Answer:
Let v(t) be the velocity of the car t hours after 2:00 PM. Then
. By the Mean Value Theorem, there is a number c such that
with
. Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly
.
Step-by-step explanation:
The Mean Value Theorem says,
Let be a function that satisfies the following hypotheses:
- f is continuous on the closed interval [a, b].
- f is differentiable on the open interval (a, b).
Then there is a number c in (a, b) such that

Note that the Mean Value Theorem doesn’t tell us what c is. It only tells us that there is at least one number c that will satisfy the conclusion of the theorem.
By assumption, the car’s speed is continuous and differentiable everywhere. This means we can apply the Mean Value Theorem.
Let v(t) be the velocity of the car t hours after 2:00 PM. Then
and
(note that 20 minutes is
of an hour), so the average rate of change of v on the interval
is

We know that acceleration is the derivative of speed. So, by the Mean Value Theorem, there is a time c in
at which
.
c is a time time between 2:00 and 2:20 at which the acceleration is
.
Answer:
48x -5
Step-by-step explanation:
(fog)(x) = f(g(x)) = 6(8x)-5 =48-5
Answer:
70°
found by considering A-frame ladder as a triangle
Step-by-step explanation:
Given that,
angle form on either side of A-frame ladder with the ground = 125°(exterior)
As it is a A-frame ladder so its a triangle, we will find the angle at the top of ladder by using different properties of triangle
1) find interior angle form by A-frame ladder with the ground
125 + x = 180 sum of angles on a straight line
x = 180 - 125
x = 55°
2) find the angle on top of ladder
55 + 55 + y = 180 sum of angle of a triangle
110 + y = 180
y = 180 - 110
y = 70°