I need help with this question

Mathematics

2 answers:

Masja [62]3 years ago

5 0

Answer:

B (39)

Step-by-step explanation:

Using the Pythagorean theorem (a^2+b^2=c^2) and X=BC length

15^2+36^2=x

225+1296=x

√1521=x

x=39

Basile [38]3 years ago

4 0

Answer:

Step-by-step explanation:

The Pythagorean Theorem

a^2+b^2=c^2

In this case it's c^2=a^2+b^2

c^2=15^2+36^2

c^2=225+1296

c^2=1521

c= the square root of 1521

c=39

So...

the length of line segment BC is 39

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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.)