University:
Augusta University
Course:
MATH 4800 | Secondary Mathematics from an Advanced Perspective
Academic year:

2024
Views:

165

Pages:

2
Author:

Autumn Cox

Question 1 min The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm long. At what rate are the edges changing at that instant? Answer The volume of a cube with edge length e is given by: V = e³ Differentiate with respect to t: dV/dt = 3e²(de/dt) Substitute dV/dt = 1200 cm³/min and e = 20 cm then solve for de/dt: 1200 = 3(20)²(de/dt) 1200 = 1200(de/dt) 1 = de/dt or de/dt = 1 cm/min Question 2 A certain television is advertised as a 50-inch TV(the diagonal length). If the width of the TV is 14 inches, how many inches tall is the TV? Answer Let l be the length of the TV, in inches. Since the diagonal of the TV forms a right triangle with the length and width (legs), the Pythagorean Theorem can then be used to determine l: l² + 14² = 50² l² + 196 = 2500 l² = 2304 l = √2304 l = 48 Consequently, the TV is 48 inches long. Question 3 A kite in the shape of a rhombus has diagonals that are 25 inches long and 15 inches long. What is the area of the kite? Answer The area of a rhombus or kite with diagonals d1 and d2 is given by: A = (1/2)d₁d₂ Substitute d₁ = 25 inches and d₂ = 15 inches: A = (1/2) (25)(15) A = (1/2)(375) A = 187.5 in² Question 4 Suppose, a policeman orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel? Answer V = lwh V = (20)(6)(6) V = 720 cubic inches Since 1ft = 12in., then (1ft)³ = (12in.)³ or 1ft³ = 1728in³ so: V = 720 cubic inches x (1 cubic foot/1728 cubic inches) = 5/12 cubic foot (54 pounds/cubic foot) x (5/12) cubic foot = 22.5 pounds Question 5 Three rectangle triangles are giving: Suggest that hypotenus is c, leg 1 is a and leg 2 is b. A. a = 5√2 c=10 b=? B. a = b = 2√2 c=? C. c = 6√2 a=6 b=? Answer Pythagorean Theorem: a² + b² = c² A. (5√2)² + b² = 10² 50 + b² = 100 b² = 100 - 50 b² = 50 b = √50 b = 5√2 B. c² = (2√2)² + (2√2)² c² = 8 + 8 c² = 16 c = √16 = 4 C. 6² + b² = (6√2)² 36 + b² = 72 b² = 72 - 36 b² = 36 b = √36 b = 6