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2 years ago

If 40q=p+p÷3+p÷9+p÷27 find the ratio of q to p help please I don't get it.

Mathematics

1 answer:

8_murik_8 [283]2 years ago

8 0

We must follow "PEMDAS" rules for "order of operations."

Multiplication and division must be done before addition and subtraction:

40q = p + (p/3) + (p/9) + p/27

The LCD of this expression is 27. 1, 3 and 9 all divide evenly into 27. The equation thus becomes:

27(40q) = 27p + 9p + 3p + p

Adding up the four "p" terms, we get 40p. Then 27(40q) = 40p.

Simplifying thru division by 40, 27q = p. Alternatively, p = 27q.

Find the ratio of p to q by dividing both sides by q: (p/q) = 27 (answer)

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Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

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$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

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