Jim writes 10^4 words every day how many words does he writes in 10^3 days?

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

Rashid [163]

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

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

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

3 0

3 years ago

8. Bella has 6.3 kilograms of berries. She packs 0.35 kilogram of berries into each

vovangra [49]

Answer:

If my math is correct it should be $53.82

Step-by-step explanation:

You Divide 6.3kg by 0.35kg that would give you 18. Then you multiply $2.99 by 18 and that should get you $53.82

7 0

2 years ago

Solve the system using substitution: y = -6x + 7 3x – 2y = 16 helppp

bearhunter [10]

Answer:

x=-6 y=-1

Step-by-step explanation:

// Solve equation [2] for the variable y

[2] y = -x - 7

// Plug this in for variable y in equation [1]

[1] 3x - 2•(-x -7) = -16

[1] 5x = -30

// Solve equation [1] for the variable x

[1] 5x = - 30

[1] x = - 6

// By now we know this much :

x = -6

y = -x-7

// Use the x value to solve for y

y = -(-6)-7 = -1

Solution :

{x,y} = {-6,-1}

7 0

2 years ago

Read 2 more answers

Consider the table representing an exponential function.

Gnesinka [82]

Answer: f(x) is just a fancy way of writing y in an equation

Step-by-step explanation:

Example: f(x)= 2x+4 is the same as y= 2x+4

8 0

3 years ago

5y + 3 > −7y + 13 Multi-step linear inequalities

Artemon [7]

Answer:

y > $\frac{5}{6}$

Step-by-step explanation:

Given

5y + 3 > - 7y + 13 ( add 7y to both sides )

12y + 3 > 13 ( subtract 3 from both sides )

12y > 10 ( divide both sides by 12 )

y > $\frac{10}{12}$ , that is

y > $\frac{5}{6}$

3 0

3 years ago

Jim writes 10^4 words every day how many words does he writes in 10^3 days?​

Jim writes 10^4 words every day how many words does he writes in 10^3 days?