What is the next 4 terms-0.02,0.04,0.07,0.10

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:20 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:20 the acce

Bad White [126]

Answer:

Let v(t) be the velocity of the car t hours after 2:00 PM. Then $\frac{v(1/3)-v(0)}{1/3-0}=\frac{50 \:{\frac{mi}{h} }-30\:{\frac{mi}{h} }}{1/3\:h-0\:h} = 60 \:{\frac{mi}{h^2} }$ . By the Mean Value Theorem, there is a number c such that $0 < c$ with $v'(c)=60 \:{\frac{mi}{h^2}}$ . Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly $60 \:{\frac{mi}{h^2}}$ .

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

$f'(c)=\frac{f(b)-f(a)}{b-a}$

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 $v(0 \:h) = 30 \:{\frac{mi}{h} }$ and $v( \frac{1}{3} \:h) = 50 \:{\frac{mi}{h} }$ (note that 20 minutes is $20/60=1/3$ of an hour), so the average rate of change of v on the interval $[0 \:h, \frac{1}{3} \:h]$ is

$\frac{v(1/3)-v(0)}{1/3-0}=\frac{50 \:{\frac{mi}{h} }-30\:{\frac{mi}{h} }}{1/3\:h-0\:h} = 60 \:{\frac{mi}{h^2} }$

We know that acceleration is the derivative of speed. So, by the Mean Value Theorem, there is a time c in $(0 \:h, \frac{1}{3} \:h)$ at which $v'(c)=60 \:{\frac{mi}{h^2}}$ .

c is a time time between 2:00 and 2:20 at which the acceleration is $60 \:{\frac{mi}{h^2}}$ .

4 0

4 years ago

4 Three intersecting lines form triangle BCE as shown below.

Lapatulllka [165]

Answer:

A, C, E

Step-by-step explanation:

<u>Options:</u>

A. m∠C + m∠E = m∠A

Correct. Exterior angle equals to sum of non-adjacent interior angles.

B. m∠D + m∠F = m∠B

Incorrect. Exterior angles have greater value.

C. m∠B + m∠C + m∠E = 180°

Correct. Interior angles of a triangle sum to 180°

D. m∠B + m∠C + m∠D = 180°

Incorrect. Angles C and D sum to 180°

E. m∠A + m∠ B = m∠E + m∠F

Correct. Both sides of equation refer to straight angle.

F . m∠B + m∠C + m∠ E = m∠A + m∠D + m∠F

Incorrect. Some of interior angles is not equal to sum of exterior angles.

5 0

3 years ago

Read 2 more answers

If p = 12 and q = 3, evaluate 4p – q.

borishaifa [10]

Answer:

45

Step-by-step explanation:

Plug in the values into the equation

4(12) - 3

48 - 3 = 45

8 0

3 years ago

Read 2 more answers

Ronald and Tim did their laundry today. Ronald does laundry every 6 days and Tom does laundry every 9 days. How many days will i

Luden [163]

Least common multiple question

Ronald: count by 6's
6, 12, 18, 24, 30, 36, 42, 48, 54 ....

Tim: count by 9's
9, 18, 27, 36, 45, 54,

every 18 days they do their laundry together

7 0

4 years ago

6. Ray Rodriguez will be eligible for retirement benefits in 72 months. How many years remain before Ray

Aloiza [94]

6 calandre years hope y get it correct and mark me brainliest plsssss

6 0

3 years ago