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 simplified expression of (-11/2x+30)-2(-11/4x-5/2) is 35
<h3>How to simplify the expression?</h3>
The expression is given as:
(-11/2x+30)-2(-11/4x-5/2)
Expand the bracket
-11/2x + 30 + 11/2x + 5
Collect the like terms
11/2x -11/2x + 30 + 5
Evaluate the like terms
35
Hence, the simplified expression of (-11/2x+30)-2(-11/4x-5/2) is 35
Read more about expressions at:
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C. because 2.25 X 3 = 6.75 and 6.75 X 3 is 20.25
1 - 2x < 11
-2x < 10
x < -5
Jack's mistake is that he was supposed to divide by -2 on both sides of the inequality, but he did not do that. By dividing by -2, he will get x < -5.
F(x) = 30.eˣ
We notice that the graph intercept y-axis at 30
in f(x) = 30.eˣ , for x=0, e⁰ =1 and f(x) = 30
In short it's the only function that has a y-intercept = 30 (answer B)
