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2 answers:
Answer:
Step-by-step explanation:
Hello There!
First things first, we need to find the value of x
If you didn't know the measures of supplementary angles add up to equal 180 so we can use this equation to solve for x
180 = 2x + 3x - 5
step 1 combine like terms
2x + 3x = 5x
now we have
180 = 5x - 5 step 2 add 5 to each side
-5 + 5 cancels out
180 + 5 = 185
now we have 185 = 5x
step 3 divide each side by 5
5x/5=x
185/5=37
we're left with x = 37
Now we want to plug in 37 into x for angle A
angle a = 2(37)
2*37=74
so we can conclude that angle A = 74
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Answer:
(a) P = 2x + 2r + 2πr
(b) x = ½(P - 2r - 2πr)
(c) x = 123 feet
Step-by-step explanation:
See Attachment for sketch of the track
Solving for (a): Perimeter of the track
This is calculated by adding the perimeter of the rectangle to the 2 semicircles as follows.
P = Perimeter of Rectangle + Perimeter of 2 Semicircles
P = 2(x + r) + 2 * πr
[Where r is the radius of both semicircles]
Open bracket
P = 2x + 2r + 2πr
Solving for (b): Formula for x
P = 2x + 2r + 2πr
Make x the subject of formula
2x = P - 2r - 2πr
Divide both sides by 2
x = ½(P - 2r - 2πr)
Solving for (c): the value of x when r = 50 and P = 660
Substitute the given values in the formula in (b) above
x = ½(P - 2r - 2πr)
x = ½(660 - 2 * 50 - 2π * 50)
x = ½(660 - 100 - 100π)
x = ½(560 - 100π)
Take π as 3.14
x = ½(560 - 100 * 3.14)
x = ½(560 - 314)
x = ½ * 246
x = 123 feet
