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2 years ago

7 divided by 4 x + 3 Y + 4 divided / 4 x minus 3 Y is equal to 5 / 4

Mathematics

1 answer:

DerKrebs [107]2 years ago

7 0

9514 1404 393

Answer:

(x, y) = (4, 4)

Step-by-step explanation:

If you attempt to solve this by clearing fractions, you end up with an extraneous solution. Here, we'll solve the linear equations ...

7a +4b = 5/4

8b -14a = 3/2

where a = 1/(4x+3y) and b = 1/(4x-3y)

Dividing the second equation by 2 and adding the first, we have ...

(7a +4b) +1/2(8b -14a) = (5/4) +1/2(3/2)

8b = 8/4

b = 1/4

Substituting into the first equation gives ...

7a +4/4 = 5/4

a = 1/28

Now, we can get back to solving for x and y.

4x +3y = 1/a = 28

4x -3y = 1/b = 4

8x = 32 . . . . . . . . . add the two equations

x = 4

3y = 28 -4x = 28 -4(4) = 12 . . . . . use x in the equation for 'a'; rearrange

y = 4 . . . . divide by 3

The solution to the system of equations is (x, y) = (4, 4).

_____

Additional comment

If you graph these equations, you find they describe hyperbolas that intersect at (0, 0) and (4, 4). The "solution" (0, 0) is extraneous, as both equations are undefined there.

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Answer:

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Step-by-step explanation:

step 1

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Let

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t ---> the time in seconds

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$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

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$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

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