This table displays the height of a balloon as it floats away.
2 answers:
Answer:
The height increases by 9.5 ft as the time increases by 1 minute.
Step-by-step explanation:
We have been given a table that displays the height of a balloon as it floats away. We are asked to find the rate of change for the height as the time increases by 1 minute.
Rate of the change for the height of balloon with each minute will be equal to slope of line.
Substitute coordinates of points (10,64) and (14,102) in slope formula.
Therefore, the rate of change is 9.5 feet per minute.
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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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