Evaluate the following integral over the specified region. assume (r comma theta )(r,θ) are polar coordinates. modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper r startfraction da over (16 plus x squared plus y squared )squared endfraction∫∫r da 16+x2+y22; upper r equals startset (r comma theta ): 1 less than or equals r less than or equals 3 comma 0 less than or equals theta less than or equals pi endsetr={(r,θ): 1≤r≤3, 0≤θ≤π} m

Step-by-step explanation:

We have to integrate the function

over the region

Let us convert into polar coordinates

x=cost : y = sint

Then we get dxdy = rdr dt

So we get the integral as

Substitute the limits to get

Answer

=

answer:

125 yards

explanation:

75+50=125. that is my answer

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).