The answer is f
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Answer is: Radius = 8.6 cm
Answer:
The average rate of change for the given function in the interval (-5, -1) is 0 (zero)
Step-by-step explanation:
The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:
the average rte of change of h(t) in the interval (-5, -1) is:
![\frac{h(-1)-h(-5)}{-1+5}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%28-1%29-h%28-5%29%7D%7B-1%2B5%7D)
so we find:
![h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9](https://tex.z-dn.net/?f=h%28-1%29%3D%28-1%2B3%29%5E2%2B5%3D2%5E2%2B5%3D4%2B5%3D9%5C%5Cand%5C%5Ch%28-5%29%3D%28-5%2B3%29%5E2%2B5%3D%28-2%29%5E2%2B5%3D4%2B5%3D9)
then the average rate of change becomes:
![\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0](https://tex.z-dn.net/?f=%5Cfrac%7Bh%28-1%29-h%28-5%29%7D%7B-1%2B5%7D%3D%5Cfrac%7B9-9%7D%7B4%7D%20%3D%5Cfrac%7B0%7D%7B4%7D%20%3D0)
<h3>Given</h3>
- C(t) = 40 cm + t·(2/5 cm/s) . . . circumference of a circle vs time
<h3>Find</h3>
- dr/dt for radius r
- r at t=4 seconds
<h3>Solution</h3>
The circumference and radius of a circle are related by
... C = 2πr
so the radius in terms of circumference is
... r = C/(2π)
... r(t) = (40 +0.4t)/(2π) = (1/π)(20 cm + 0.2t cm/s)
Then dr/dt is
... dr/dt = 0.2/π cm/s
And the radius at t=4 s is
... r(4) = (1/π)(20 + 0.2·4) cm
... r(4) = 20.8/π cm
Answer:
![(g\cdot f) = -3x^2-3](https://tex.z-dn.net/?f=%28g%5Ccdot%20f%29%20%3D%20%20-3x%5E2-3)
Step-by-step explanation:
![f(x) = x^2 + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%201)
![g(x) = -3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-3)
The problem state to multiply the function
and
so the symbol seems to be incorrect.
We actually want to calculate
![g(x) f(x) =gf(x) = (-3) \cdot (x^2+1)= -3x^2-3](https://tex.z-dn.net/?f=g%28x%29%20%20f%28x%29%20%3Dgf%28x%29%20%3D%20%20%28-3%29%20%20%5Ccdot%20%28x%5E2%2B1%29%3D%20-3x%5E2-3)
Note
![g\circ f(x)=g(f(x))=g(x^2+1)=-3](https://tex.z-dn.net/?f=g%5Ccirc%20f%28x%29%3Dg%28f%28x%29%29%3Dg%28x%5E2%2B1%29%3D-3)