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