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2 years ago

Determine the measure of

Mathematics

1 answer:

Lorico [155]2 years ago

4 0

Answer:

M: 74.579° = 74°34'43" = 1.30164

O: 49.421° = 49°25'17" = 0.86256 rad

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In a research lab, a cell biologist is growing a strain of bacteria under two different conditions. Culture A had an initial pop

zhannawk [14.2K]

Answer:

They will have the same population after 6 hours

Step-by-step explanation:

The general exponential equation format for this is;

P = P_o(e^(kt))

For Culture A, we are told that it had an initial population of 200 and doubles every hour.

Thus;

After 1 hour, P = 400

After 2 hours, P = 800

After 3 hours, P = 1600

Thus;

At t = 1, we have;

400 = 200(e^(k × 1))

400/200 = e^(k)

e^(k) = 2 - - - (eq 1)

At t = 2, we have;

800 = 200(e^(k × 2))

800/200 = e^(2k)

e^(2k) = 4 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 4/2

e^(2k - k) = 2

e^(k) = 2

k = In 2

k = 0.6931

Thus;

P = 200e^(0.6931t)

For Culture B, we are told that it had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour.

Thus;

After 1 hour, P = 409600

After 2 hours, P = 204800

After 3 hours, P = 102400

Thus;

At t = 1, we have;

409600 = 819200(e^(k × 1))

409600/819200 = e^(k)

e^(k) = 0.5 - - - (eq 1)

At t = 2, we have;

204800 = 819200(e^(k × 2))

204800/819200 = e^(2k)

e^(2k) = 0.25 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 0.25/0.5

e^(k) = 0.5

k = In 0.5

k = -0.6931

Thus;

P = 819200(e^(-0.6931t))

We want to find the time when the 2 cultures will have the same population. Thus;

200e^(0.6931t) = 819200(e^(-0.6931t))

Arranging, we have;

(e^(0.6931t))/(e^(-0.6931t)) = 819200/200

e^(0.6931t - (-0.6931t) = 4096

e^(1.3862t) = 4096

1.3862t = In 4096

1.3862t = 8.3178

t = 8.3178/1.3862

t ≈ 6 hours

3 0

4 years ago

64 for each cube there is a bigger cube that is 3/4feet on each side what is the volume in cubic feet in fraction form if necess

Contact [7]

Answer:

Step-by-step explanation:

harmful

6 0

3 years ago

Donato is 6 feet 2 inches tall. His sister is 68 inches tall. Donato is how many inches taller.

mixas84 [53]

6 inches taller

Step-by-step explanation:

There’s 12 inches in a foot. So 12•6 is 72 then plus another 2 then you get 74. Then subtract 74 by 68 and you get 6

8 0

3 years ago

Read 2 more answers

Raphael is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is-20t+

Afina-wow [57]

Answer:

Speed = 20 mi/h

Explanation:

There are two points A and B

Distance between both the points are define with function -20t + 45 miles

where t represent the number of hours of travelling.

Now firstly we find the initial position. At starting time is 0, so we put t=0 in given function of t.

At t=0;

d₀ = -20(0) + 45 = 0 + 45 = 45 miles

Now we find the distance travell after starting first hour.

Than we put t = 1 in the given function

At t = 1;

d₁ = -20(1) + 45 = -20 + 45 = 25 miles

Difference between d₁ & d₀ is

45 - 25 = 20 miles

We see that in one hour, total distace is covered 20 miles

Now we use time, speed, distance relation

Speed = $\frac{distance}{time}$

S = $\frac{20}{1}$

S = 20 miles/hour

That's the final answer.

I hope it will help you.

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3 years ago

HELP PLZZZ HURRY !!! Which word is an antonym of the underlined word in the paragraph?

PtichkaEL [24]

Step-by-step explanation:

I'm guessing the underlined word is hail, if it's not then let me know.

8 0

3 years ago