(show the work please)

Mathematics

1 answer:

stiv31 [10]2 years ago

5 0

Convert the mixed number into an improper fraction.

3 1/2 x 2 : 16/5 x 2

Calculate the product!

16/5 x 2 : 32/5

Solution: 32/5, (Alternative Forms: 6 2/5, 6.4)

Hope this helps!

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100 aluminum cans weigh 5 pounds, If Ray collects 300 cans on clean up day, how many pounds of cants does he have?

padilas [110]

Easy, 100 x 3 is 300 pounds, 5 x 3 is 15, so 15 pounds. :)

7 0

2 years ago

Read 2 more answers

Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$