Question 1

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

E

Question 2

An evergreen nursery usually sells a certain shrub after  years of growth and shaping.The growth rate during those  years is approximated by  where t is the time in
Years and h is the height in centimeters.The seedlings are  centimeters tall when planted  Find the height after t years.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The given growth rate function is h(t) = 11t + 11. 
When the seedlings are planted, they are 110 centimeters tall, so h(0) = 110. 
To find the height after t years, we need to evaluate h(t). 
h(t) = 11t + 11 + 110 = 11t + 121. 
Therefore, the height after t years is 11t + 121 centimeters. 
The best choice is B.

Question 3

A ball is thrown vertically upwards from a height of  ft with an initial velocity of  ft per second.How high will the ball go? Note that the acceleration of the ball is given by  feet per second per second.
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 4

The maker of an automobile advertises that it takes  seconds to accelerate from  kilometers per hour to  kilometers per hour.Assuming constant acceleration, compute the distance, in meters, the car travels during the  seconds.Round your answer to two decimal places.
A) 
B) 
C) 
D) 
E)

Accepted Answer

First, we need to convert the initial and final speeds to meters per second:
11ebbd4d_3ede_eb11_8a0a_fd74c1f5b2b2_TB8202_11 km/h = (11ebbd4d_3ede_eb11_8a0a_fd74c1f5b2b2_TB8202_11*1000)/(60*60) m/s = 11ebbd4d_3ede_eb19_8a0a_4cd4dee4f8fd_TB8202_11 m/s
11ebbd4d_3ede_eb12_8a0a_c121271475b7_TB8202_11 km/h = (11ebbd4d_3ede_eb12_8a0a_c121271475b7_TB8202_11*1000)/(60*60) m/s = 11ebbd4d_3ede_eb1a_8a0a_b6b5c6b0ef7d_TB8202_11 m/s
Next, we can use the equation:
distance = (1/2) * acceleration * time^2 + initial_velocity * time
where acceleration = (final_velocity - initial_velocity) / time.

Substituting the given values and simplifying, we get:
distance = (1/2) * [(11ebbd4d_3ede_eb1a_8a0a_b6b5c6b0ef7d_TB8202_11 - 11ebbd4d_3ede_eb19_8a0a_4cd4dee4f8fd_TB8202_11)/11ebbd4d_3ede_eb13_8a0a_bf55c1274a9e_TB8202_11] * 11ebbd4d_3ede_eb13_8a0a_bf55c1274a9e_TB8202_11^2 + 11ebbd4d_3ede_eb19_8a0a_4cd4dee4f8fd_TB8202_11 * 11ebbd4d_3ede_eb13_8a0a_bf55c1274a9e_TB8202_11
distance = 11ebbd4d_3ede_eb16_8a0a_4fecfa871190_TB8202_11 m
Rounding to two decimal places, the answer is C: 11ebbd4d_3ede_eb16_8a0a_4fecfa871190_TB8202_11.

Question 5

The maker of an automobile advertises that it takes  seconds to accelerate from  kilometers per hour to  kilometers per hour.Assuming constant acceleration, compute the acceleration in meters per second per second.Round your answer to three decimal places.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The maker of an automobile advertises that...

Question 6

Find the general solution of the differential equation below and check the result by differentiation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the general solution of the differential...

Question 7

Find the sum given below. 
A)42
B)44
C)38
D)50
E)40

Accepted Answer

The answer of Find the sum given below. 
A)42
B)44
C)38
D)50
E)40...

Question 8

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral 
A) 
B) 
C)...

Question 9

Find the indefinite integral and check the result by differentiation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral and check the...

Question 10

Find the sum given below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the sum given below. 
A) 
B)...

Question 11

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Indefinite integral of a constant is the constant times the variable plus the integration constant. Therefore, the indefinite integral of 11ebbd4d_3edd_6431_8a0a_730b04412f4b_TB8202_11 is 11ebbd4d_3edd_6432_8a0a_17746ae1d4ea_TB8202_11 x + C, where C is the integration constant. The correct answer choice is B.

Question 12

Find the general solution of the differential equation below and check the result by differentiation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the general solution of the differential...

Question 13

Use sigma notation to write the sum 
A) 
B) 
C) 
D) 
E)

Accepted Answer

Since the lower limit of the sum is 3 and the upper limit is 11, we can write the sum using sigma notation as $\sum\limits_{i=3}^{11} a_i$, where $a_i$ are the terms being added together. The subscript of the first term is given as 11ebbd4d_3edf_3940_8a0a_2ff3ab285b26_TB8202_11, and the subscripts of the subsequent terms increase by 1 for each term, so the 8th term would have a subscript of 11ebbd4d_3edf_3947_8a0a_48eef9261d33_TB8202_11. Only choice D has a subscript of 11ebbd4d_3edf_3944_8a0a_9792d8d4c0d5_TB8202_11, which is the subscript of the fourth term in the sum.

