Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
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Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
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For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
Answer:
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Step-by-step explanation:
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Answer:10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.
Step-by-step explanation:
Let x represent the number of gallons of the 30% solution that should be mixed.
Let y represent the number of gallons of the 70% solution that should be mixed.
The total number of gallons of the mixture to be made is 40. This means that
x + y = 40
The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that
0.3x + 0.7y = 0.6 × 40
0.3x + 0.7y = 24- - - - - - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.3(40 - y) + 0.7y = 24
12 - 0.3y + 0.7y = 24
- 0.3y + 0.7y = 24 - 12
0.4y = 12
y = 12/0.4
y = 30
x = 40 - y = 40 - 30
x = 10
Volume = PI x r^2 x H/3
3.14 x 8^2 x 13.5/3
3.14 x 64 x 4.5 = 904.32 cubic feet
