14&15 The total amount of installations (in megawatts) of solar energy systems i

Question

14&15

The total amount of installations (in megawatts) of solar energy systems in the United States are shown in the table below for various years. Let f(t) be the total amount of installations (in thousands of megawatts) of solar-energy systems in United States in the year that is t years since 2000. A reasonable model is f(t) = 1/6 t^2 - 8/3 t + 11. Use f to estimate in which years the total amount of installations solar-energy systems was 3 thousand megawatts. A rectangular painting (not including the frame) has a width of 10 inches and a length of 12 inches. If the area of the frame (of uniform width) is 104 square inches, what is the width of the frame?

Explanation / Answer

f(t) = t^2/6 - 8t/3 +11

f(t) = 3 (thousand megawatts)

3 = t^2/6 - 8t/3 +11

solve for t : t = 3

So, in year 2003 we have 3 (thousand megawatts)

15) length = 10 inch ; width= 12inch

Let the width of frame be x : So, length of frame = 10 -2x and width = 12 -2x

Total area of painting including frame = 10*12 = 120

area of painting : (10 -2x)(12-2x)

So, area of frame : 120 - (10 -2x)(12-2x) = 104

Now solve for x which gives width

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