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inn [45]
3 years ago
15

Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as it’s length and jointly

as its width and the square of its height. Suppose also that a beam 5 inches wide, 2 inches high and 10 feet long can support a maximum weight of 8 tons. What is the maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long
Mathematics
1 answer:
Gre4nikov [31]3 years ago
8 0

Way: W = k * w  * h^2/ L

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Answer:

The answer is below

Step-by-step explanation:

The growth of the bacteria is in the form of an exponential growth. It is given by the formula:

P(t)=ae^{rt}\\\\where\ t\ is\  the\ number\ of \ hours, P(t)\ is\ the \ population\ at\ t\ hours\\\and\ a=population\ at\ start

At 2 hours, the population is 62 cells, hence:

P(2)=ae^{2r}\\\\62=ae^{2r}\ \ .\ \ .\ \ .\ (1)

After another 2 hours (4 hours), the population is 1 million:

P(4)=ae^{4r}\\\\1000000=ae^{4r}\ \ .\ \ .\ \ .\ (2)\\\\Divide \ equation\ 2\ by\ equation\ 1:\\\\\frac{1000000}{62}=\frac{ae^{4r}}{ae^{2r}} \\\\16129=e^{2r}\\\\ln(e^{2r})=ln(16129)\\\\2r=9.688\\\\r=4.844

Put r = 4.844 in equation 1

62=ae^{2*4.844}\\\\62=16129a\\\\a=0.003844

P(t)=0.003844e^{4.844t}\\\\at \ start,t=0\\\\P(0)=0.003844

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