Answer:
b. A year and a half
Step-by-step explanation:
First, we can find the total cost
Next, we can divide by 50 in order to find out how many months it will take for the panel to pay for itself.
months
This is very close to 36 months, which is <u>A year and a half</u>.
Finite approximation method of estimating the area under the curve of the
given function makes use of rectangular approximation of the area.
The correct responses are;
i) The estimated area using a lower sum with two rectangles of equal width is <u>1,715 square units</u>.
ii) The estimated area using a lower sum with four rectangles of equal width is <u>3,001.25 square units</u>.
iii) The estimated area using an upper sum with two rectangles of equal width is<u> 8,575 square units</u>.
iv) The estimated area using a upper sum with four rectangles of equal width is <u>6,431.25 square units</u>.
Reasons:
The given function is f(x) = 5·x²
The given domain is x₀ to x₁₄
i) Estimate using lower sum with two rectangles of equal width;
f(0) = 0
f(7) = 5 × 7² = 245
A = 0 × 7 + 245 × 7 = 1,715
The estimated area using a lower sum with two rectangles of equal width
is <u>1,715 square units</u>.
ii) Estimate using lower sum with four rectangles of equal width;
f(0) = 0
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
A = 0 × 3.5 + 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 = 3,001.25
The estimated area using a lower sum with four rectangles of equal width is <u>3,001.25 square units</u>.
iii) Estimate using an upper sum with two rectangles of equal width;
f(7) = 5 × 7² = 245
f(14) = 5 × 14² = 980
A = 245 × 7 + 980 × 7 = 8575
The estimated area using an upper sum with two rectangles of equal width
is <u>8,575 square units</u>.
iv) Estimate using an upper sum with four rectangles of equal width;
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
f(14) = 5 × 14² = 980
A = 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 + 980 × 3.5 = 6,431.25
The estimated area using a upper sum with four rectangles of equal width
is <u>6,431.25 square units</u>.
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