A banner in the shape of an isosceles triangle is hung over the side of a building. The banner has a base of 30ft (at the roof), a height of 20ft, and weighs 50lb. Write down an integral for the work required to lift the banner entirely onto the roof of the building.

W = 9600000 joules

Step-by-step explanation:

From the given information:

The area of the banner = 1/2 × 30 × 20 = 300 ft²

The mass of the banner = 300 × 50 = 15000 pounds

Now; the integral for the required work is:

here;

h = height of the building

F = mg = 15000g

g = 32 ft/s²

Therefore;

W = 9600000 joules

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere