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olga nikolaevna [1]
3 years ago
11

A wooden plank is leaning against a wall.

Mathematics
1 answer:
disa [49]3 years ago
8 0
Did you leave out any part of the problem?
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The perimeter may not be small enough to measure with just a ruler. For example, if a side of a rectangle was 30 inches, how would you use a 12 inch ruler to accurately measure that side? Also, if you were measuring a shape like a circle or oval, a tape measure is flexible.
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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
What is the unit used for measuring the size of an angle?
GuDViN [60]

Answer:

Degree

Step-by-step explanation:

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Kisachek [45]

Answer:

3 vertices

Step-by-step explanation:

Vertices are the "points" of a 2D figure. In this case, we see the 2D figure as a triangle. There are 3 points on the triangle, so there are 3 vertices.

3 0
1 year ago
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