:

D. All three functions have the same rate of change.

Step-by-step explanation:

1. For the function f(x):

at $x=\pi,$ $f(\pi)=0;$
at $x=\dfrac{3\pi }{2},$ $f\left(\dfrac{3\pi}{2}\right)=-4.$

The rate of change is

$\dfrac{f(\frac{3\pi}{2})-f(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.$

2. For the function g(x):

at $x=\pi,$ $g(\pi)=0;$
at $x=\dfrac{3\pi }{2},$ $g\left(\dfrac{3\pi}{2}\right)=-4.$

The rate of change is

$\dfrac{g(\frac{3\pi}{2})-g(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.$

3. For the function h(x):

at $x=\pi,$ $h(\pi)=4\cdot \sin \pi+2=2;$
at $x=\dfrac{3\pi }{2},$ $h\left(\dfrac{3\pi}{2}\right)=4\cdot \sin \frac{3\pi}{2}+2=-4+2=-2.$

The rate of change is

$\dfrac{h(\frac{3\pi}{2})-h(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-2-2}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.$

All three functions have the same rate of change.

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QUESTIONS

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Given:

Amount of salt containing in jar = 32 gram

Total amount of salt in jar = 15 kg

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Number of jars can be filled from 15kg of the salt

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