A tire is slowly deflating. The graph below shows the pounds per square inch (psi) of pressure as a function of time.
1 answer:
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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:
c) (-2, 1)
Step-by-step explanation:
3x - 3y = -9
2x + y = -3
2x + y = -3
-2x -2x
y = -2x - 3
3x - 3y = -9
y = -2x - 3
3x - 3(-2x - 3) = -9
3x + 6x + 9 = -9
9x + 9 = -9
- 9 -9
9x = -18
/9 /9
x = -2
y = -2x - 3
y = -2(-2) -3
y = 4 - 3
y = 1
(x, y) --> (-2,1)
Check your answer:
y = -2x - 3
1 = -2(-2) - 3
1 = 4 - 3
1 = 1
This statement is true
Hope this helps!
