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Leona [35]
3 years ago
6

What is 3.2 x 10^-4 m/h in centimeters per second?

Mathematics
1 answer:
Iteru [2.4K]3 years ago
4 0
1m=100cm\\h=3600s\\\\3.2\times10^{-4}\ m/h=3.2\times10^{-4}\times\frac{100}{3600}\ cm/s\\\\=3.2\times10^{-4}\times\frac{1}{36}\ m/s=\frac{3.2}{36}\times10^{-4}\ m/s\\\\=0.888...\times10^{-4}\ m/s=\boxed{8.889\times10^{-5}\ m/s}\\\\Answer:\boxed{b)}
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a) identity property of multiplication

b) commutative property in addition

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Find r(t) if r'(t)=ti+e^tj+te^tk and r(0)=i+j+k
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How long will it take for an investment to triple, if interest is compounded continuously at 8%?
maw [93]

Answer:

<em>It will take 14 years before the investment triples</em>

Step-by-step explanation:

<u>Continuous Compounding</u>

Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.

The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

FV = PV\cdot e^{i.t}

Where:

FV = Future value of the investment

PV = Present value of the investment

i     = Interest rate

t     = Time

It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.

Substituting the known values:

3PV = PV\cdot e^{i.t}

Dividing by PV:

3 = e^{i.t}

Taking logarithms:

\ln 3=i.t

Solving for t:

\displaystyle t=\frac{\ln 3}{i}

\displaystyle t=\frac{\ln 3}{0.08}

t = 13.7 years

Rounding up:

It will take 14 years before the investment triples

6 0
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