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sukhopar [10]
3 years ago
13

What is 3/5s of 75 ???????????????????????????

Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
8 0
45 because 75 divide 5 equal to 15. 15 multiply 3 equal is 45
Iteru [2.4K]3 years ago
4 0
The answer is:  45 .
________________________________

3/5 * 75 = 3/5 * 75/1 ;

The "5" cancels to a "1"; and the "75" cancels to a "15" ; 
  since "75÷5 = 15" ; and since "5÷5 =1" .

So, rewrite the problem:

3/1 = 15/1 = 45/1 = 45.
___________________________
Other method:
___________________________
3/5 * 75  = 6/10 * 75 = 0.6 * 75 = 45.0 = 45 .
_______________________________________

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Answer:

e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...

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Step-by-step explanation:

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\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...

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\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...

\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If  $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}

\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4

\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4

\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4

Substituting the values in the series expansion gives:

e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...

Factoring out e⁴:

e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]

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\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n

Therefore:

\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n

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