Answer:
168 units^3
Step-by-step explanation:
The volume of triangular prism is calculated like this : 1/2 × b×h×l (b: base, h: height, l: length)
1/2 × 7 × 6 × 8 = 168 units^3
Answer:
21 minutes
Step-by-step explanation:
Her expected commute time is given by the probability of having to wait for the train (0.2) multiplied by the commute time in this scenario (25 min), added to the probability of not having to wait for the train (1 - 0.2) multiplied by the commute time in this scenario (20 min). The expected commute time is:

Her expected commute time is 21 minutes.
For first question, you can let t=1.5 and calculate h=140 ft. For second question, we can change the equation to the form of h=-16[(t-2)^2-9]. So you can see from the equation that the maximum height is created when t=2, equals to 144 ft. For question 3, let h=128. From equation, we can get t=3 or t=1. For last question, the rocket hit the lake means h=0, so t=5 or t=-1(not applicable). So the answer is t=5. You can also draw the graphic for the equation to help.
Answer:
The inner function is
and the outer function is
.
The derivative of the function is
.
Step-by-step explanation:
A composite function can be written as
, where
and
are basic functions.
For the function
.
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have
inside parentheses. So
is the inner function and the outer function is
.
The chain rule says:
![\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29g%27%28x%29)
It tells us how to differentiate composite functions.
The function
is the composition,
, of
outside function: 
inside function: 
The derivative of this is computed as

The derivative of the function is
.
Answer:
The answer is 120.
Step-by-step explanation: