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kvasek [131]
2 years ago
6

1 a. A cube has an edge length of 4.3 meters. What is the volume of the cube?

Mathematics
1 answer:
kozerog [31]2 years ago
3 0
The volume for 1 a. is 79.50700. (You just multiply 4.3 by itself three times)
I don't know what the second one is though, sorry.
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If W is the center of the circle below and measures 52°, what is the measure of XZY?
Zinaida [17]

Answer:

Option (B)

Step-by-step explanation:

By the theorem of the inscribed angle,

"An angle inscribed in a circle measures half of the central angle subtended by the same arc."

Since m(arc XY) = 52°

Angle subtended by the the arc at the center (Central angle) = m∠XWY = 52°

Measure of inscribed angle = m∠XZY

By theorem, m∠XZY = \frac{1}{2}(\angle XWY)

m∠XZY = \frac{1}{2}(52)

             = 26°

Therefore, Option (B) will be the answer.

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Find the values of m and b that make the following function differentiable. the piecewise function f of x equals x cubed when x
aalyn [17]

f(x)=\begin{cases}x^3&\text{for }x\le1\\mx+b&\text{for }x>1\end{cases}

f must be continuous in order to be differentiable, so we need to have

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)

By its definition, f(1)=1^3=1, and

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}x^3=1

\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}(mx+b)=m+b

so that \boxed{m+b=1}.

We want the derivative to exist at x=1, which requires that we pick an appropriate value for f'(1) so that f'(x) is also continuous. At the moment, we know

f'(x)=\begin{cases}3x^2&\text{for }x1\end{cases}{/tex]so we need to pick [tex]f'(1) such that

\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1^+}f'(x)

We have

\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1}3x^2=3

\displaystyle\lim_{x\to1^+}f'(x)=\lim_{x\to1}m=m

so that \boxed{m=3} (which means we need to pick f'(1)=3) and so m+b=1\implies\boxed{b=-2}

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