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Answer:
(a) 120 square units (underestimate)
(b) 248 square units
Step-by-step explanation:
<u>(a) left sum</u>
See the attachment for a diagram of the areas being summed (in orange). This is the sum of the first 4 table values for f(x), each multiplied by 2 (the width of the rectangle). Quite clearly, the curve is above the rectangle for the entire interval, so the rectangle area underestimates the area under the curve.
left sum = 2(1 + 5 + 17 + 37) = 2(60) = 120 . . . . square units
<u>(b) right sum</u>
The right sum is the sum of the last 4 table values for f(x), each multiplied by 2 (the width of the rectangle). This sum is ...
right sum = 2(5 +17 + 37 +65) = 2(124) = 248 . . . . square units
The values are and
Explanation:
From the figure, we can see that the two quadrilaterals are similar.
Thus, by the property of quadrilateral, for similar quadrilaterals, their corresponding angles and sides are congruent. Thus, we have,
∠D = ∠S, ∠E = ∠P, ∠G = ∠R and ∠F = ∠Q
Also, GF = QR and DE = PS
Where QR = and ∠D = 102°, ∠G = 84° and ∠F = 68°, ∠Q =
°
Hence, to determine the value of x for the side QR, we have,
Equating the values in GF = QR,we get,
Thus, the value of x is 8.
Substituting x in the angle Q to determine the value of y.
Thus, we have,
∠F = ∠Q
Thus, the value of y is 10.
Hence, The values are and