Answer:
x=4
Step-by-step explanation:
We can find the length of RT by using the Pythagorean theorem
sin theta = opposite side/ hypotenuse
sin 60 = 2 sqrt(3)/ RT
Multiply each side by RT
RT sin 60 = 2 sqrt(3)
Divide by sin 60
RT = 2 sqrt(3)/ sin 60
RT = 4
Then
tan theta = opposite side/ adjacent side
tan 45 = x/RT
tan 45 = x/4
4 tan 45 = x
4 = x
1. Add x on both sides of the equation.
2. Subtract 5 from both sides of the equation.
3. Divide both sides of the equation by 3.
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In terms of its radius
, the volume of the balloon is

The diameter
is twice the radius, so that in terms of its diameters, the balloon's volume is given by

Differentiate both sides with respect to time
:

The diameter increases at a rate of
. When the diameter is
, we have

or about 23,562 cc/min (where cc = cubic centimeters)
Check the picture below.
the lateral area, namely the area of the sides, as you see in the picture, is really just the area of 6 rectangles.
front and back, two rectangles of 5x25,
left and right, two rectangles of 2x25.
simply get the area of each and sum them up, that's the lateral area of the prism.