A frog is climbing out of a well that is 31 feet deep. The frog can climb 3 feet per hour but then it rests for an hour, during which it slips back 2 feet. How long will it take for the frog to get out of the well?

What if the well was 74 feet deep, the frog climbs 7 feet per hour, and it slips back 2 feet while resting? (Round your answer to the nearaest hour.)


(c) What if a caterpillar is climbing out of a glass that is 11 inches high and can climb 1 and 1/2 inches in an hour but slides and falls back 1/4th inch during the hour it rests. How long will it take the caterpillar to climb to the top of the jar? (Round your answer to the nearest hour.)

find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a sphere with radius 50cm

Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4.3% interest. How much would you need to deposit in the account each month?
Round your answer to the nearest cent as needed.
$

How much would you need to deposit in an account each month in order to have $20,000 in the account in 9 years? Assume the account earns 2.6% interest.

You have $500,000 saved for retirement. Your account earns 6.4% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

State two characteristics of line integrals of scalar field

A Ferris wheel is boarding platform is 3 meters above the ground, has a diameter of 76 meters, and rotates once every 7 minutes.
How many minutes of the ride are spent higher than 49 meters above the ground?

The equation of the line that goes through the point (3,2) ( 3 , 2 ) and is parallel to the line going through the points (−2,3) ( − 2 , 3 ) and (5,6) ( 5 , 6 ) can be written in the form ?=??+? where:

m=

b=

A. Use the Product Rule or the Quotient Rule to find the derivative of the function.

g(x) = x³ cot(x) + 6x cos(x)

B. Use the Product Rule or the Quotient Rule to find the derivative of the function.

f(x) =

C. Use the Product Rule or the Quotient Rule to find the derivative of the function.

f(x) = (8x² + 4)(x² − 6x − 9)

1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx
Your answer should be in the form kπkπ, where k is an integer. What is the value of k?
Hint: d/dx arctan(x)=1/x^2+1
k=
(b) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.) =

2.

The function f(x)=8xln(1+x) is represented as a power series
f(x)=∞∑n=0 cn x^n.
Find the specified coefficients in the power series.
c2=   
c3=   
c4=   
c5=   
c6=   
Find the radius of convergence R of the series.
R=

(1 point) Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 38 grams of A and 14 grams of B, and for each gram of B, 1.2 grams of A is used. It has been observed that 13 grams of C is formed in 5 minutes. How much is formed in 30 minutes? What is the limiting amount of C after a long time ?

grams of C are formed in 30 minutes
grams is the limiting amount of C after a long time

Question 4: Homogeneous Second Order Differential equation

Solve the following equation for the particular solution.
i. 2?′′ + 5?′ + 3? = 0; ?(0)=3, ?′(0)=−4

ii. 4 (?²?/??²) + 8 (??/??) + 3y = 0 ?(0)=1, ?′(0)=2

iii. ?′′ + 6?′ + 13? = 0; ?(0)=2, ?′(0)=1

Solve the following integral  ∫ (x^2 + x + 2) / (x + 1)(x^2 + 1) dx. Use partial fraction decomposition. Show all work and steps to get to solution.

Q1) Velocity and acceleration: a ball is thrown verticality up word from the ground level with initial velocity of 2 feet per second and initial position 10 feet. Use a(t)=2cos⁡(2x+3)

   Find the equation of the velocity of the ball

   After how many seconds is the velocity of the ball one -half the initial velocity?

   Find the equation of the motion of the ball

   Calculate that displacement from t=1 till t=5 seconds

Joe leaves an intersection traveling west in his car. He is 20 feet from the intersection 4 seconds later. At the same time, Joshua leaves the intersection heading north in his car so that his position 4 seconds later is 26 feet from the intersection. If, at that instant time, Joe's speed is 8 feet per second and Joshuas' speed is 12 feet per second, find the rate at which the distance between the two cars is changing to the nearest tenth.

A bath tub with a volume of 400 liters at first is full of 100 liters of water with a bath salt concentration of 10 grams per liter. During some time, water with a bath salt concentration of .8 grams per liter starts to stream at 4 liters per minute simultaneously a leak in the tub causes the water and bath salt mix to stream out of the bath tub at the same pace. Determine the amount of time needed for the water and bath salt mix in the bath tub to be lessen to 3 grams per liter, please show all work and explanations!