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Rainbow [258]
2 years ago
12

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

Mathematics
1 answer:
Alchen [17]2 years ago
7 0
1,000 words

10^4=10,000
10^3=1,000
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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

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

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

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2 years ago
Solve the system using substitution:<br> y = -6x + 7<br><br> 3x – 2y = 16<br><br> 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

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// Solve equation [1] for the variable  x  

  [1]    5x = - 30  

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// 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}

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2 years ago
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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

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Artemon [7]

Answer:

y > \frac{5}{6}

Step-by-step explanation:

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

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y > \frac{5}{6}

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3 years ago
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