-11/75 is the answer. The first step would be to write the numerators above the lcd and then subtract and rewrite the fraction.
Estimate the volume of the solid that lies below the surface z = xy and above the following rectangle. R = (x, y) | 2 ≤ x ≤ 8, 6
≤ y ≤ 10 (a) Use a Riemann sum with m = 3, n = 2, and take the sample point to be the upper right corner of each square. (b) Use the Midpoint Rule to estimate the volume of the solid.
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Given to points to us are :-
- ( 3 , -6 )
- ( -1 , -8 )
( As these are plotted on graph with yellow dots .)
Now , we can use Distance Formula , which is :-
Here ,
- x1 = 3 .
- x2 = -1.
- y1 = (-6)
- y2 = (-8).
<u>→ Substituting the respective values , </u>
⇒ Distance = √ [ { 3 - (-1)}² + { -6 -(-8)²} ] .
⇒ Distance = √ (3+1)² + (8-6)²
⇒ Distance = √ 4² + 2²
⇒ Distance = √ 16 + 4
⇒ Distance = √20 = √4 × √5
⇒ Distance = 4√5units .
<u>Hence the distance between two points is 4√5u.</u>