Need help solving this. Thanks

Mathematics

2 answers:

kap26 [50]2 years ago

8 0

Answer:

solving what ? there is nothing here

Vlad1618 [11]2 years ago

5 0

Answer:

Where is the question?

Step-by-step explanation:

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The league championship 800 meter race has 6 runners.

s2008m [1.1K]

Answer: 120

Step-by-step explanation:

Given : The league championship 800 meter race has 6 runners.

The number of positions = 3

Since order matters here , so we use Permutation.

The permutation of n things taking r at a time is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Then, the number of different ways they place first, second, and third :_

$^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6\times5\times4\times3!}{3!}=120$

Hence, they can place first, second, and third in 120 different ways .

7 0

3 years ago

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)