If the area of a rectangle is 42 what is the perimeter?
1 answer:
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Answer:
1. c. 628 cubic cm
2. c. 502 cubic inches
Step-by-step explanation:
1.) 3.14 x 5^2 x 8
3.14 x 25 x 8 = 628
2.) 3.14 x ( 8/2 )^2 x 10
3.14 x 4^2 x 10
3.14 x 16 x 10 = 502.4
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
<h3>What is Riemann sum?</h3>
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
- x0 = 0
- n = 6
- xn = 3
Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
Learn more about Riemann sum here:
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