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2 years ago

If f(x) = 3 – 2x and g (x) = 1/x+5 , what is the value of f/g (8)?

Mathematics

1 answer:

snow_tiger [21]2 years ago

4 0

Answer:

-104/41

Step-by-step explanation:

f(8) = -13

g(8) = 41/8

f/g(8) = -13/1 / 41/8 = -(13×8) / (41×1) = -104 / 41

f/g(x) = (3-2x) / (1/x + 5) = (3-2x)/1 / ((1+5x)/x) =

= x×(3-2x) / (1+5x) = (3x - 2x²) / (1 + 5x)

for x=8 this gives the same result.

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Therefore $k= \frac{ln2 }{18}$ , A=184

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She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

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$\Rightarrow -Ae^{-18k}=138-230$

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Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

$184=230-Ae^{-k\times 36}$

$\Rightarrow Ae^{-36k}=230-184$

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Dividing (2) by (1)

$\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}$

$\Rightarrow e^{-18k}=\frac{46}{92}$

Taking ln both sides

$ln e^{-18k}=ln\frac{46}{92}$

$\Rightarrow -18k =ln (\frac12)$

$\Rightarrow -18k= ln1-ln2$

$\Rightarrow k= \frac{ln2 }{18}$

Putting the value k in equation (1)

$Ae^{-18\frac{ln2}{18}}=92$

$\Rightarrow A e^{ln2^{-1}}=92$

$\Rightarrow A.2^{-1}=92$

$\Rightarrow \frac{A}{2}=92$

$\Rightarrow A= 92 \times 2$

⇒A= 184.

Therefore $k= \frac{ln2 }{18}$ , A=184

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