Calculus Answers

At time t=0 a car is moving 6m/s then smoothly accelerate so that the acceleration after t seconds is a a(t)=3t m/s

A farmer plans to fence his rectangular lot to secure his plantation. The lot is bounded at the back by a river; hence, no fence is needed along this side. In the front, the farmer wants to have a 24-ft opening. He surveyed the cost of the fence and noted that the fence along the front costs Php 75 per ft and Php 50 per ft along the sides. His budget for the fence is Php 15,000. 

As an architect, you were asked to prepare a plan for the fence. The plan is expected to present the dimensions of the largest lot that can be fenced given the budget.

Find the domain of the vector function ?

t^5,4log(t-2),3ln(t+1)

A Cannon ball is shot from the ground with velocity 'v' at an angle 'a' , so that it has a vertical

component of velocity 'vsina' and a horizontal Component 'vcosa' . Its distance s(t) above the ground obeys the law s(t) = - 16t² + (vsina)t , while its horizontal velocity remains constantly

'vcosa'

(a) show that the path of the Cannon ball is a parabola ( find the position at each time t

and show that these points lie on parabola)

(b) find the angle 'a' which will maximize the horizontal distance traveled by the Cannon ball

before striking the ground.

A ball is thrown vertically upward from the ground with an initial velocity of 64 ft/sec. If the positive direction of the distance from the starting point is up, the equation of the motion is s =-16t²+64t. Let t seconds be the time that has elapsed since the ball was thrown and s feet be the distance of the ball from the starting point at t seconds.

A. Find the instantaneous velocity of the ball at the end of 1 sec. Is the ball rising or talling at the end of 1 sec?

B. Find the instantaneous velocity of the ball at the end of 3 sec. Is the ball rising or falling at the end of 3 sec?

C. How many seconds does it take the ball to reach its highest point?

D. How high will the ball go?

E. Find the speed of the ball at the end of 1 sec and 3 sec.

F. How many seconds does it take the ball to reach the ground?

G. Find the instantaneous velocity of the ball when it reaches the ground.

A farmer plans to fence his rectangular lot to secure his plantation. The lot is bounded at the back by a river; hence, no fence is needed along this side. In the front, the farmer wants to have a 24-ft opening. He surveyed the cost of the fence and noted that the fence along the front costs Php 75 per ft and Php 50 per ft along the sides. His budget for the fence is Php 15,000. 

As an architect, you were asked to prepare a plan for the fence. The plan is expected to present the 

dimensions of the largest lot that can be fenced given the budget.

z=f(x-y)

A ball is thrown vertically upward from the ground with an initial velocity of 64 ft/sec. If the positive direction of the distance from the starting point is up, the equation of the motion is s =-16t²+64t. Let t seconds be the time that has elapsed since the ball was thrown and s feet be the distance of the ball from the starting point at t seconds.

A. Find the instantaneous velocity of the ball at the end of 1 sec. Is the ball rising or talling at the end of 1 sec?

B. Find the instantaneous velocity of the ball at the end of 3 sec. Is the ball rising or falling at the end of 3 sec?

C. How many seconds does it take the ball to reach its highest point?

D. How high will the ball go?

E. Find the speed of the ball at the end of 1 sec and 3 sec.

F. How many seconds does it take the ball to reach the ground?

G. Find the instantaneous velocity of the ball when it reaches the ground.

A farmer plans to fence his rectangular lot to secure his plantation. The lot is bounded at the back by a river; hence, no fence is needed along this side. In the front, the farmer wants to have a 24-ft opening. He surveyed the cost of the fence and noted that the fence along the front costs Php 75 per ft and Php 50 per ft along the sides. His budget for the fence is Php 15,000. 

As an architect, you were asked to prepare a plan for the fence. The plan is expected to present the 

dimensions of the largest lot that can be fenced given the budget.

An object falls from rest, and s =-16t² where s feet is the distance of the object from the starting point at t seconds, and the positive direction is upward. If a stone is dropped from a building 256 ft high, find

A. the instantaneous velocity of the tone 1 sec after it is dropped;

B. the instantaneous velocity of the stone 2 sec after it is dropped;

C. how long it takes the stone to reach the ground;

D. the instantaneous velocity ot the stone when it reaches the ground.