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nirvana33 [79]
3 years ago
8

Helps asap please help

Mathematics
2 answers:
mash [69]3 years ago
6 0

Answer:

Yes,

2 and 5

Step-by-step explanation:

A function has an inverse if and only if it is one to one.

To tell if this equation is a function, and to tell if it is one to one, we must do the vertical line test, and the horizontal line test.

It passes the vertical line test and the horizontal line test.

Therefore it has an inverse.

To get the inverse of this equation, we have to know that inverses are reflections over Y = X. So if we plot that line, we can have an idea of where the inverse would be.

f^-1 (0) = 2

f^-1 (3) = 5

The easiest way to do this... is to know that the inverse equation just flips all the coordinates.

(0,1) -> (1,0)

So... if they give you the Y intercept the (0 and the 3) go look at where the line crosses X! I mean, why not? They gave you half the inverse coordinate point an

Novosadov [1.4K]3 years ago
5 0
Yes because the line is curved
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Verdich [7]

Answer:

A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length

Step-by-step explanation:

3 0
2 years ago
The ratio of boys to girls in Ms. smith’s class is 3 to 4. If there are 12 boys, how many girls are there?
Lorico [155]

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❖ There will be 16 girls.

The relationship is x4. If we multiply 3 x 4, we get 12. What we do to one number we do to the other so 4 x 4 = 16.

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3 years ago
Phythagoras was born about 582bc.issac Newton was born in 1643 ad .how many years apart were they born
tigry1 [53]

Answer:

2,225

Step-by-step explanation:

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Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.
igor_vitrenko [27]

Answer:

y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}

Step-by-step explanation:

y′′ + 4y′ − 21y = 0

The auxiliary equation is given by

m² + 4m - 21 = 0

We solve this using the quadratic formula. So

m = \frac{-4 +/- \sqrt{4^{2} - 4 X 1 X (-21))} }{2 X 1}\\ = \frac{-4 +/- \sqrt{16 + 84} }{2}\\= \frac{-4 +/- \sqrt{100} }{2}\\= \frac{-4 +/- 10 }{2}\\= -2 +/- 5\\= -2 + 5 or -2 -5\\= 3 or -7

So, the solution of the equation is

y = Ae^{m_{1} t} + Be^{m_{2} t}

where m₁ = 3 and m₂ = -7.

So,

y = Ae^{3t} + Be^{-7t}

Also,

y' = 3Ae^{3t} - 7e^{-7t}

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,

y(1) = Ae^{3X1} + Be^{-7X1}\\1 = Ae^{3} + Be^{-7}\\Ae^{3} + Be^{-7} = 1      (1)

y'(1) = 3Ae^{3X1} - 7Be^{-7X1}\\0 = 3Ae^{3} - 7Be^{-7}\\3Ae^{3} - 7Be^{-7} = 0 \\3Ae^{3} = 7Be^{-7}\\A = \frac{7}{3} Be^{-10}

Substituting A into (1) above, we have

\frac{7}{3}B e^{-10}e^{3} + Be^{-7} = 1      \\\frac{7}{3}B e^{-7} + Be^{-7} = 1\\\frac{10}{3}B e^{-7} = 1\\B = \frac{3}{10} e^{7}

Substituting B into A, we have

A = \frac{7}{3} \frac{3}{10} e^{7}e^{-10}\\A = \frac{7}{10} e^{-3}

Substituting A and B into y, we have

y = Ae^{3t} + Be^{-7t}\\y = \frac{7}{10} e^{-3}e^{3t} + \frac{3}{10} e^{7}e^{-7t}\\y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}

So the solution to the differential equation is

y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}

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Step-by-step explanation:

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