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3 years ago

How many feet are in 84 yards. (im really bad at converting) :(

Mathematics

2 answers:

Gre4nikov [31]3 years ago

7 0

1 yard = 3 feet, so we would do 3×84, which is 252.

There are 252 feet in 84 yards.

lisov135 [29]3 years ago

3 0

Do I have a trick for you then!

First, you will need a knowledge of fractions. I'm sure you do.

Now, search up how many feet are in a single yard. I Googled it and I got 1 yard = 3 feet.

Now let's make a fraction out of that. 1 yard / 3 feet.

You can do 3 feet / 1 yard if you want to. They are both equal to each other.

Now we need to convert the 84 yards into a fraction.

Simply make the 84 yards over 1. 84 yards / 1.

Now we need to multiply these two fractions in a way that will cancel out the yards unit and leave us with only the feet units.

84 yards/1 * 3 feet/1 yard

The reason why I switched from using 1 yard/3 feet to 3 feet/1 yard is because in that setup the yards unit would cancel and leave us only with the feet units.

84 yards / 1 * 3 feet / 1 yard = 252 feet

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3 years ago

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3 years ago

Read 2 more answers

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

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3 years ago

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Step-by-step explanation:

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While Bob on the other hand rounded to the nearest tenth. Which resulted in the number going down because the number in the hundredth place value was less than 5.

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