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3 years ago

Solve x=2√(x-4) + 4.

Mathematics

1 answer:

stich3 [128]3 years ago

8 0

Answer:x=4,8

Step-by-step explanation:

Given

$x=2\sqrt{x-4}+4$

$x-4=2\sqrt{x-4}$

Squaring both sides

$(x-4)^2=4(x-4)$

$x^2+16-8x=4x-16$

$x^2-12x+32=0$

$x=\frac{12\pm \sqrt{12^2-4\times 32}}{2}$

$x=\frac{12\pm 4}{2}$

$x=4,8$

You might be interested in

Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

4 years ago

a construction worker has rope 9 m long he needs to cut it in pieces that are each 3 /5 m long how many such pieces can he cut w

lapo4ka [179]

Dividing a whole number and an improper fraction seems tricky, but it just has one or two more steps than the normal process. First, convert the whole number "9" into a fraction by giving it a denominator of "1". It should look like 9/1. Now that both numbers are converted into like formats (improper fractions), you should have 9/1 divided by 5/3.

Second, flip 5/3 over into 3/5 - this is the "reciprocal". Now you have 9/1 divided by 3/5. It's just a matter of multiplying across the math sentence. Multiply the numerators (9x3) and the denominators (1 x 5). Your new fraction should be 27/5. This is your answer in the improper fraction format.

You can create other formats depending on the expected answer. For a mixed number, "divide your fraction UP" (27 divided by 5) which gives you 5 and 2/5. This can be further converted into 5.4 if you need your answer in decimal form.

4 0

4 years ago

HELPPPPP SOMEONEEEEE

velikii [3]

QR = 23

Because the triangles are equal to each other, sides QR and TV are also equal. You can create an 3 or 4 step equation by writing the the QR equation is equal to the TV equation and then solving for X. After you solve for X, plug it back into the QR equation to solve for QR.

7 0

3 years ago

What's 23 x 5/8 I need help

vitfil [10]

14 3/8
Hope that helps you!

3 0

3 years ago

Read 2 more answers

Need Help ASAP! Thank you!

shtirl [24]

Answer:

Step-by-step explanation: