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Wewaii [24]
2 years ago
6

in one hour, the human body processes about 11.5% of the caffeine in the blood. if your teacher drank a cup of coffee with 175 m

g of caffeine 3 hours ago, how much caffeine remains in her blood
Mathematics
1 answer:
Y_Kistochka [10]2 years ago
3 0

121.3 grams of caffeine is remaining in her blood

<h3>How to determine the amount of caffeine?</h3>

The given parameters are:

  • Initial, a = 175 mg
  • Rate, r = 11.5%
  • Time, t = 3 hours

The amount of caffeine is calculated as:

A(t) = a(1 - r)^t

This gives

A(t) = 175 * (1 - 11.5%)^t

At 3 hours, we have:

A(3) = 175 * (1 - 11.5%)^3

Evaluate

A(3) = 121.3

Hence, 121.3 grams of caffeine is remaining in her blood

Read more about exponential functions at:

brainly.com/question/2456547

#SPJ1

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Answer:

\huge\boxed{  \red{ \boxed{ \tt{ \frac{ {y}^{2} }{ {10}^{2} }  -  \frac{ {x}^{2} }{ {12}^{2} }  = 1}}}}

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • conic sections
  • PEMDAS
<h3>tips and formulas:</h3>
  • \sf hyperbola \:equation :  \\  \sf  \frac{ {x}^{2} }{ {a}^{2} }   -  \frac{ {y}^{2} }{ {b}^{2} }  = 1
  • vertices of hyperbola:(±a,0) and (0,±b) if reversed
  • \sf \: asymptotes :  \\ y =   \pm\frac{b}{a} x
<h3>given:</h3>
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  • the hyperbola equation is inversed since the vertices is (0,±10)
  • asymptotes:\pm \frac{5}{6}x
<h3>let's solve:</h3>
  • the asymptotes are in simplest and we know b is ±10

according to the question

  1. y =  \sf  \frac{5 \times 2}{6 \times 2} x \\ y =  \frac{10}{12} x

therefore we got

  • a=12
  • b=10

note: the equation will be inversed

let's create the equation:

  1. \sf substitute \: the \: value \: of \: a \: and \: b :  \\  \sf  \frac{ {y}^{2} }{ {10}^{2} }  -  \frac{ {x}^{2} }{ {12}^{2} }  = 1

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