Question

For each problem below, solve the equation for the missing variable. Then, use that equation to find the missing quantity in the situation. Show all steps.
1.) A train travels 616 miles at a speed of 55 miles per hour. Use the equation d equals r t to find the time the train travels.

2.) The equation I equals P invisible times r t gives the amount of interest a bank account receives after a certain period. An individual invests $6,000 into an account that receives 7% interest. How much time has passed if the amount of interest is $3,360?
3.) The area of a triangle is 84 square meters. What is the base if the height is 12 meters?
4.) If the perimeter of a rectangle is 37 inches and the width is 10 inches, what is the length of the rectangle?

5.)
The volume of a right cylinder is found by the formula V equals pi r squared h. Two cylinders both have a height of 10 centimeters. One has a volume of 2009.6 cubic centimeters. The other has a volume of 196.25 cubic centimeters. What is the radius of each cylinder? (Use 3.14 as an approximation of pi.)


Please help me im so confused ive been at this for hours

Answer 1

The time taken for the for the train to arrive is 11.2 hours.

1) We have;

distance (d) = 616 miles

Speed (v) = 55 miles per hour

time (t) = distance/speed = 616 miles/55 miles per hour = 11.2 hours

2) We have;

Interest (I) =  $3,360

Principal (P) = $6,000

Rate (R) = 7%

Time = 100 I/PR

Time = 100 × 3,360/6,000 × 7

Time = 8 years

3) Area (A) = 84 square meters

Height (h) = 12 meters

Base (b) = 2 A/h = 2 × 84/12 = 14 meters

4) Perimeter = 37 inches

width = 10 inches

length = P/2 - w = 37/2 - 10 = 8.5 inches

5) V = πr^2h

For the first cylinder;

V = 2009.6 cubic centimeters

h = 10 centimeters

r = √V/πh

r = √2009.6 /3.14 × 10

r = 8 centimeters

For the second cylinder;

r = √V/πh

r = √196.25/3.14 × 10

r= 2.5 centimeters

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