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4 years ago

10

Write a first step question and answer.Then solve the problem.The store owner gets a shipment of 7 boxes of games.There are 6 ga

mes in each box.He sells 18 games.How many games are left?

2 answers:

n200080 [17]4 years ago

3 0

(7 x 6) - 18 = 24 games left

White raven [17]4 years ago

3 0

Answer:

7(6) - 16 = x

thats the equation.

x= 26

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

Shirley has a circular rug in her dining room that has an area of 36 pie Square meters what is the radius of the circular rug

ValentinkaMS [17]

Answer: The radius of the circular rug is 6 meters.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

<em>Area of a circle (A) = pi r² </em>

Where r is the radius:

Replacing with the values given:

36 pi=pi r²

Dividing both sides by pi:

36 = r²

√36= r

r = 6 meters

So, the radius of the circular rug is 6 meters.

Feel free to ask for more if needed or if you did not understand something.

8 0

3 years ago

Read 2 more answers

Help Please.<br> .<br> .<br> .<br> .

Anika [276]

Answer:

angle 5 = angle 1

angle 6=angle 3

angle 2+angle 1+angle 3=180 degrees

angle 2+5+6=180 degrees

8 0

3 years ago

Farmer Tom's chickens and sheets are in a jumble. He counts 48 heads and 134 legs, how many sheep does he have?

svetlana [45]

48=x+y
143= 2x+4y
y= sheep
48-y = x
143=2(48-y)+4y
143= 96-2y+4y
143=96+2y
47=2y
y=19
19 sheep

4 0

3 years ago

Read 2 more answers

If you only have a

cestrela7 [59]

Hi! I'm happy to help!

To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:

15 $\frac{1}{6}$ ÷ $\frac{1}{6}$

This problem is hard to do with mixed numbers, so we need to turn 15 $\frac{1}{6}$ into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra $\frac{1}{6}$ .

(15×6)+1

90+1

91

So, our improper fraction would be $\frac{91}{6}$ , now, let's solve.

$\frac{91}{6}$ ÷ $\frac{1}{6}$

It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.

$\frac{91}{6}$ × $\frac{6}{1}$

Now, we just multiply the top by the top, and bottom by the bottom.

$\frac{546}{6}$

We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.

$\frac{91}{1}$

Anything over 1, is just a whole number

91.

<u>Therefore, the recipe should require 91 uses of the 1/6 cup.</u>

I hope this was helpful, keep learning! :D

3 0

3 years ago