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Lunna [17]
3 years ago
13

{(-3,9), (-2, 4), (0, 0), (1, 1)} Find the inverse

Mathematics
1 answer:
Elena-2011 [213]3 years ago
5 0

Answer:

Step-by-step explanation:

to find the inverse, just switch x and y

so if u have these points : (-3,9) , (-2,4), (0,0), (1,1)

the inverse would be : (9,-3) , (4,-2), (0,0), (1,1)

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Find the solution to the initial value problem
Karo-lina-s [1.5K]

Answer:

y = (11x + 13)e^(-4x-4)

Step-by-step explanation:

Given y'' + 8y' + 16 = 0

The auxiliary equation to the differential equation is:

m² + 8m + 16 = 0

Factorizing this, we have

(m + 4)² = 0

m = -4 twice

The complimentary solution is

y_c = (C1 + C2x)e^(-4x)

Using the initial conditions

y(-1) = 2

2 = (C1 -C2) e^4

C1 - C2 = 2e^(-4).................................(1)

y'(-1) = 3

y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)

3 = -4(C1 - C2)e^4 + C2e^4

-4C1 + 5C2 = 3e^(-4)..............................(2)

Solving (1) and (2) simultaneously, we have

From (1)

C1 = 2e^(-4) + C2

Using this in (2)

-4[2e^(-4) + C2] + 5C2 = 3e^(-4)

C2 = 11e^(-4)

C1 = 2e^(-4) + 11e^(-4)

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The general solution is now

y = [13e^(-4) + 11xe^(-4)]e^(-4x)

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