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3 years ago

How to make 1.4 into a fraction

Mathematics

2 answers:

Sphinxa [80]3 years ago

7 0

Well for one it's improper. which would mean it would have to be 12/5

inessss [21]3 years ago

4 0

As an improper fraction, the answer is 7/5.

As a mixed number, the answer is 1 2/5.

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2 years ago

The circulation of a newsletter decreased from 6000 to 3710. Find the percent of decrease in circulation to the nearest percent.

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2 years ago

Consider the geometric series S(x)=1+2(x−3)+4(x−3)^2+8(x−3)^3+⋯

sergij07 [2.7K]

Consider the geometric series S(x)=1+2(x−3)+4(x−3)^2+8(x−3)^3+⋯
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3 years ago

Read 2 more answers

If an ecosystem can only hold about 12-15 animals what is this called?

V125BC [204]

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2 years ago

Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

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3 years ago