The surface are of a cylinder is given by the formula sa=2pir^2+2pirh, where r is the radius of the base of the cylinder and h is the height of the cylinder. solve the formula for h in the space given below. show all the steps.

h = (x-2πr²)/2πr

Step-by-step explanation:

Given the surfaces area of a cylinder by the formula

SA = 2πr²+2πrh

To solve for h means making h the subject of the formula from the equation.

Let x be the surface area of the cylinder. The formula can be rewritten as;

x = 2πr²+2πrh

Subtracting 2πr² from both sides of the equation will give;

x-2πr² = 2πr²+2πrh-2πr²

x-2πr²= 2πrh

Dividing both sides by 2πr wikk results into;

(x-2πr²)/2πr = 2πrh/2πr

h = (x-2πr²)/2πr where x is the surface area of the cylinder.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.