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3 years ago

-6x+6y=6 -6x + 3y=-12 ???

Mathematics

2 answers:

Tcecarenko [31]3 years ago

7 0

Answer

:x=5 y=6

Step-by-step explanation:

Darina [25.2K]3 years ago

5 0

Answer:

x=5 y=6

Step-by-step explanation:

Need to get rid of one variable to find one first. So I multiplied the second equation by -2 to get rid of y. So second equation becomes 12x-6y=24. add that to the first equation.

6x+6y=6

12x-6y=24

6x=30 then divide

x=5

then plug x into the original equation to get y.

-6(5) +6y=6

-30+6y=6 add 30 to both sides

6y=36 then divide

y=6

then put both into the original to make sure it makes sense

-6(5) +6(6)=6

-30+36=6

6=6

correct

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Solve the given initial-value problem. the de is a bernoulli equation. x2 dy dx − 2xy = 4y4, y(1) = 1 2

mario62 [17]

$x^2\dfrac{\mathrm dy}{\mathrm dx}-2xy=4y^4$
$x^2y^{-4}\dfrac{\mathrm dy}{\mathrm dx}-2xy^{-3}=4$

Substitute $z=y^{-3}$ , so that $\dfrac{\mathrm dz}{\mathrm dx}=-3y^{-4}\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE in terms of $z(x)$ is

$-\dfrac13x^2\dfrac{\mathrm dz}{\mathrm dx}-2xz=4$
$x^2\dfrac{\mathrm dz}{\mathrm dx}+6xz=-12$
$x^6\dfrac{\mathrm dz}{\mathrm dx}+6x^5z=-12x^4$

$\dfrac{\mathrm d}{\mathrm dx}\left[x^6z\right]=-12x^4$
$\implies x^6z=-\dfrac{12}5x^5+C$
$\implies z=-\dfrac{12}{5x}+\dfrac C{x^6}$
$\implies\dfrac1{y^3}=-\dfrac{12}{5x}+\dfrac C{x^6}$

and you can attempt to solve for $y$ explicitly from here if you wish.
In any case, given that $y(1)=\dfrac12$ (presumably that's what you meant to write), we'd get

$\dfrac1{\left(\frac12\right)^3}=-\dfrac{12}{5\cdot1}+\dfrac C{1^6}$
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giving a particular solution of

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3 years ago

last tuesday, Regal Cinemas sold a total of 8500 movie tickets. proceeds totaled $64,600. tickets can be bought in one of 3 ways

Verizon [17]

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s = 2m

m + 2m + r = 8500
3m + r = 8500
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5m + 6(2m) + 8.50(8500 - 3m) = 64600
5m + 12m + 72250 - 25.50m = 64600
-8.50m = 64600 - 72250
-8.50m = -7650
m = -7650 / - 8.50
m = 900 <=== 900 matinee tickets

s = 2m
s = 2(900)
s = 1800 <===1800 student tickets

r = 8500 - 3m
r = 8500 - 3(900)
r = 8500 - 2700
r = 5800 <=== regular

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4 years ago

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masya89 [10]

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4 years ago

Read 2 more answers

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il63 [147K]

Answer:

the slope of the line would be 3/4

Step-by-step explanation:

to find this use your equation for slope: y2-y1/x2-x1

this will give you 5-2/4-0

simplified it is 3/4

another way to know the slope is that the slope will be rise/run, so since the line is going up 3 places and over 4 places, your slope would be 3/4