March 2020

Problem
A farmer owned a square field measuring exactly 2261 m on each side. 1898 m from one corner and 1009 m from an adjacent corner stands Narra tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the Narra tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. What was the area of the field the neighbor received and how long was the fence? Hint: Use the Cosine Law.

A.   A = 972,325 m2 and L = 2,236 m
B.   A = 950,160 m2 and L = 2,122 m
C.   A = 946,350 m2 and L = 2,495 m
D.   A = 939,120 m2 and L = 2,018 m

 

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Problem
A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume V of the balloon as a function of time t (in seconds). Hint: Use composite function relationship Vsphere = 4/3 πr3 as a function of x (radius), and x (radius) as a function of t (time).

A.   V(t) = 5/2 πt3 C.   V(t) = 9/2 πt3
B.   V(t) = 7/2 πt3 D.   V(t) = 3/2 πt3

 

Problem
Earth is approximately 93,000,000.00 miles from the sun, and the Jupiter is approximately 484,000,900.00 miles from the sun. How long would it take a spaceship traveling at 7,500.00 mph to fly from Earth to Jupiter?

A.   9.0 years C.   6.0 years
B.   5.0 years D.   3.0 years

 

Problem
The formula $v = \sqrt{2gh}$ give the velocity, in feet per second, of an object when it falls h feet accelerated by gravity g, in feet per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 80 feet per second.

A.   80 feet C.   70 feet
B.   100 feet D.   90 feet

 

Problem
In the expansion of (2x - 1/x)10, find the coefficient of the 8th term.

A.   980 C.   960
B.   970 D.   990