MA 3972-MA-Book April 11, 2018 14:46190 STEP 4. Review the Knowledge You Need to Score High
- Find a number in the interval (0, 2) such
that the sum of the number and its
reciprocal is the absolute minimum. - An open box is to be made using a piece of
cardboard 8 cm by 15 cm by cutting a
square from each corner and folding the
sides up. Find the length of a side of the
square being cut so that the box will have a
maximum volume. - What is the shortest distance between the
point(
2,−1
2
)
and the parabolay=−x^2?- If the cost function isC(x)= 3 x^2 +
5 x+12, find the value ofxsuch that the
average cost is a minimum. - A man with 200 meters of fence plans to
enclose a rectangular piece of land using a
river on one side and a fence on the other
three sides. Find the maximum area that the
man can obtain.
Part B Calculators are allowed.- A trough is 10 meters long and 4 meters
wide. (See Figure 9.4-2.) The two sides of
the trough are equilateral triangles. Water is
pumped into the trough at 1 m^3 /min. How
fast is the water level rising when the water
is 2 meters high?
4 m10 mFigure 9.4-2- A rocket is sent vertically up in the air with
the position functions= 100 t^2 wheresis
measured in meters andtin seconds. A
camera 3000 m away is recording the
rocket. Find the rate of change of the angle
of elevation of the camera 5 sec after the
rocket went up. - A plane lifts off from a runway at an angle
of 20◦. If the speed of the plane is 300 mph,
how fast is the plane gaining altitude? - Two water containers are being used. (See
Figure 9.4-3.)
10 ft4 ft6 ft8 ftFigure 9.4-3One container is in the form of an inverted
right circular cone with a height of 10 feet
and a radius at the base of 4 feet. The other
container is a right circular cylinder with a
radius of 6 feet and a height of 8 feet. If
water is being drained from the conical