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mr Goodwill [35]

3 years ago

9

Quincy is trying to estimate the height of a tree in his backyard. He measures the tree’s shadow as 12 ft. He stands near the tr

ee and measures his own shadow as 5 ft. Quincy knows that he is 4 ft tall how tall is the tree what ratio can he use to find the height

1 answer:

marishachu [46]3 years ago

8 0

Write this as a large fraction, meaning one number over top the other number. The answer is "12/x = 5/4"

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A bag contains 4 red marbles, 3 blue marbles and 7 green marbles. If three marbles

shepuryov [24]

Answer:

20%

Step-by-step explanation:

4+3+7=14

14÷7=2

2×10=20

If I am wrong please tell me I haven't had to do this me method in 3 years

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3 years ago

Kali trains for a race by running around a track. Each lap around the track is 400 meters . She runs 4 kilometers each day how m

Savatey [412]

30 laps is the definite answer to the question

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3 years ago

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.

6 0

4 years ago

Someone pls help it’s for my exams

Anna35 [415]

Answer:

Step-by-step explanation:

you know that both angles=180

6x+20+2x+4=180

8x+24=180

8x=180-24

8x=156

x=19.5

angle TQS=19.5*60+20=137

angle SQR=2*19.5+4=43

6 0

3 years ago

A group of 24 students have recess together. They are making teams to play a game. Each team has to have exactly 5 players, and

AysviL [449]

They can make 4 teams and have 4 players that won’t be in a team.

This is because 5*5 is 25 but they don’t have 25 players so you would have to go down which is 4*5=20. Sorry if that’s very confusing but hope that helps!

5 0

3 years ago