1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svlad2 [7]
3 years ago
15

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

s are green kryptonite and red kryptonite, but it comes in a variety of colors. All varieties of kryptonite satisfy the modified separable kryptonite decay equation
dy/dt = y(1/t- k) for t > 0

where y is the amount of kryptonite present t hours after we begin to measure the decay of the kryptonite. After one hour, 15 grams of red kryptonite are present, but amazingly enough, after three hours, 30 grams of red kryptonite are present. Strange stuff, indeed! What is the maximum amount of red kryptonite present, and after how much time will this occur?
Mathematics
1 answer:
Rashid [163]3 years ago
3 0

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

\frac{y}{t} = e^{-kt + C}  \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt}   (A = e^{C})\\y = Ate^{-kt}

when t = 1 hour, y = 15 grams. So,

y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}(1)

when t = 3 hours, y = 30 grams. So,

y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k} (2)

dividing (2) by (1), we have

\frac{30}{15}  = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36

Substituting A and k into y, we have

y = 18.36te^{-0.203t}

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

You might be interested in
At a school fair, a box contains 36 yellow balls and 64 red balls. One-fourth of the balls of each color are
belka [17]

Answer:

The probability that a randomly selected ball labeled "Win a prize" is red is

16%

Step-by-step explanation:

I think thats correct but i dont know about the others

5 0
3 years ago
Harrison and Sherry are making decisions about their bank accounts Harrison wants to deposit $200 as a principal amount with an
AlekseyPX

Answer:

Sherry's Method of depositing $200 as a principal now with an interest at 4% compound at monthly will result in more money after two years.

Step-by-step explanation:

We use the Total Amount generated using compound interest formula to solve this question

Formula =

Total Amount(A) = P(1 + r/n)^nt

a) For Harrison

Principal = $200

Interest rate = 2% = 0.02

Time = 2 years

n = compounding quarterly = 4

A = P(1 + r/n)^nt

A = $2,000(1 + 0.02/4)^2×4

A = $2,000(0.005)^8

A = $ 2081.4140878

A = $ 2,081.41

b) For Sherry

Principal = $200

Interest rate = 4% = 0.04

Time = 2 years

n = compounding monthly = 4

A = P(1 + r/n)^nt

A = $2,000(1 + 0.04/12)^2×12

A = $2166.2859184

A = $ 2,166.29

The Total Amount for

Harrison = $ 2,081.41

Sherry = $ 2,166.29

Hence, from the above calculation, Sherry's Method of depositing $200 as a principal now with an interest at 4% compound at monthly will result in more money after two years.

7 0
3 years ago
Carlos biked 24 mi and dan 6 mi what is the ratio of the distance Carlos ran to the distance he biked
netineya [11]
Ran to biked.

24:6

Divide both sides by 6. 

4:1 <=== the answer

He biked 4 miles for every 1 mile he ran.

I hope this helps!
~kaikers 
5 0
3 years ago
Read 2 more answers
Plz help plz plz plzzzz
Fynjy0 [20]
It would be breacking down so the answer would be 3.33% :)
6 0
3 years ago
Which expression is equivalent to -4y-x-3y-9x
alukav5142 [94]

Answer:

-10x-7y hope this helps yous.

8 0
2 years ago
Read 2 more answers
Other questions:
  • Solve the following inequality algebraically. ∣x−5∣≤11
    11·1 answer
  • If 8^y=16^y+2, what is the value of y?<br> A) -8<br> B) -4<br> C) -2<br> D) -1
    9·1 answer
  • What is the slope of line P / answers: -3, 1.5, 3
    8·2 answers
  • Really really really need help PLEASE!!!!!!
    10·1 answer
  • Starting at noon, the temperature dropped steadily at a rate of 2 degrees
    5·1 answer
  • A cookie recipe uses V2 teaspoon of vanilla with 3/4 cups of flour. How
    10·1 answer
  • Find the value of b if ∛b = 2. <br> Question 17 options: <br> A) 4 B) 27 C) 16 D) 8
    7·2 answers
  • Brice has $1200 in the bank. He wants to save a total of $3000 by depositing $40 per week from his paycheck. Write and use an eq
    7·1 answer
  • Helpppppp pleaseeeeee
    8·1 answer
  • The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. Af
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!