Answer:
The integral is equal to for an arbitrary constant C.
Step-by-step explanation:
a) If then so the integral becomes . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)
b) In this case hence . We rewrite the integral as .
c) We use the trigonometric identity is part b). The value of the integral is . which coincides with part a)
Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.
Answer:
Step-by-step explanation:
Let
x-------> the number of pies
we know that
-----> linear equation that represent the situation
solve for x
Round to the nearest whole number
Answer:
(-1,8)
(4,-27)
Step-by-step explanation:
y+7x=1
Let x = -1 and find y
y+7(-1)=1
y -7 =1
Add 7 to each side
y-7+7 = 1+7
y = 8
(-1,8)
Let x = 4 and find y
y+7(4)=1
y +28 =1
Subtract 28 from each side
y+28-28 = 1-28
y = -27
(4,-27)