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Tanya [424]
3 years ago
12

Sarah paid $18,444 for a new car last week. This price was 6 percent above the vehicle’s invoice price. What was the dollar amou

nt of the invoice price?
Mathematics
2 answers:
Anastasy [175]3 years ago
7 0

Answer:

vehicle's invoice price is:

$17,400

Step-by-step explanation:

Sarah paid $18,444 for a new car last week.

This price was 6 percent above the vehicle’s invoice price.

Let the vehicle's invoice price be x.

⇒ \dfrac{100+6}{100}\times  x=18444

⇒ \dfrac{106}{100}\times x=18444

⇒ x=\dfrac{100}{106}\times 18444

⇒ x=17400

Hence,  vehicle's invoice price is:

$ 17,400

Phoenix [80]3 years ago
4 0
$18,444/(100+6)=$174 is amount of one percent
$174*100=$17,400 is vehicle's invoice price
Vehicle's invoice price is $17,400

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A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum
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Answer:

Differential equation

\frac{dy}{dt} =ky(1-y)

Solution

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Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

\frac{dy}{dt} =ky(1-y)

Solving the differential equation

\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}

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y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48

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