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joja [24]
3 years ago
13

Follow the instructions below.

Mathematics
1 answer:
sergeinik [125]3 years ago
4 0

Answer:

1.    0.83 = 83%

2.    6.1% = 0.061

Step-by-step explanation:

The answer in number one is because when you're trying to find a percentage from a decimal, all you have to do is multiply your decimal by 100, this is because a percentage is always out of 100.

The answer in number two is exactly the opposite, all you have to do is divide by 100 if you are trying to find your decimal from a percentage.

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17

Step-by-step explanation:

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How to differentiate y=x^n using the first principle. In this question, I cannot use the rule of differentiation. I have to do t
Zarrin [17]

By first principles, the derivative is

\displaystyle\lim_{h\to0}\frac{(x+h)^n-x^n}h

Use the binomial theorem to expand the numerator:

(x+h)^n=\displaystyle\sum_{i=0}^n\binom nix^{n-i}h^i=\binom n0x^n+\binom n1x^{n-1}h+\cdots+\binom nnh^n

(x+h)^n=x^n+nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n

where

\dbinom nk=\dfrac{n!}{k!(n-k)!}

The first term is eliminated, and the limit is

\displaystyle\lim_{h\to0}\frac{nx^{n-1}h+\dfrac{n(n-1)}2x^{n-2}h^2+\cdots+nxh^{n-1}+h^n}h

A power of h in every term of the numerator cancels with h in the denominator:

\displaystyle\lim_{h\to0}\left(nx^{n-1}+\dfrac{n(n-1)}2x^{n-2}h+\cdots+nxh^{n-2}+h^{n-1}\right)

Finally, each term containing h approaches 0 as h\to0, and the derivative is

y=x^n\implies y'=nx^{n-1}

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3 years ago
Worth 10 points if correct answer you will get brainliest :)
barxatty [35]

Answer:

16/21

Step-by-step explanation:

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Step-by-step explanation:

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