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Ede4ka [16]
3 years ago
12

to win a basketball game, one team scored 151 points. They made a total of 62 two-pointers and three pointers how many of the ba

skets were worth 2 points, and how many were 3 pointers.
Mathematics
1 answer:
wolverine [178]3 years ago
3 0

That's a huge number of points.

First: Calculate the value of 62 two pointers

62 * 2 = 124

Second: find the number of points that were due to 3 pointers.

151 - 124 = 27

Third: Divide by 3 to find the number of 3 pointers.

27÷3 = 9

Answer: There were 9 three pointers.

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b) y(t) = y_{0}e^{-4t} + 2. It has a steady state.

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a) y' -4y = -8

The first step is finding y_{n}(t). So:

y' - 4y = 0

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

r - 4 = 0

r = 4

So:

y_{n}(t) = y_{0}e^{4t}

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

y_{p}(t) = C

So

(y_{p})' -4(y_{p}) = -8

(C)' - 4C = -8

C is a constant, so (C)' = 0.

-4C = -8

4C = 8

C = 2

The solution in the form is

y(t) = y_{n}(t) + y_{p}(t)

y(t) = y_{0}e^{4t} + 2

b) y' +4y = 8

The first step is finding y_{n}(t). So:

y' + 4y = 0

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

r + 4 =

r = -4

So:

y_{n}(t) = y_{0}e^{-4t}

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

y_{p}(t) = C

So

(y_{p})' +4(y_{p}) = 8

(C)' + 4C = 8

C is a constant, so (C)' = 0.

4C = 8

C = 2

The solution in the form is

y(t) = y_{n}(t) + y_{p}(t)

y(t) = y_{0}e^{-4t} + 2

6 0
3 years ago
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