Age c) The group is planning to build a fence around the garden. How many yards of fencing materials do they need for the fence?
1 answer:
Answer:
Step-by-step explanation:
The perimeter is obtained by taking the sun of the fence :
Outer fencing :
Let's obtain b :
From Pythagoras :
b² = 15² - 12²
b = sqrt(225 - 144)
b = 9
Outer fencing = 2(12+6) + 2(8+9)
= 2(18) + 2(17)
= 36 + 34
= 70
Inner fencing :
(8 + 9 + 12 + 6 + 15 + 10) = 60
(70 + 60) = 130 yards
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To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine: