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2 years ago

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There is a ratio of 5 to 3, dogs to cats. There are 15 cats; how many dogs would you have?

2 answers:

LenaWriter [7]2 years ago

8 0

Since we have 5 dogs to 3 cats, we can find a scale factor. Our new proportion is x:15.
To solve for this, we need to divide 15 by 3 to get our scale factor to find x.
15/3 = 5, so our scale factor is 5.
Multiply 5 dogs by 5 to get the new ratio.
Our new ratio is 25:15, meaning that we have 25 dogs total.
Your answer is 25 dogs.
I hope this helps!

denpristay [2]2 years ago

3 0

15×5/3=25. As a result, I would have 25 dogs. Hope it help!

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Answer:

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Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

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$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

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To find the commission on sale ad of $2000, we have to multiply 2000 by 17%

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