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geniusboy [140]

3 years ago

14

The minute hand on a watch is 14 millimeters. In the course of an hour, how much area does it cover? Leave answers in terms of π

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1 answer:

Lesechka [4]3 years ago

8 0

In an hour the minute hand goes all the way around, or a 360 loop. so it's its $\pi$ times the radius squared.

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There are seven cars parked in a row exactly the same distance from each other the first car is 31 inches from the second car th

MakcuM [25]

Answer:

the distance of the 3rd car from the 7th car is

217 inch

8 0

3 years ago

Mar 19, 17:52:58 AM<br> What are the odds that the spinner lands on red.

raketka [301]

Answer:

3/8

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the perimeter of the triangle

vredina [299]

We can find the area of the big triangle, and subtract it from the small 4 x 2 triangle.

bh/2
3*8/2
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bh/2
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12 - 8
4 unit²

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4 0

3 years ago

Read 2 more answers

CALC- limits<br> please show your method

gladu [14]

A. Factor the numerator as a difference of squares:

$\displaystyle\lim_{x\to9}\frac{x-9}{\sqrt x-3}=\lim_{x\to9}\frac{(\sqrt x-3)(\sqrt x+3)}{\sqrt x-3}=\lim_{x\to9}(\sqrt x+3)=6$

c. As $x\to\infty$ , the contribution of the terms of degree less than 2 becomes negligible, which means we can write

$\displaystyle\lim_{x\to\infty}\frac{4x^2-4x-8}{x^2-9}=\lim_{x\to\infty}\frac{4x^2}{x^2}=\lim_{x\to\infty}4=4$

e. Let's first rewrite the root terms with rational exponents:

$\displaystyle\lim_{x\to1}\frac{\sqrt[3]x-x}{\sqrt x-x}=\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}$

Next we rationalize the numerator and denominator. We do so by recalling

$(a-b)(a+b)=a^2-b^2$
$(a-b)(a^2+ab+b^2)=a^3-b^3$

In particular,

$(x^{1/3}-x)(x^{2/3}+x^{4/3}+x^2)=x-x^3$
$(x^{1/2}-x)(x^{1/2}+x)=x-x^2$

so we have

$\displaystyle\lim_{x\to1}\frac{x^{1/3}-x}{x^{1/2}-x}\cdot\frac{x^{2/3}+x^{4/3}+x^2}{x^{2/3}+x^{4/3}+x^2}\cdot\frac{x^{1/2}+x}{x^{1/2}+x}=\lim_{x\to1}\frac{x-x^3}{x-x^2}\cdot\frac{x^{1/2}+x}{x^{2/3}+x^{4/3}+x^2}$

For $x\neq0$ and $x\neq1$ , we can simplify the first term:

$\dfrac{x-x^3}{x-x^2}=\dfrac{x(1-x^2)}{x(1-x)}=\dfrac{x(1-x)(1+x)}{x(1-x)}=1+x$

So our limit becomes

$\displaystyle\lim_{x\to1}\frac{(1+x)(x^{1/2}+x)}{x^{2/3}+x^{4/3}+x^2}=\frac{(1+1)(1+1)}{1+1+1}=\frac43$

3 0

3 years ago

4/9+r=-4/9<br> What is r

julsineya [31]

Answer:

r = - 8/9

Step-by-step explanation:

$\frac{4}{9} + r = \frac{ - 4}{9} \\ r = \frac{ - 4}{9} - \frac{4}{9} \\ r = \frac{ - 8}{9}$

6 0

3 years ago