Substitution & Evaluation Homework
#1. The formula for the perimeter of a rectangle is P = 2W + 2L.
If the width is 12 cm and the length is 3.5 cm, what is the perimeter of the rectangle?
#2. To find the number of diagonals in a polygon (d) based on the number of sides (n) we use the formula
d = 0.5n(n - 3).
If a polygon has 6 sides, how many diagonals does it have?
#3. The area of a trapezoid (A) is found using the formula
A = 0.5a(b + B),
where a is the length of the altitude, b is the shorter base, and B is the longer base.
If the altitude measures 5mm, and the two bases measure 9 mm and 7 mm, what is the area of the trapezoid?
#4. The distance in feet (d) that a free-falling object travels in time (t) seconds is calculated using
d = 16t2
What is the distance travelled if an object falls for 15 seconds?
#5. The approximate weight (w) of an ice cube measured in pounds with an edge (e) in inches:
w = 0.033e3
If an ice cube has an edge of 12 inches, what is its approximate weight?
#6. An engine's horsepower rating (h) depends on the number of cylinders (c) and their diameter (d) in inches:
h = 0.4cd2
If your car has a 4 cylinder engine of diameter 3.5 inches, what is its horsepower rating?
#7. The stopping distance (d) in feet of a car on dry pavement when travelling at a speed (s) in miles per hour:
d = 1.1s + 0.05s2
If you are travelling at 50 miles per hour, what will your stopping distance be?
Answers (show your work!):
#1. 31 cm #2. 9 diagonals #3. 40 mm2 #4. 3600 feet #5. 57.02 pounds #6. 19.6 horsepower #7. 180 feet
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