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Math B Regents Exam Questions by Type - 4 Point Free Response Page 15
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85. An architect is using a computer program to
design the entrance of a railroad tunnel. The
outline of the opening is modeled by the
function f( x) = 8sin x+
2 , in the interval
0 ≤ x ≤π, where x is expressed in radians.
Solve algebraically for all values of x in the
interval 0 ≤ x ≤π, where the height of the
opening, f(x), is 6. Express your answer in
terms of π .
If the x-axis represents the base of the tunnel,
what is the maximum height of the entrance
of the tunnel?
88. The current population of Little Pond, New
York, is 20,000. The population is
decreasing, as represented by the formula
− . t
P = A(.) 13 0234 , where P = final population, t
= time, in years, and A = initial population.
What will the population be 3 years from
now? Round your answer to the nearest
hundred people.
To the nearest tenth of a year, how many
years will it take for the population to reach
half the present population? [The use of the
grid is optional.]
86. Point P lies outside circle O, which has a
diameter of AOC . The angle formed by
tangent PA and secant PBC measures 30°.
Sketch the conditions given above and find
the number of degrees in the measure of
minor arc CB.
87. Depreciation (the decline in cash value) on a
car can be determined by the formula
V = C( 1 −r)
t , where V is the value of the car
after t years, C is the original cost, and r is the
rate of depreciation. If a car's cost, when
new, is $15,000, the rate of depreciation is
30%, and the value of the car now is $3,000,
how old is the car to the nearest tenth of a
year?
89. Tim Parker, a star baseball player, hits one
home run for every ten times he is at bat. If
Parker goes to bat five times during tonight's
game, what is the probability that he will hit
at least four home runs?
90. Navigators aboard ships and airplanes use
nautical miles to measure distance. The
length of a nautical mile varies with latitude.
The length of a nautical mile, L, in feet, on
the latitude line θ is given by the formula
L = 6, 077 −31cos 2θ.
Find, to the nearest degree, the angle
θ, 0≤θ
≤ 90° , at which the length of a
nautical mile is approximately 6,076 feet.