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3 years ago

a clock face has a radius of 8 inches.what is the area of the clock face.round your answer to the nearest hundreths.

Mathematics

1 answer:

ch4aika [34]3 years ago

4 0

Answer:

201.06 or 200.96

Step-by-step explanation:

Area of a circle=πr^2

Area=π8^2

Area=π64

π=3.14

Area=200.96

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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 $m+b=1\implies\boxed{b=-2}$

5 0

3 years ago

Trey bakes 70 cupcakes for the school Bake Sale. Worried they might run out, he bakes some extra and now has 112 cupcakes.

Ber [7]

Answer:

60%

Step-by-step explanation:

$112:70*100= (112*100):70\\(112*100)=11200\\11200:70=160$

so if 70 is 100%, 112 is 160%

and that is a 60% difference

5 0

2 years ago

Pleasseee help!!!<br> Find M1 and m2

blagie [28]

Answer:

The answer are

$m < 1 = 76 \\ m < 2 = 61$

Step-by-step explanation:

By using the laws of parallelism

Then

$m < 2 + 119 = 180 \\ m < 2 = 61 \\ by \: the \: same \: way \: \\ m < 1 = m < q \: External \\ then \\ m < 1 = 76$

8 0

2 years ago

Linear relations are not functions when they appear graphically as:

malfutka [58]

Answer:

Vertical lines

Step-by-step explanation:

5 0

3 years ago

Can someone HELP ME ASAP<br> sorry I know this might be a lot.

Tatiana [17]

Answer:

I'll abbreviate each one:

V - 8 x 10^-4

AR- 1.3 x 10^-4

A- 2.27 x 10^-5

AG- 4.5 x 10^-4

L- 3.5 x 10^-4

O- 1.5 x 10^-3

5 0

3 years ago