# Differentiation Questions and Answers

Calculus

Differentiation Solutions

The traffic flow rate (cars per hour) across an intersection is r(t) 300 +900t 180t², where t is in
hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 8 am?
cars

Calculus

Differentiation Solutions

Find the accumulated present value of an investment over a 7 year period if there is a continuous money flow of $5,000 per year and the interest rate is 1.2% compounded continuously.

Calculus

Differentiation Solutions

A cell culture contains 2 thousand cells, and is growing at a rate of r(t) = 6e0.00t thousand cells per hour. Find the total cell count after 3 hours. Give your answer accurate to at least 2 decimal

Calculus

Differentiation Solutions

(1 point) Let F = xi + (x + y) j + (x − y + z) k. Let the line / be (a) Find a point P = (xo, Yo, Zo) where F is parallel to 1. P = Find a point Q = (x₁, №₁, Z₁ ) at which I and I are perpendicular.

Calculus

Differentiation Solutions

In Exercises 33-42, find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line. 33. (5, 1), (-5,5) 38. (1, 1), (6, −3)

Calculus

Differentiation Solutions

Recently, the bowling scores of a certain bowler were normally distributed with mean 202 and standard deviation 19. a) Find the probability that a score is from 185 to 215. b) Find the probability

Calculus

Differentiation Solutions

Use the Test for Independence to determine if events A and B are independent. P(A)=0.3, P(B) = 0.4, P(An B) = 0.12 Select the correct choice below and fill in the answer box(es) to complete your

Calculus

Differentiation Solutions

A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t) = 100(1.3)¯t. a) What is the half-life for this substance? Round to 2

Calculus

Differentiation Solutions

Recently, the bowling scores of a certain bowler were normally distributed with mean 202 and standard deviation 19. a) Find the probability that a score is from 185 to 210. b) Find the probability

Calculus

Differentiation Solutions

. Walter drives 7 mph over the speed limit on a suburban street. In the time that Walter drives 4 miles, a car driving the posted speed limit could drive 3 1/3 miles. What is the speed limit and how

Calculus

Differentiation Solutions

Find the first three non-zero terms of the Taylor series about 0 for the func-tion y(x)=√1+2x².sin(3x) by multiplying the Taylor series for √1+ 2x² and the Taylor series for sin (3x).

Calculus

Differentiation Solutions

Find the center, foci, and vertices of the ellipse. Graph the equation. 4x²+36y²-24x+288y +468 = 0