"a kite 100 ft above the ground moves horizontally at a speed of 2 ft/s. at what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out

Step-by-step explanation:

We have in the image a representation of the triangle that is formed by the kite. The data that we have is:

We need to find .

As we can see in the attached image we can write the tangent of theta as:

Then the cot of theta is:

Derivating we have:

Changing we have:

as we can see in the figure attached using this we have:

Finally we just need to find then:

and we know that then:

b) 36

step-by-step explanation:

18 times 2 is 36

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