Search & Filtering
1Using Lagrange’s Mean value theorem Prove that log10(x + 1) =
x log10e
(1+θx)
Q.2 Show that excosx = 1 + x + (x2
/2) - (x3
/3) - (11x4
/24)
You decide to be on the safe side I only make 150 shirts a local vendor agrees to make them for only seven each you plan to sell them for 50 each what type of function is represented by this story
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.
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.
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 centroid of the area enclosed by y = 1 + sin(x) and y = 1 − sin(x) on
the interval [0, π]
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.
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.
Two hallways, of widths 'a' and 'b', meet at right angles. What is the greatest possible length of a ladder which can be carried horizontally around the corner ?
A right triangle with hypotenuse of length 'a' is rotated about one of its legs to generate a right circular cone. Find the greatest possible volume of such a cone.
