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MAXImum [283]
3 years ago
12

Calculate the distance between points A(4, 6) and B(-3, 9)

Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

Step-by-step explanation:

Hey there!

The points are; A(4,6) and B(-3,9).

<u>Using</u><u> </u><u>distance formula</u><u>,</u>

<u>d =  \sqrt{ {(x2 - x1)}^{2} +  {(y2 - y1)}^{2}  }</u>

<u>Putc</u><u> </u><u>all</u><u> </u><u>values</u><u> </u><u>.</u>

<u>d =  \sqrt{ {( - 3 - 4)}^{2} + ( {9 - 6)}^{2}  }</u>

<u>Simplify</u><u> </u><u>it</u><u>.</u>

<u>d =  \sqrt{ {( - 7)}^{2} +  {3}^{2}  }</u>

<u>d =  \sqrt{49 + 9}</u>

<u>= \sqrt{58}</u>

<u>Therefore the</u><u> </u><u>distance</u><u> </u><u>between two points</u><u> </u><u>is</u><u> </u><u>root</u><u> </u><u>5</u><u>8</u><u> </u><u>units</u><u> </u><u>Or</u><u> </u><u>7</u><u>.</u><u>6</u><u>1</u><u> </u><u>units</u><u>. </u>

<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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To model this situation, we are going to use the decay formula: A=Pe^{rt}
where 
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P is the initial population 
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r is the decay rate 
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A. We know for our problem that the initial population is 1,250, so P=1250; we also know that after a year the population is 1000, so A=1000 and t=1. Lets replace those values in our formula to find r:
A=Pe^{rt}
1000=1250e^{r}
e^{r}= \frac{1000}{1250}
e^{r}= \frac{4}{5}
ln(e^{r})=ln( \frac{4}{5} )
r=ln( \frac{4}{5} )
r=-02231

Now that we have r, we can write a function to model this scenario:
A(t)=1250e^{-0.2231t}.

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C. 
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- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0: 
A(0)=1250e^{(-0.2231)(0)
A_{0}=1250e^{0}
A_{0}=1250
- Over the interval [0,10], the function will have a minimum at t=10:
A(10)=1250e^{(-0.2231)(10)
A_{10}=134.28

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: m= \frac{A(0)-A(10)}{10-0}
where 
m is the rate of change 
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A(0) is the function evaluated at 0
We know from previous calculations that A(10)=134.28 and A(0)=1250, so lets replace those values in our formula to find m:
m= \frac{134.28-1250}{10-0}
m= \frac{-1115.72}{10}
m=-111.572
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

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It took Kelly 5 2/3 hours to fly from City A to City B then it took her another 2 3/5hours to fly from City B toCity C. Kelly fl
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Answer:

eto na po

Step-by-step explanation:

5 2/3 × 2 3/5 = 5 6/15 answer

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2 years ago
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Vertically opposite angles are always equal.

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4^-3 * 3^4 * 4^2 = 4^-1 * 3^4

(4^-1 * 3^4)/(4^-2 * 3^5)

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Answer:

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Step-by-step explan2ation:

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