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Find the dimensions of the right circular cone of least volume which can be
circumscribed about a right circular cylinder of radius 4 cm and height of 5 cm.
For every function f(x) that is smoothly continuous on (a,b], the average rate of change of f(x) from x = a to x = b, approaches the instantaneous rate of change at x = a as x approaches a from the left.
Please explain this with a graph
A ball is dropped from a height of 126.8 meters. Its height above ground (in meters) t seconds later is given by: s(t)=−17t^2 +126.8
What is the instantaneous velocity of the ball when it strikes the ground?
a) Determine the Laplace transforms of the following functions
(i) f(t) = t3-2t
(ii) f(t) = sin3t-e2t
(iii) f(t) = e2t sinh4t
b) Find the Laplace transform of the following
(i) f(t) = 3e-4t- 5e4t
(ii) f(t) = t sin 3t + cos 4t
find the inverse transform of
(i) F (s) = 2/3-1/2s-3
(ii) F (s) = 5s-8/s(s-4), using partial fractions.
Interior and exterior walls of a rectangular 80,000 square foot building cost 90$ per running foot. The building is to be divided into 10 rooms by four interior walls in the x direction and one interior wall in the y direction. What should be the building dimensions if the wall cost is to be minimum.
Derive a formula for Summation n i=1 i3 by using a telescoping sum with terms f(i)=i2
They want to introduce 400ml and one liter tin packs for
the promotion of their brand. For making these tin packs the cost of the top and bottom of a tin is 5/3
times the cost of the body/cylinder. The company assign you to suggest the dimensions of the required
tin packs which also minimize the cost of production of the tin packs. Moreover, check whether there
are more options or is only one option to construct the required tin packs to get optimize solution.
Furthermore, the total budget for this new brand was assigned only $1 million. Therefore, also find how
many tin packs of two sizes must be prepared to get the maximum profit if there is profit on each tin of
400ml is one dollar and $3 for each tin pack of one liter.
A tent of a given volume has a square base of side 2a, has its four sides vertical of height b and is surmounted by a regular pyramid of height 1. find the values of a and b in terms of height I such that the canvas required for its construction is minimum.
Find critical points of f (x,y) = 1/4x^2 -4xy^2 - 2x^2 +8y^2
Use taylors formula to find quadratic and cubic approximations of f(x, y) =exsin y at origin. Estimate the error of the approximations if modx less than equal to 0.1 and mod y less than equal to 0.1
