The midpoint of the segment is (-15/2, -15/2)
<h3>How to determine the midpoint?</h3>
The complete question is in the attached image
The points are given as:
(-8, -7) and (-7, -8)
The midpoint is calculated as:
(x,y) = 1/2 * (x1 + x2, y1 + y2)
So, we have:
(x,y) = 1/2 * (-8 - 7, -7 - 8)
Evaluate the difference
(x,y) = 1/2 * (-15, -15)
Evaluate the product
(x,y) = (-15/2, -15/2)
Hence, the midpoint of the segment is (-15/2, -15/2)
Read more about midpoints at:
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Answer:
0.53πrad
Explanations:
Given the radius of the circular track = 60metres
If she walks a total of 100 meters, the length of the arc of the circle = 100metres
To calculate the radian angle she rotates about the center of the track, we will use the formula for calculating the length of an arc
L = θ/360° × 2πr
100 = θ/360× 2π(60)
36000 = 120π × θ
36000 = 376.8θ
θ = 36000/376.8
θ = 95.5°
Since 180° = πrad
95.5° = x
x = 95.5π/180
x = 0.53π rad
Answer:
Radius =6.518 feet
Height = 26.074 feet
Step-by-step explanation:
The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder
Volume of a Hemisphere 
Volume of a Cylinder 
Therefore:
The Volume of the Solid formed

Area of the Hemisphere =
Curved Surface Area of the Cylinder =
Total Surface Area=

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.
Therefore total Cost, C

Recall: 
Therefore:

The minimum cost occurs at the point where the derivative equals zero.


![-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518](https://tex.z-dn.net/?f=-27840%2B32%5Cpi%20r%5E3%3D0%5C%5C27840%3D32%5Cpi%20r%5E3%5C%5Cr%5E3%3D27840%20%5Cdiv%2032%5Cpi%3D276.9296%5C%5Cr%3D%5Csqrt%5B3%5D%7B276.9296%7D%20%3D6.518)
Recall:

Therefore, the dimensions that will minimize the cost are:
Radius =6.518 feet
Height = 26.074 feet
Two basic ways in which to do this problem:
1. Find and apply the LCD.
2. Convert all of the given numbers to their decimal form, to 2 or 3 places only.
Try #2 first:
5/6 = 0.83
4/5 = 0.80 is not between 5/6 and 1. Reject it.
4/7 = 0.57 Reject
6/7 = 0.86 This is between 5/6 and1. This is the answer.
Answer:
0.0027 - zero-point-zero-zero-twenty-seven
Step-by-step explanation: