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4 years ago

7

Thelma and Vivian are running a race. Thelma runs the first 50 meters in 30 seconds. Vivian runs the first 21 meters in 14 secon

ds. If they continue running at the same rates throughout the race, who will win?

1 answer:

sladkih [1.3K]4 years ago

7 0

The person who would win would be thelma

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Precalculus. Please look at the picture

erik [133]

Answer:

<u>Exponential model</u>

$y=Ae^{rt}$

where:

y = value at "t" time
A = initial value
r = rate of growth/decay
t = time (in years)

<h3><u>Part (a)</u></h3>

Given:

y = 100 g
t = 0 years

Substituting given values into the formula and solving for A:

$\begin{aligned}y & =Ae^{rt}\\\implies 100 & = Ae^{r \times 0}\\100 & = Ae^0\\100 & = A(1)\\A & = 100\end{aligned}$

<h3><u>Part (b)</u></h3>

Given:

A = 100 g
y = 50 g when t = 30.17

Substituting the given values into the equation and solving for r:

$\begin{aligned}y& =Ae^{rt}\\\\\implies 50 & =100e^{30.17r}\\\\\dfrac{1}{2} & = e^{30.17r}\\\\ln \dfrac{1}{2} & = \ln e^{30.17r}\\\\\ln 1-\ln2 & =30.17r \ln e\\\\0-\ln 2 & =30.17r(1)\\\\-\ln 2 & =30.17r\\\\r & = \dfrac{-\ln 2}{30.17}\end{aligned}$

Therefore, the final equation is:

$y=100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}$

<h3><u>Question 1</u></h3>

<u>Part (a)</u>

Q: From 100g how much remains in 80 years?

$\begin{aligned}t=80 \implies y & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)80}\\& = 15.91389949 \: \sf g\end{aligned}$

<u>Part (b)</u>

Q: How long will it take to have 10% remaining?

10% of 100 g = 10 g

$\begin{aligned}y=10 \implies 10 & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\dfrac{1}{10} & =e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln \dfrac{1}{10} & =\ln e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln 1 - \ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t\ln e\\\\0 - \ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t(1)\\\\-\ln 10 & =\left(-\dfrac{\ln 2}{30.17}\right)t\\\\t & = \dfrac{- \ln 10}{\left(-\dfrac{\ln 2}{30.17}\right)}\\\\t & = 100.2225706\: \sf years\end{aligned}$

<h3><u>Question 2</u></h3>

<u>Part (a)</u>

Q: How much remains after 50 years (time)?

<u></u>

$\begin{aligned}t=50 \implies y & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)50}\\& = 31.70373153 \: \sf g\end{aligned}$

<u>Part (b)</u>

Q: How long to reach 20 g (amount remaining)?

<u></u> $\begin{aligned}y=20 \implies 20 & =100e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\dfrac{1}{5} & =e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln \dfrac{1}{5} & =\ln e^{\left(-\dfrac{\ln 2}{30.17}\right)t}\\\\\ln 1 - \ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t\ln e\\\\0 - \ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t(1)\\\\-\ln 5 & =\left(-\dfrac{\ln 2}{30.17}\right)t\\\\t & = \dfrac{- \ln 5}{\left(-\dfrac{\ln 2}{30.17}\right)}\\\\t & = 70.05257062\: \sf years\end{aligned}$

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2 years ago

How many different ways can the first ten letters of the alphabet be arranged

OleMash [197]

The first ten letters of the alphabet can be arranged 3,628,8000 different ways.

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3 years ago

The temperature started at 87 degrees Fahrenheit is the temperature went down 10 degrees Fahrenheit then went up 17 degrees Fahr

SIZIF [17.4K]

Answer:

i think the answer is D

Step-by-step explanation:

87 degrees minus 10 degrees would give you 77 (which is the lowest temperature). then 77 degrees plus 17 degrees is 94 degrees. the difference between the highest temp and lowest (94-77) would be 17.

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3 years ago

The endpoints of a segment are (4,2) and (-2,2). What are the endpoints of the segment after it has been translated 6 units down

Yuki888 [10]

(4,-4) and (-2,-4)

hope that helps!

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3 years ago

Samira needs 22 quarts of lemonade to fill a dispenser. She plans to buy 7 jugs of lemonade. Each jug contains 3.3 quarts.

-BARSIC- [3]

I think its b iam not to sure i have the same question myself

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3 years ago

Read 2 more answers