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3 years ago

7

A box of muffin mix has dimensions of 5 3/8 inches by 3 inches by 1 5/8 inches. What is the volume of the box? 15 15/64 cubic in

ches, 26 13/64 cubic inches, 21 cubic inches, 30 cubic inches

2 answers:

anyanavicka [17]3 years ago

7 0

Answer is 26 13/64

first u need to simplify mixed number then multiply them all

43/8*3*13/8=1677/64

DedPeter [7]3 years ago

7 0

Answer:

Step-by-step explanation:

answer is 26 13/64

first u need to simplify mixed number then multiply them all

43/8*3*13/8=1677/64

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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

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

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

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.

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

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

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

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 $v(x)=\dfrac{y(x)}x$ :

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

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

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

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3 years ago

How to simply 7a+3(9+5a)?

makvit [3.9K]

To solve for this, we need to use the Distributive Property, which allows us to multiply the number/variable outside of the parenthesis by all numbers/variables inside of the parenthesis. Once we've done that, we can attempt to simplify the equation.
Our current equation is:
7a + 3(9+5a) = 0
Let's use the Distributive Property.
3(9 + 5a)
3(9) + 3(5a)
27 + 15a
Our current equation now is:
7a + 27 + 15a = 0
Combine like-terms.
15a + 7a = 22a
22a + 27 (If this is not being solved, THIS is your answer as an expression)
Subtract 27 from both sides
22a = -27
Divide both sides by 22 to get a.
a = -27/22.
If we are not solving for a, but getting an expression, your answer is:
22a + 27.
If we are solving for a, our answer is:
a = -27/22.
I hope this helps!

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