Answer:
D -9
Step-by-step explanation:
(g o f)(-1) = g(f(-1))
f(-1) = 
g(-4) = -4 - 5 = -9
So, (g o f)(-1) = -9
Step-by-step explanation:
5 gallons 3 quarts +4 gallons 2 quarts
5.3
+
4.2
=9.5 gallons
The question might have some mistake since there are 2 multiplier of t. I found a similar question as follows:
The population P(t) of a culture of bacteria is given by P(t) = –1710t^2+ 92,000t + 10,000, where t is the time in hours since the culture was started. Determine the time at which the population is at a maximum. Round to the nearest hour.
Answer:
27 hours
Step-by-step explanation:
Equation of population P(t) = –1710t^2+ 92,000t + 10,000
Find the derivative of the function to find the critical value
dP/dt = -2(1710)t + 92000
= -3420t + 92000
Find the critical value by equating dP/dt = 0
-3420t + 92000 = 0
92000 = 3420t
t = 92000/3420 = 26.90
Check if it really have max value through 2nd derivative
d(dP)/dt^2 = -3420
2nd derivative is negative, hence it has maximum value
So, the time when it is maximum is 26.9 or 27 hours
Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let 
and 
. Then, the given equation is essentially 
. Thus, we can use the chain rule.
Recall the chain rule: ![\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29%5Ccdot%20g%27%28x%29)
. So, let's find the derivative of each function:
We can use the Power Rule here:
Now:
Again, use the Power Rule and Sum Rule
Now, we can put them together:
