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3 years ago

The diameter of a circle is 15in. Find the circumference to the nearest tenth (urgent)

Mathematics

2 answers:

givi [52]3 years ago

7 0

Answer:

I believe it is 47.1

ivann1987 [24]3 years ago

3 0

Answer:

Answer is 47 inches.

Answer is rounded to the nearest tenth place.

Step-by-step explanation:

$given \: that \: \\ diameter \: of \: circle \: = 15 \: in \\ we \: know \: that \: \\ circumference \: of \: circle \: = d\pi \\ on \: substitutig \: d \: = 15 \: in \: \\ in \: the \: formula \: we \: get \\ circumference \: of \: circle \: = 15\pi \\ substitute \: \pi = 3.14 \\ = 5 \times 3.14 \\ = 47.123 \\ when \: the \: answer \: is \: rounded \: to \ \\ the \: nearest \: tenth \: we \: \\ get \: 47 \: in \: as \: the \: answer.$

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3 years ago

For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

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

$P=4700$

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

$t=9 \:years$

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

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

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