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White raven [17]
3 years ago
6

What is the circumference of this circle r = 2 km

Mathematics
2 answers:
zlopas [31]3 years ago
5 0

Answer: 4*pi, or 12.57 rounded to the nearest hundredth.

Step-by-step explanation: Circumference= pi*diameter. Diameter=2*radius. Radius=2, so diameter=4. 4*pi=12.57

VikaD [51]3 years ago
4 0
Circumference = 12.57km
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Ples help me find slant assemtotes
FrozenT [24]
A polynomial asymptote is a function p(x) such that

\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0

(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form p(x)=ax+b.

Ignore the negative root (we don't need it). If y=2x-1+2\sqrt{x^2-x}, then we want to find constants a,b such that

\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0

We have

\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}
\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}
\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}

since x\to\infty forces us to have x>0. And as x\to\infty, the \dfrac1x term is "negligible", so really \sqrt{x^2-x}\approx x. We can then treat the limand like

2x-1+2x-ax-b=(4-a)x-(b+1)

which tells us that we would choose a=4. You might be tempted to think b=-1, but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of b, we have to solve for it in the following limit.

\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0

\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2

We write

(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}

Now as x\to\infty, we see this expression approaching -\dfrac12, so that

-\dfrac12=\dfrac{b+1}2\implies b=-2

So one asymptote of the hyperbola is the line y=4x-2.

The other asymptote is obtained similarly by examining the limit as x\to-\infty.

\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0

\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0

Reduce the "negligible" term to get

\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0

Now we take a=0, and again we're careful to not pick b=-1.

\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0

\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2

(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}

This time the limit is \dfrac12, so

\dfrac12=\dfrac{b+1}2\implies b=0

which means the other asymptote is the line y=0.
4 0
3 years ago
Each equation represents a linear relationship. Examine each and determine the slope and y- intercept
marysya [2.9K]

Answer:

Slope is -3/7. Y intercept is 250/7.

Step-by-step explanation:

Since they asking for the slope and y intercept, let put it in slope intercept form.

y = mx + b

where m is the slope and b is the y intercept.

The equation given is in standard form so we will convert it to slope intercept.

3x + 7y = 250

7y = 250 - 3x

y =  \frac{250}{7}  -  \frac{3}{7} x

y =  -  \frac{3}{7} x +  \frac{250}{7}

The slope is -3/7

The y intercept is 250/7

6 0
2 years ago
Write the following fraction as a decimal.<br> 2<img src="https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B10%7D" id="TexFormula1" title
vfiekz [6]

Answer:

2/10 or 1/2 = .5 you would divide 2 by 2 and 10 divided by 2 (whatever you multiply or divide by on the top you must do on the bottom)

2/10=.50

3/100=.03 (divide 3 by 10=.0

5 0
2 years ago
Read 2 more answers
Marcella incarica Dora di aiutarla a suddividere 35 perle tra le sue tre figlie. Alla figlia maggiore vuole regalare la metà, al
Blizzard [7]

Answer:

La hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.

Step-by-step explanation:

Dado que Marcella le pide a Dora que la ayude a dividir 35 perlas entre sus tres hijas, y quiere darle la mitad a la hija mayor, la tercera parte a la del medio y la novena a la menor y, además, Marcella quiere darle una perla a Dora como recompensa, para determinar cuántas perlas recibirá cada hija se debe realizar el siguiente cálculo:

35 / 2 = Mayor = 17.5 perlas

35 / 3 = Medio = 11.66 perlas

35 / 9 = Menor = 3.88 perlas

Así, la hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.

5 0
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Biscuits Betty uses 5 1/3
Aleonysh [2.5K]
Gabby's recipe calls for 3 1/3 pounds of flour. If you divide 3 1/3 by 1/6, you get 5 measuring cups full. (1/3 is 2/6 so you add 2+3)
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3 years ago
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