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
Answer:
(0, -2)
Step-by-step explanation:
The slope equation is written as y = mx + b where m is the slope and b is the y-intercept. In this equation the slope, which is m, is -2/3 and the y-intercept is -2, which is the value of b. So the y-intercept on the graph would be found at point (0, -2)
D=4Step-by-step explanation:
Answer: x = 7 or x = -8
x² + x - 56 = 0
⇔ x² + 8x - 7x - 56 = 0
⇔ x(x + 8) - 7(x + 8) = 0
⇔ (x - 7)(x + 8) = 0
⇔ x - 7 = 0
or x + 8 = 0
⇔ x = 7 or x = -8
Step-by-step explanation:
Answer: here
Step-by-step explanation:riangles QST and RST are similar. Therefore, the following is true:
q s
--- = ---- This results in 10q=rs.
r 10
Also, since RST is a right triangle, 4^2 + s^2 = q^2.
Since QST is also a right triangle, s^2 + 10^2 = r^2.
4 s
Also: ---- = ----- which leads to s^2 = 40
s 10
Because of this, 4^2 + s^2 = q^2 becomes 16 + 40 = 56 = q^2
Then q = sqrt(56) = sqrt(4)*sqrt(14) = 2*sqrt(14) (answer)
hope it helps