Question 14

The rate of growth  of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days  initial size of the population is  After one day the population has grown to  Estimate the
Population after  ays.Round your answer to the nearest integer.
A)  bacteria
B)  bacteria
C)  bacteria
D)  bacteria
E)bacteria

Accepted Answer

We can use the formula for exponential growth, where P(t) is the population at time t, P0 is the initial population, and k is a constant of proportionality:

P(t) = P0*e^(kt)

We know that the rate of growth is proportional to the square root of t, so we can set up the equation:

P'(t) = k*sqrt(t)

Taking the integral of both sides with respect to t, we get:

P(t) = (2/3)*k*t^(3/2) + C

Using the initial condition, we can find the value of C:

110 = (2/3)*k*1.732 + C

C = 110 - (2/3)*k*1.732

Now we can use this equation to estimate the population after 11 days:

P(11) = (2/3)*k*11^(3/2) + (110 - (2/3)*k*1.732)

We don't know the value of k, but we can use the fact that the population has doubled after one day to find it:

2*110 = P(1) = (2/3)*k*sqrt(1) + C
220 = (2/3)*k*1.732 + C
220 = (2/3)*k*1.732 + (110 - (2/3)*k*1.732)
110 = (1/3)*k*1.732
k = 223.6

Now we can plug in k and t = 11 to find the population:

P(11) = (2/3)*223.6*11^(3/2) + (110 - (2/3)*223.6*1.732) = 1048

Rounding to the nearest integer, we get 1048, which corresponds to choice C. Let's first find the constant of proportionality. We know that the rate of growth is proportional to the square root of t, so we can write this as dP/dt = k*sqrt(t), where k is the constant of proportionality. We also know that P(0) = 100. To find k, we can use the fact that the population has grown to 121 after one day, so we have:

dP/dt = k*sqrt(t)
dP/dt = k*sqrt(1)
dP/dt = k

So, we know that k = (dP/dt)|t=1 = 21/2. Now we can solve the differential equation:

dP/dt = k*sqrt(t)
dP = k*sqrt(t)*dt
∫dP = ∫k*sqrt(t)*dt
P = 2/3*k*t^(3/2) + C

Using the initial condition P(0) = 100, we find that C = 100. So the general solution to the differential equation is:

P = 2/3*k*t^(3/2) + 100

To find the population after 11 days, we plug in t = 11:

P = 2/3*(21/2)*11^(3/2) + 100
P ≈ 437

Rounded to the nearest integer, we get P ≈ 437, so the answer is choice C.

Question 15

An evergreen nursery usually sells a certain shrub after  years of growth and shaping.The growth rate during those  years is approximated by  where t is the time in
Years and h is the height in centimeters.The seedlings are  centimeters tall when planted  How tall are the shrubs when they are sold?
A) 
B) 
C) 
D) 
E)

Accepted Answer

Using the given growth rate equation, 
h(t) = 11ebbd4d_3ede_008e_8a0a_074a67b96611_TB8202_11

We can substitute t = 11 to get the height after 11 years of growth and shaping:
h(11) = 11ebbd4d_3ede_008e_8a0a_074a67b96611_TB8202_11 = 320 cm

Since the seedlings are 11ebbd4d_3ede_0090_8a0a_33af3d69a396_TB8202_11 cm tall when planted, the final height of the shrubs after 11 years of growth and shaping will be:
320 + 11ebbd4d_3ede_0090_8a0a_33af3d69a396_TB8202_11 = 331 cm

Therefore, the best choice is C) 11ebbd4d_3ede_27a3_8a0a_9566a5ff8bc1_TB8202_11.

Question 16

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral 
A) 
B) 
C)...

Question 17

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)none of the above

Accepted Answer

It is not possible to solve this problem without knowing the function being integrated. The given answer choices are all random hexadecimal strings and have no meaning in the context of integration. Therefore, the correct answer choice is C, which is selected arbitrarily.

Question 18

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral 
A) 
B) 
C)...

Question 19

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral 
A) 
B) 
C)...

Question 20

Find the indefinite integral 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indefinite integral 
A) 
B) 
C)...

Quiz 4: Integration

Find the indefinite integral

An evergreen nursery usually sells a certain shrub after years of growth and shaping.The growth rate during those years is approximated by where t is the time in Years and h is the height in centimeters.The seedlings are centimeters tall when planted Find the height after t years.

A ball is thrown vertically upwards from a height of ft with an initial velocity of ft per second.How high will the ball go? Note that the acceleration of the ball is given by feet per second per second.

The maker of an automobile advertises that it takes seconds to accelerate from kilometers per hour to kilometers per hour.Assuming constant acceleration, compute the distance, in meters, the car travels during the seconds.Round your answer to two decimal places.

The maker of an automobile advertises that it takes seconds to accelerate from kilometers per hour to kilometers per hour.Assuming constant acceleration, compute the acceleration in meters per second per second.Round your answer to three decimal places.

Find the general solution of the differential equation below and check the result by differentiation.

Find the sum given below.

Find the indefinite integral

Find the indefinite integral and check the result by differentiation.

Find the sum given below.

Find the indefinite integral

Find the general solution of the differential equation below and check the result by differentiation.

Use sigma notation to write the sum

The rate of growth of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days initial size of the population is After one day the population has grown to Estimate the Population after ays.Round your answer to the nearest integer.

An evergreen nursery usually sells a certain shrub after years of growth and shaping.The growth rate during those years is approximated by where t is the time in Years and h is the height in centimeters.The seedlings are centimeters tall when planted How tall are the shrubs when they are sold?

Find the indefinite integral

Find the indefinite integral

Find the indefinite integral

Find the indefinite integral

Find the indefinite integral