Answer:
Step-by-step explanation:
Table
<h3>x I y</h3><h3>-------</h3><h3>1 I 2</h3><h3>2 I 4</h3><h3>3 I 6</h3><h3>4 I 8</h3><h3>5 I 10</h3>
The area of the region shown in the coordinate plane is 2.7823 units square.
<h3>What is integration?</h3>
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
The graph of a function:
y = sinx
And a line segment passed through:
(0, 0) and (7π/6, -1/2)
First, find the equation of the line:
y = (-1/2)/(7π/6)[x]
y = (-3/7π)x
The area by definite integration:
After solving the above definite integral:
Area = 2.7823 units square
Thus, the area of the region shown in the coordinate plane is 2.7823 units square.
Learn more about integration here:
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Given:
1 pack = 5 pencils and cardboard.
1 pack must be between 60 grams and 95 grams
60g < x < 95g ; where x represents 1 pack.
Card board: 15 grams.
95g - 15g = 80g maximum total weight of 5 pencils
80g / 5 = 16g maximum weight of a single pencil
60g - 15g = 45g minimum total weight of 5 pencils
45g / 5 =9g minimum weight of a single pencil
9 < x < 16 ; where x represents a single pencil in the pack.
Answer: length of the drive way = 56 feet
Width of the driveway = 12 feet
Step-by-step explanation:
The rectangular driveway has two equal lengths and two equal widths. The area of the driveway is expressed as
length,l × width,w
The area is 672 feet squared. It means that
L×W = 672
The length of the rectangular driveway is four feet less than five times the width. It means that
L = 5W - 4
Substituting L = 5W - 4 into LW = 672
W(5W - 4) = 672
5W^2 - 4W - 672 = 0
5W^2 + 56W - 60W - 672 = 0
W(5W + 56) - 12(5W + 56) = 0
(W - 12)(5W + 56) = 0
W - 12 = 0 or 5W + 56 = 0
W = 12 or 5W = -56
W= 12 or W = - 56/5
The Width cannot be negative , so
W = 12
LW = 672
12L = 672
L = 672/12 = 56