Problems:
Solutions For Five Problems of Mixed Type
Trigonometry/Algebra
1) An open-top box with a square base is to be constructed from 150 square centimeters of material.
What dimensions will produce a box with largest possible volume?
A) 6.639 cm x 6.639 cm x 18.075 cm
B) 6.639 cm x 6.639 cm x 18.075 cm
C) 5.946 cm x 5.946 cm x 20.182 cm
D) 7.725 cm x 7.725 cm x 15.534 cm
E) 6.146 cm x 6.146 cm x 19.525 cm
2) Assume h 0. Compute and simplify the difference quotient for f(x) = 1 / x.
f(x + h) - f(x)/h
3) Solve the inequality.
3x2 + 8x - 3/x2 - 4x + 4 > 0
A) x∈(-∞, -3] U [1/3,4) U (4,∞)
B) x∈(-∞, -2] U [1/3,2) U (2,∞)
C) x∈(-∞, -3] U [1/4,2) U (2,∞)
D) x∈(-∞, -3] U [1/3,2) U (2,∞)
E) x∈(-∞, -2] U [1/3,2) U (4,∞)
4) Solve the equation without using logarithms.
72X2+3X = 496-X
x=_________ Large x-Value
x=__________ Smaller x-Value
5) Solve the equation.
log(3x + 1) = log(x + 1) + log(2)
x=________