Calculus AB
- Correct Answers >
∫-24tan²(2θ)sec²(2θ)dθ - Correct Answers >
∫(0→3)(x³-6x²+9x)dx - Correct Answers >-6.75
∫(5→1)(-2x²+12x-10)dx - Correct Answers >64/3
∫(13→10)1/√(y-9)dy - Correct Answers >
∫(a→0)(x(1+x²)³)dx - Correct Answers >1/8(1+a²)-1/8
A 13 ft. ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft. from the house, the base is moving at the rate of 5 ft/sec. a. How fast is the top of the ladder sliding down the wall
b. At what rate is the area of the triangle formed by the ladder, wall, and grou nd changing at that moment?
c. At what rate is the angle θ between the ladder and the ground changing at that moment. - Correct Answers >a. dy/dt= -12ft/sec
b. dA/dt= -59.5 ft²/sec
c. dθ/dh= -1 radian/sec
A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. At the instant when the balloon is 65 feet above the ground, a bicycle is moving at a constant rate of 17 ft/sec passes directly under it. How fast is the distance between the bicycle and balloon increasing 3 seconds later? - Correct Answers >dh/dt= 11ft/sec
A blimp is flying horizontally at an altitude of 1500 feet and a speed of 80 ft/sec when is passes over New Trier High School. Find the rate which the distance from the blimp to the school is increasing 5 seconds after it passes the school - Correct Answers >?
A boat is being pulled toward a dock by means of a rope attached to the front tip of the bow. Initially there are 30 ft. of rope out and the rope is taught and being reeled in by a circular device by the top of which is 10 feet and higher than the point where the rope is attached to the board. This circular device has a radius of 1 ft. and turns at the rate of one revolution every pi seconds. How fast is the boat moving along the water when there are 15 ft of rope out? - Correct Answers >...
A camera is positioned 4600 feet from the base of a rocket launching pad. The angle of elevation
of the camera has to change at the correct rate to keep the rocket in its sight. The rocket rises vertically at a speed of 680ft/sec. How fast is the camera angle changing 4 seconds after the rocket takes off? - Correct Answers >.110 radians per sec
A circle is inscribed in a square. the circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square also expands to maintain the condition of tangency. -Find the rate at which the perimeter is increasing.
-At the instant where the area of the circle is 25 π square inches, find the rate of increase in the area enclosed between the circle and the square. - Correct Answers >...
A company manufactures cylindrical barrels to store nuclear waste. If each barrel is to hold 5 cubic feet of waste, find the dimensions of the barrel that will minimize the surface area. - Correct Answers >r= 0.927ft.
h= 1.853 ft.
A farmer has 400 feet of fencing to make a rectangular pen for his animals. He wants to three pens of equal size to keep his pigs, sheep, and cows separated from each other. What is the largest total area that the farmer can enclose with the fencing to give the animal maximum space? - Correct Answers >a= 5,000ft²
w= 50
l= 33.33
A man 6 feet tall walks at the rate 5 ft/sec toward a streetlight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10 feet from the base of the light. - Correct Answers >...
A man in a boat at a location in the water 5 miles from the nearest point A, on a straight beach wishes to reach a hut 5 miles along the shore from point A in the shortest possible time. If he can
rose at a rate of 6 miles per hour, where should he land? - Correct Answers >...
A particle moves along a line so that its velocity at time t is v(t)=2t-5, measured in feet per second. a. Find the displacement of the particle during the time period 2≤t≤6
b. Find the distance traveled during this time period. - Correct Answers >
A particle moves along the x axis, s(t)=2/3t³+7/2t²-4t+6
a. What is an equation for the velocity?
b. What time will the object stop and change direction?
c. Where is the particle at t=5?
d. What is the displacement of the particle from t=0 to t=5
e. What is the total distance traveled? - Correct Answers >a. v(t)=2t²+7t-4
b. at -4 and ½
c. 156.83m
d. 150.833m
e. 152.917m
A particle moves at s(t)=t³-12t²+36t, t≥0. a. Find the velocity of particle at time t. What is the velocity at t=1.
b. Find the acceleration of the particle at time t. What is the acceleration at t=1.
c. Graph the position, acceleration and velocity from t=0-8.
d. What is the displacement after 8 sec.
e. When is the particle moving left?
f. When is it at rest?
g. When is the velocity increasing?
h. When is the speed increasing?
