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3 years ago

The following data gives the number of cars

Mathematics

1 answer:

faltersainse [42]3 years ago

5 0

Answer:

Step-by-step explanation:

2 : (2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1) = 1/30 ≈ 3.33% ≈ 3%

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Write a compound inequality for the graph shown below.

irina [24]

A compound inequality for the graph would be:

x >= 0 and x < 2

7 0

4 years ago

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

What is 9a - 3 (2a - 4) = 15

faltersainse [42]

<span>9a + -3(2a + -4) = 15 Reorder the terms: 9a + -3(-4 + 2a) = 15 9a + (-4 * -3 + 2a * -3) = 15 9a + (12 + -6a) = 15 Reorder the terms: 12 + 9a + -6a = 15 Combine like terms: 9a + -6a = 3a 12 + 3a = 15 Solving 12 + 3a = 15 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 3a = 15 + -12 Combine like terms: 12 + -12 = 0 0 + 3a = 15 + -12 3a = 15 + -12 Combine like terms: 15 + -12 = 3 3a = 3 Divide each side by '3'. a = 1 Simplifying a = 1</span>

5 0

3 years ago

Read 2 more answers

Jonh's collection contains 20 books including 2 historical novels if John randomly selects a book to read what is the probility

Anarel [89]

Answer:2/20 or 20%

Step-by-step explanation:

7 0

3 years ago

89 POINTS!!! You are given an isosceles trapezoid ABCD with median XY. Complete the following.

Sauron [17]

Answer:

(Given m∠DCB = 105, m∠DAB = 75) m∠ADC=75, m∠AXY=105, m∠DYX=105, m∠BXY=75, m∠CYX=75, m∠ABC=105

Step-by-step explanation:

Definition of consecutive interior angles

3 0

3 years ago