Math Answers

7. A helicopter takes off from a point 80 m away from an observer located on the
ground, and rises vertically at 2 m/s. At what rate is elevation angle of the
observer’s line of sight to the helicopter changing when the helicopter is 60 m
above the ground.

8. An oil slick on a lake is surrounded by a floating circular containment boom.
As the boom is pulled in, the circular containment boom. As the boom is
pulled in, the circular containment area shrinks (all the while maintaining the
shape of a circle.) If the boom is pulled in at the rate of 5 m/min, at what
rate is the containment area shrinking when it has a diameter of 100m?

9. Consider a cube of variable size. (The edge length is increasing.) Assume that
the volume of the cube is increasing at the rate of 10 cm3/minute. How fast
is the surface area increasing when the edge length is 8 cm?

4. An airplane flying horizontally at an altitude of y = 3 km and at a speed of
480 km/h passes directly above an observer on the ground. How fast is the
distance D from the observer to the airplane increasing 30 seconds later?

5. A kite is rising vertically at a constant speed of 2 m/s from a location at
ground level which is 8 m away from the person handling the string of the
kite
(a) Let z be the distance from the kite to the person. Find the rate of change
of z with respect to time t when z = 10.
(b) Let x be the angle the string makes with the horizontal. Find the rate
of change of x with respect to time t when the kite is y = 6 m above
ground.

6. A balloon is rising at a constant speed 4m/sec. A boy is cycling along a
straight road at a speed of 8m/sec. When he passes under the balloon, it is
36 metres above him. How fast is the distance between the boy and balloon
increasing 3 seconds later.

1. A ladder 15 ft long rests against a vertical wall. Its top slides down the wall
while its bottom moves away along the level ground at a speed of 2 ft/s. How
fast is the angle between the top of the ladder and the wall changing when the
angle is p/3 radians?

2. A ladder 12 meters long leans against a wall. The foot of the ladder is pulled
away from the wall at the rate 12 m/min. At what rate is the top of the ladder
falling when the foot of the ladder is 4 meters from the wall?

3. A rocket R is launched vertically and its tracked from a radar station S which
is 4 miles away from the launch site at the same height above sea level.
At a certain instant after launch, R is 5 miles away from S and the distance
from R to S is increasing at a rate of 3600 miles per hour. Compute the
vertical speed v of the rocket at this instant.

The expression I = 6t^3 + 2t^2 + 5t - 2 shows the relationship between current and time in seconds. How would you find the electric charge passing between t = 2s and t = 5s.

3.5 – 2.52/f = 0 When f= 5.04

Q. Find an equation of orthogonal trajectory of the curve of each of the following:
(i) x=cy2
(ii) x2+y2=cx
(iii) y=ecx
(iv)xy=c
(v)y2=x2+cx

Q: show that if zn=(an+bn)1/n where 0<a<b, then lim(zn)=b.

Q: If a>0, b>0, show that lim(√((n+a)(n+b))-n)=(a+b)/2

Q: If 0<a<b, determine lim((a^(n+1)+b^(n+1))/(a^n+b^n ))