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1 year ago

Suppose y varies directly with x, and y = 16 when x = -4. Find x when y = 24.

Mathematics

1 answer:

Amanda [17]1 year ago

3 0

The value of x when y= 24 is -26

<h3>How to determine the value of x?</h3>

The given parameters are:

y varies directly with x, and y = 16 when x = -4.

This means that

y = kx

Where k is the constant of variation

So, we have:

16 = -4k

Divide by -4

k = -4

Substitute k = -4 in y = kx

y = -4x

When y = 24, we have:

24 = -4x

Divide by -4

x = -6

Hence, the value of x when y= 24 is -26

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3 years ago

The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli

ira [324]

Answer:

$\dfrac{40}{42}$

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

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The fraction is therefore:

$\dfrac{x}{x+2}$

If both numerator and denominator are decreased by six, the fraction becomes:

$\dfrac{x-6}{x+2-6}$

The simplified result is $\dfrac{17}{18}$

Therefore:

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Substituting x=40 into the initial fraction

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3 years ago

A school rent a bus for 90 bucks if 72 students ride the bus what is the cost per student

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Step-by-step explanation:

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3 years ago

Read 2 more answers

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

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3 years ago

What is the surface area of the rectangular prism

AnnZ [28]

Answer:

40.5 inch²

Step-by-step explanation:

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2 years ago