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kondaur [170]
3 years ago
15

The rate at which a plant grows is constant. At the 3rd week it is 12 inches tall and at the 5th week it is 20 inches tall. If t

his information is plotted on a coordinate plane, what is the y-coordinate of the the point (1, y)?
A) 1
B) 2
C) 4
D) 9
Mathematics
1 answer:
mote1985 [20]3 years ago
4 0
Answer: C) 4. Explanation: Since the rate is constant, you can find the y coordinate by simplifying the given coordinates. Image that the graph is (week, height), which means that the given points are (3, 12) and (5, 20). Put these into a fraction, and simplify them to get x as 1. y/x = 12/3 = 4, and 20/5 = 4. Since the rates are consistent with 4 when simplified to get the x variable to 1, that means that the y coordinate of (1, y) is 4.
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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

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The complimentary solution is

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

Using the initial conditions

y(-1) = 2

2 = (C1 -C2) e^4

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y'(-1) = 3

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

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

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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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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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