Calculus Answers

A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?

2. An ice cube tray filled with tap water is placed in the freezer and the temperature of the water is changing at the rate of -12e^-0.2t degree fahrenheit per hour after t hours. The original temperature of the tap water was 70 degrees.
Questions:
a. Find a formula for the temperature of the water that has been in the freezer for t hours.
b. When will be the ice be ready? (Water freezed at 32 degrees)

A firm has an estimated pension liability of Rs. 1.5 million due 27 years from today. If the firm can invest in a risk-free security with an interest rate of 8 percent, how much must the firm invest today to be able to make the Rs. 1.5 million payment?

1. Exponential and Logarithmic Integration:

1. A flue epidemic hints a college community beginning with five cases on day t=0, the rate of growth of the epidemic (new case per day) is given by the following function r(t) where t is the number of days the epidemic began.
Questions:
a. Find a formula for the total number of cases of flu in the first t days.
b. Use the formula to part (a) to find the total number of cases in the first 20 days.

Exponential and Logarithmic Integration:

1. A flue epidemic hints a college community beginning with five cases on day t=0, the rate of growth of the epidemic (new case per day) is given by the following function r(t) where t is the number of days the epidemic began.
Questions:
a. Find a formula for the total number of cases of flu in the first t days.
b. Use the formula to part (a) to find the total number of cases in the first 20 days.

Differentiate from first principles
F(x)= 1/ 2+√x

If a pizza costs £2.85 (Ex VAT) to produce and is sold to the guest for £8.29 (Ex VAT), what percentage gross profit is made from this dish? (To 1 decimal place)

Find the answer to 1-3x squared

Using first principles