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:
24-18=6+6+12
hope this helps you!!
Step-by-step explanation:
Answer:
(x + 1)(x + 3)eˣ
Step-by-step explanation:
Since f(x) = (x + 1)²eˣ
df(x)/dx = d[(x + 1)²eˣ]/dx
By the product rule, duv/dx = udv/dx + vdu/dx
where u = (x + 1)² and v = eˣ
So, df(x)/dx = d[(x + 1)²eˣ]/dx
= (x + 1)²deˣ/dx + eˣd(x + 1)²/dx
= (x + 1)²eˣ + eˣd(x + 1)²/d(x + 1) × d(x + 1)/dx (by the chain-rule dy/dx = dy/du × du/dx)
= (x + 1)²eˣ + eˣ[2(x + 1) × 1]
= (x + 1)²eˣ + 2eˣ(x + 1)
= (x + 1)eˣ(x + 1 + 2)
= (x + 1)eˣ(x + 3)
= (x + 1)(x + 3)eˣ
Answer:
I believes the answer is B
Step-by-step explanation:
I said that because for it to be linear the branch needs to add up by the same number to give for the next two year therefor when we look at the picture the branch measure are not stable so the answer is exponential.
Hope that it help!