Dare to do this if you are geiness

Mathematics

1 answer:

hoa [83]2 years ago

3 0

Answer:

2^3 x 3^3 x 5^4

Step-by-step explanation:

750 x 900 = 675000

675000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5

Which in product of prime factors is = 2 to the power of 3 x 3 to the power of 3 x 5 to the power of 4

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0.2(x+50)-6=0.4(3x+20)

podryga [215]

Distrivute 0.2 to x and +50 and you get 0.2x+10-6 now for the other side we do the same and we get 1.2x+8 or an easier way... Let's solve your equation step-by-step.0.2(x+50)−6=0.4(3x+20)Step 1: Simplify both sides of the equation.0.2x+4=1.2x+8Step 2: Subtract 1.2x from both sides.0.2x+4−1.2x=1.2x+8−1.2x−x+4=8Step 3: Subtract 4 from both sides.−x+4−4=8−4 −x=4 now you divide by negative x (technically it is -1x=4 so your answer is x=-4

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Step-by-step explanation:

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2 years ago

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