WEEK 2 PART 2 Flashcards
(100 cards)
The center of the hyperbola 16y2 – 9x2 – 64y – 80 = 0.
A. (2, 0)
C. (0, -2)
B. (0, 2)
D. (-2, 0)
B. (0, 2)
The center of the ellipse 9x2 + 16y2 – 36x – 32y – 92 = 0 is at:
A. (2, 1)
C. (-1, -2)
B. (-2, -1)
A. (2, 1)
The vertex of the parabola x2 - 4x - 8y - 28 = 0 is at:
A. (2, 4)
B. (2, -4)
C. (4, 2)
D. (-4, 2)
B. (2, -4)
The slope of the line whose equation is given by x + 3y – 6 = 0 is:
A. 3
C. 1/3
B. 1
D. -1/3
D. -1/3
Find the area of the region bounded by the curve y = 3x – x2, the x-axis and the vertical lines x = 0 and x = 3:
A. 27/6 sq units
C. 5/6 sq units
D. 9/2 sq units
D. 9/2 sq units
The cost of annual production of an agricultural feed is given by C(x) = 5000 + 80000000/x + x/20, where x is
the average batch size per production run. The value of x which makes the production cost a minimum is:
A. 30,000
B. 40,000
C. 45,000
C. 45,000
D. 30,000
B. 40,000
Find the area of the region bounded by the graphs of y = x2 – 2 and y = x.
A. 31/6 sq units
B. 9/2 sq units
C. 5/6 sq units
D. 5 sq un
B. 9/2 sq units
The value of the definite integral ∫ 𝑥(3 − 𝑥)𝑑𝑥
3
1
A. 10/3
B. 17/3
C. 27/6
D. 5/6
A. 10/3
A product manufactured by a company is sold in bulk at a price of 200 pesos per unit. If the total production cost
in pesos for x units is C(x) = 500000 + 80x + 0.003x2 and if the production capacity of the firm is at most 30,000
units in a specified time, how many units of the product must be manufactured and sold in that time to maximize
the profit?
A. 30,000
B. 25,000
C. 20,000
D. 15,000
C. 20,000
A conservationist is stocking a lake with fish. The more fish he puts in, the more competition there will be for
available food supply, and the fish will gain weight more slowly. It is known from a previous study that if there
are n fish per unit volume of water, the average weight that each fish gains in a season is given by w = 600 – 30n.
What value of n will give the maximum total weight of fish in the lake?
A. 10
C. 20
B. 15
D. 25
A. 10
Dmax = a/2b
= 600/2(30)
= 10
At what rate was the number of live spores decreasing 5 minutes after the treatment was completed?
A. 47 spores/min
C. 49 spores/min
B. 48 spores/ min
D. 50spores/min
A. 47 spores/min
An open box is to be made from a 16-inch by 30-inch piece of cardboard cutting out squares of equal size from
the four corners and bending up the sides. What should be the length of the side of the squares to be cut to obtain
a box with largest possible volume?
A. 10/3 inches
B. 5 inches
C. 6 inches
D. 3 inche
D. 3 inche
A farmer has 4km of fencing wire and wishes to enclose a rectangular piece of land through which flows a straight
river which is to be utilized as one side of the enclosure. What is the length of the rectangular area that would to
enclose as much land as possible?
A. 1 km
B. 1.5km
C. 2 km
D. 2.5km
C. 2 km
The radius of a balloon is increasing at the rate of 2 cm/sec. How fast is the volume of the balloon increasing
when its radius is 2cm?
A. 800π cm2/s
C. 800π cm3/s
B. 400π cm2/s
D. 800π cm/s
C. 800π cm3/s
. A cylindrical water tank of radius 10 feet is being drained at the rate of 200 ft3/min. How fast is the height of the
water in the tank changing?
A. 2/π ft/min
C. -2π ft/min
B. -2/π ft/min
D. 2π ft/min
B. -2/π ft/min
A boat is being pulled into a dock by a rope that passes through a ring on the bow of the boat. The dock is 8 feet
higher than the bow ring. If the boat is being pulled in at the rate of 3 ft/sec, how fast is the boat approaching the
dock when the length of the rope from the boat to the bow ring is 10 feet?
A. 2 ft/sec
C. 4 ft/sec
B. – 3 ft/sec
D. 5 ft/sec
D. 5 ft/sec
When a circular plate made of metal is heated in an oven, its radius increases at the rate of 0.01 cm/min. At what
rate is the plate’s area increasing when the radius is 50 cm?
A. π cm/min
B. π cm2/min
C. 2π cm/min
D. 2π cm2/min
B. π cm2/min
. A foodstuff is susceptible to contamination from bacterial spores. In order to kill the spores, the food was
subjected to a temperature of 120 degrees Centigrade. The number N of spores still alive t minutes after the high
temperature treatment has been completed is given by N = 1200e-0.5t
18. How many live spores were there when t = 0?
A. 0
C. 1000
D. 12
D. 1200
What percentage of the original spores were still alive when t = 5?
A. 8%
B. 9%
C. 10%
D. 11%
A. 8%.
Find the time required to kill 50% of the spores.
A. 1.386 min
B. 1.387 mi
C. 1.388 min
C. 1.388 min
D. 1.389 min
A. 1.386 min
0.50x1200 = 1200e^-0.5(t)
t = 1.386 min
At what rate was the number of live spores decreasing 5 minutes after the treatment was completed?
A. 47 spores/min
C. 49 spores/min
B. 48 spores/ min
D. 50spores/min
C. 49 spores/min
A rope is tied to the top of a flagpole. When it hangs straight down, it is 2 meters longer than the pole. When the
rope is pulled tight with the lower end at the ground, it makes an angle of 60 degrees to the horizontal. How tall
is the flagpole?
A. 12.6 m
B. 12.7 m
C. 12.8 m
D. 12.9 m
D. 12.9 m
The velocity of a moving object is given by the function v(x) = 3x, where x is in hours and v is in miles per hour.
What is the distance the object has traveled during the first 3 hours (0 ≤ x ≤ 3)?
A. 42 miles
B. 15.3 miles
C. 24 miles
D. 13.5 miles
D. 13.5 miles
3
∫0 3x
= 13.5 miles
A landmark A is observed from two points B and C, which are 400 meters apart. The magnitude of angle ABC is
measured as 68 degrees and the magnitude of angle ACB as 70 degrees. Find the distance from A to C.
A. 554 m
B. 555 m
C. 556 m
D. 557 m
A. 554 m