i. What is the total distance traveled? - Correct Answers >a. 15m/s
b. t=4
- Correct Answers >
∫-24tan²(2θ)sec²(2θ)dθ - Correct Answers >
∫(0→3)(x³-6x²+9x)dx - Correct Answers >-6.75
∫(5→1)(-2x²+12x-10)dx - Correct Answers >64/3
∫(13→10)1/√(y-9)dy - Correct Answers >
∫(a→0)(x(1+x²)³)dx - Correct Answers >1/8(1+a²)-1/8
A 13 ft. ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft. from the house, the base is moving at the rate of 5 ft/sec. a. How fast is the top of the ladder sliding down the wall
b. At what rate is the area of the triangle formed by the ladder, wall, and grou nd changing at that moment?
c. At what rate is the angle θ between the ladder and the ground changing at that moment. - Correct Answers >a. dy/dt= -12ft/sec
b. dA/dt= -59.5 ft²/sec
c. dθ/dh= -1 radian/sec
A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. At the instant when the balloon is 65 feet above the ground, a bicycle is moving at a constant rate of 17 ft/sec passes directly under it. How fast is the distance between the bicycle and balloon increasing 3 seconds later? - Correct Answers >dh/dt= 11ft/sec
A blimp is flying horizontally at an altitude of 1500 feet and a speed of 80 ft/sec when is passes over New Trier High School. Find the rate which the distance from the blimp to the school is increasing 5 seconds after it passes the school - Correct Answers >?
A boat is being pulled toward a dock by means of a rope attached to the front tip of the bow. Initially there are 30 ft. of rope out and the rope is taught and being reeled in by a circular device by the top of which is 10 feet and higher than the point where the rope is attached to the board. This circular device has a radius of 1 ft. and turns at the rate of one revolution every pi seconds. How fast is the boat moving along the water when there are 15 ft of rope out? - Correct Answers >...
A camera is positioned 4600 feet from the base of a rocket launching pad. The angle of elevation
of the camera has to change at the correct rate to keep the rocket in its sight. The rocket rises vertically at a speed of 680ft/sec. How fast is the camera angle changing 4 seconds after the rocket takes off? - Correct Answers >.110 radians per sec
A circle is inscribed in a square. the circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square also expands to maintain the condition of tangency. -Find the rate at which the perimeter is increasing.
-At the instant where the area of the circle is 25 π square inches, find the rate of increase in the area enclosed between the circle and the square. - Correct Answers >...
A company manufactures cylindrical barrels to store nuclear waste. If each barrel is to hold 5 cubic feet of waste, find the dimensions of the barrel that will minimize the surface area. - Correct Answers >r= 0.927ft.
h= 1.853 ft.
A farmer has 400 feet of fencing to make a rectangular pen for his animals. He wants to three pens of equal size to keep his pigs, sheep, and cows separated from each other. What is the largest total area that the farmer can enclose with the fencing to give the animal maximum space? - Correct Answers >a= 5,000ft²
w= 50
l= 33.33
A man 6 feet tall walks at the rate 5 ft/sec toward a streetlight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10 feet from the base of the light. - Correct Answers >...
A man in a boat at a location in the water 5 miles from the nearest point A, on a straight beach wishes to reach a hut 5 miles along the shore from point A in the shortest possible time. If he can
rose at a rate of 6 miles per hour, where should he land? - Correct Answers >...
A particle moves along a line so that its velocity at time t is v(t)=2t-5, measured in feet per second. a. Find the displacement of the particle during the time period 2≤t≤6
b. Find the distance traveled during this time period. - Correct Answers >
A particle moves along the x axis, s(t)=2/3t³+7/2t²-4t+6
a. What is an equation for the velocity?
b. What time will the object stop and change direction?
c. Where is the particle at t=5?
d. What is the displacement of the particle from t=0 to t=5
e. What is the total distance traveled? - Correct Answers >a. v(t)=2t²+7t-4
b. at -4 and ½
c. 156.83m
d. 150.833m
e. 152.917m
A particle moves at s(t)=t³-12t²+36t, t≥0. a. Find the velocity of particle at time t. What is the velocity at t=1.
b. Find the acceleration of the particle at time t. What is the acceleration at t=1.
c. Graph the position, acceleration and velocity from t=0-8.
d. What is the displacement after 8 sec.
e. When is the particle moving left?
f. When is it at rest?
g. When is the velocity increasing?
h. When is the speed increasing?
i. What is the total distance traveled? - Correct Answers >a. 15m/s
b. t=4
