I need help for these questions please
1 answer:
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Answer:
(a) 120 square units, underestimate
(b) 248 square units, overestimate
Step-by-step explanation:
(a) <u>left sum</u>
The left sum is the sum of the areas of the rectangles whose width is the total interval width (8-0) divided by the number of divisions (n=4). The height of each rectangle is the function value at its left edge.
We can compute the sum by adding the function values and multiplying that total by the width of the rectangles:
left sum = (1 + 5 + 17 + 37)×2 = 60×2 = 120 . . . square units
The curve is increasing throughout the interval of interest, so the left sum underestimates the area under the curve.
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(b) <u>right sum</u>
The rectangles whose area is the right sum are shown in the attachment, along with the table of function values. The right sum is computed the same way as the left sum, but using the function value on the right side of each subinterval.
right sum = (5 + 17 + 37 + 65)×2 = 124×2 = 248 . . . square units
The curve is increasing throughout the interval of interest, so the right sum overestimates the area under the curve.
_____
The actual area under the curve on the interval [0, 8] is 178 2/3, just slightly less than the average of the left- and right- sums.
Answer:
Equation to determine crystals total bill (T) =(7.7+2x) - 1.50
Step-by-step explanation:
Given:
Number of bottles of pop purchased = 4
Number of candy bars purchased = 3
Number of chips bag purchased = 2
Cost of per bottle of pop = $1.25
Cost of per candy bar = $.90
Cost of the coupon = $1.50
To Find :
Equation to determine crystals total bill (T) given the cost of one bag of chips = ?
Solution:
Let the cost of one chips bag be x
Cost of 4 bottles of pop
=>
=>$ 5
Cost of 3 candy bars
=>
=>$ 2.7
Cost of 2 bags of chips
=>
=>$ 2x
Now the total cost of the bill is
T = 5 + 2.7+ 2x
T =7.7+2x
Also Krystal had a coupon worth $1.50, the cost of the ticket will be
T =(7.7+2x) - 1.50