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anastassius [24]

3 years ago

6

What is 2,527 divided by 8 equal step by step?

1 answer:

aksik [14]3 years ago

7 0

Answer: 2527 divided by 8 equals

315 with a remainder of 7

Step-by-step explanation:

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Find all the solutions for the equation:

Contact [7]

$2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0$

Divide both sides by $x^2\,\mathrm dx$ to get

$2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}$

Substitute $v(x)=\dfrac{y(x)}x$ , so that $\dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}$ . Then

$x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}$

The remaining ODE is separable. Separating the variables gives

$\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x$

Integrate both sides. On the left, split up the integrand into partial fractions.

$\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}$

$\implies v^2+2v+1=a(v^2+1)+(bv+c)v$

$\implies v^2+2v+1=(a+b)v^2+cv+a$

$\implies a=1,b=0,c=2$

Then

$\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v$

On the right, we have

$\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C$

Solving for $v(x)$ explicitly is unlikely to succeed, so we leave the solution in implicit form,

$\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C$

and finally solve in terms of $y(x)$ by replacing $v(x)=\dfrac{y(x)}x$ :

$\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}$

7 0

3 years ago

How much money will you have if you started with $1250 and put it in an account that earned 6.7% every year for 14 years?

KatRina [158]

Answer:

$3098.93

Step-by-step explanation:

We can use the formula for compound growth to solve this. The formula is:

$F=P(1+r)^t$

Where

F is the future value (the value at end of 14 years, our answer)

P is the initial amount invested ($1250)

r is the interest rate, in decimal (6.7% is 0.067)

t is the time in years (14, in our case)

<em>Plugging in all the information</em> we have:

$F=P(1+r)^t\\F=1250(1+0.067)^14\\F=1250(1.067)^14\\F=3098.93$

The account will accrue $3098.93 after 14 years.

3 0

2 years ago

Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (0, -2) and

BaLLatris [955]

Answer:

y = -(5/2)x -2

Explanation:

The general formula for a straight line is y – mx + b.

The image below shows the graph of the line.

Step 1. <em>Calculate the slope</em>.

Slope = m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

x₁ = 0; y₁ = -2

x₂ = -2; y₂ = 3 Calculate m

m = [3-(-2)]/(-2-0)

m = (3+2)/(-2)

m = 5/(-2)

m = -5/2

Step 2. <em>Calculate the y-intercept </em>

When x = 0, y = 2.

The y-intercept (b) is at y = -2

Step 3. <em>Write the equation </em>for the graph

y = mx + b

y = -(5/2)x - 2

3 0

2 years ago

Read 2 more answers

Students are playing a game similar to blackjack (with a standard 52 card deck)- trying to get as close to 21 points without goi

son4ous [18]

1/2 wee player a just got 2 so it is out

7 0

3 years ago

Help me please this is a quiz for today

Alexandra [31]

Slope is 5
Y intersect is 0

Y= 5x

3 0

3 years ago