test 4 math

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) g(t) = 7 + t + t2/ sqrt(t)

14t^{1/2}+2/3t^3/2+2/5t^5/2+C

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 8x + 2 sec x tan x

16/3x^{\left(\frac{3}{2}\right)}+2\sec \left(x\right)+C

If 1,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

4000

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 5/2sqrt(x)+ 2 sec^2 x

5\sqrt{x}+2tan(x) +C

Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 6 cm if two sides of the rectangle lie along the legs.

6

max vertical distance between y=10x+39 nad y=x^for -3<x<13

64

max vertical distance between y=2x+63 and y=x^2 for -7<x<9

64

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 9sqrt(x)+ 3 cos x

6x^3/2+3sin x+C

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $5 per square meter. Material for the sides costs $3 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

81.77

A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used.

sides of base: 50 height:25

Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. y = 6 − x^2

width: 2\sqrt{2} height:4

A poster is to have an area of 180 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exact dimensions that will give the largest printed area.

width: sqrt{120} Height: 180\sqrt{120}}

Find the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant.

y=10-5x/2