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11111nata11111 [884]
3 years ago
14

$34,300 loan at 3.5% for 4 months.

Mathematics
1 answer:
cestrela7 [59]3 years ago
5 0

keeping in mind that 4 months is not even a year, since there are 12 months in a year, 4 months is then 4/12 years.

let's assume is simple interest.


\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$34300\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ A=34300\left[ 1+(0.035)\left( \frac{1}{3} \right) \right]\implies A= 34300(1.011\overline{6})\implies A=34700.1\overline{6}

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Answer:

a) m =589.734kg

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Step-by-step explanation:

The first step is to calculate the maximum load after safety considerations (T_{max}

Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate (T_{max} we multiply this value by \frac{2}{3} (as per the given safety consideration.

Hence

T_{max} = \frac{2}{3} (19500) \\ T_{max} = 13000N

a) Now to find the maximum load in kgs, we use the following formula

(m_{0} + m)(g + a) = T_{max}

Where

m_{0} = mass of elevator

m = maximum load

g = acceleration due to gravity

a = maximum acceleration of elevator

Inputting the values and solving

m_{0} + m)(g + a) = T_{max}\\ (490 + m)(9.8 + 2.24) = 13000\\ 12.04m = 7100.4\\ m = 589.734kg

Hence the maximum load is m =589.734kg

b) To find the number of people (n) we divide the value of m by 70kg

n = 589.734 / 70

n = 8.42 or 8 people

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