You have 2000 grams of substance A which has decay constant 0.03, and you have 3000 grams of substance B, which has decay constant 0.05. After how many years will the amounts of the two substances be equal?

Answers

Answer 1

Answer:

If you have a quantity X of a substance, with a decay constant r, then the equation that tells you the amount of substance that you have, at a time t, is:

C(t) = X*e^(-r*t)

Now, we know that:

We have 2000g of substance A, and it has a decay constant of 0.03 (i assume that is in 1/year because the question asks in years)

And we have 3000 grams of substance B, with a decay constant of 0.05.

Then the equations for both of them will be:

Ca = 2000g*e^(-0.03*t)

Cb = 3000g*e^(-0.05*t)

Where t is in years.

We want to find the value of t such that Ca = Cb.

So we need to solve:

2000g*e^(-0.03*t) = 3000g*e^(-0.05*t)

e^(-0.03*t) = (3/2)e^(-0.05*t)

e^(-0.03*t)/e^(-0.05*t) = 3/2

e^(t*(0.05 - 0.03))  = 3/2

e^(t*0.02) = 3/2

Now we can apply Ln(x) to both sides, and get:

Ln(e^(t*0.02)) = Ln(3/2)

t*0.02 = Ln(3/2)

t = Ln(3/2)/0.02 = 20.3

Then after 20.3 years, both substances will have the same mass.


Related Questions

which mortal kombat character is yalls favorite? Mine is kabal.

Answers

Answer:

omg! mine is Kabal tooo

Step-by-step explanation: i love mortal combat lol

Answer:

Scorpion

I am a normie yes I know

Leave me alone

Step-by-step explanation:

HURRY 65 POINTS


consider the reduction of the rectangle.

A larger rectangle has a length of 18 inches and width of 8 inches. A smaller rectangle has a length of x inches and width of 3 inches.

Write a proportion and then solve to find the missing measure of the reduced rectangle.

What two ratios can be used in the proportion?


What is the value of the missing measure?

Answers

Answer:

18/8 = x/3

x = 6.75 inches (length)

Step-by-step explanation:

A larger rectangle has a length of 18 inches and width of 8 inches.

Inches /width = 18/8

So, for a rectangle that has a length of x inches and width of 3 inches the ratio is :

x/3

Solving for x:

18/8 = x/3

18/8 (3) =x

6.75 in= x

Feel free to ask for more if needed or if you did not understand something.

it’s us 6.75in=x have a good day

-8x-x=x-4x plz find for x

Answers

Answer: x=0

Step-by-step explanation:

In Mrs. Madison's math classes, 15% of the students have an ‘A’. If 18 students have an ‘A’, how many students are in Mrs. Madison’s math classes? [Type your answer as a number.]

Answers

Answer:

The correct answer is 120 students!

Step-by-step explanation:

There is a proportion you need to write down to solve it but i don’t know how to write it on here!

How much will a cup of coffee that is $5.15 cost with 5% sales tax?

Answers

Answer:

It will cost $5.41

Step-by-step explanation:

You would take 5% of 5.15 since that is the price of the coffee with is about 0.26 cent than you add that to the cost of the coffee.

find the exact values of the six trigonometric functions of 0

Answers

Complete question is;

Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(-5,-4).

Answer:

Sin θ = -4/√41

Cos θ = -5/√41

tan θ = 4/5

Cosec θ = (√41)/-4

Sec θ = (√41)/-5

Cot θ = 5/4

Step-by-step explanation:

Now, we are given the point (-5, -4)

These are x and y points.

They will form a triangle and we know that from pythagoras theorem;

x² + y² = r²

Where r is the distance between the point and the origin

Thus;

r² = (-5)² + (-4)²

r² = 25 + 16

r = √41

So, y is the opposite side of the triangle while x is the adjacent side with r being the hypotenuse.

Thus, the trigonometric ratios are;

Sin θ = opp/hyp = -4/√41

Cos θ = adj/hyp = -5/√41

tan θ = opp/adj = -4/-5 = 4/5

Cosec θ = 1/Sin θ = 1/(-4/√41) = (√41)/-4

Sec θ = 1/cos θ = 1/(-5/√41) = (√41)/-5

Cot θ = 1/tan θ = 1/(4/5) = 5/4

Examine the diagram. It is not drawn to scale.
What is the m3?
m3 =_____°​

Answers

Answer:

105

Step-by-step explanation:

180 - 75 = 105

Answer:  

copy and paste this  link that imma put under your question I’m not really good at this but this video no cap help and others sorry hope this helps

A 120 pack of paper towels last 1/2 a year. How many paper towels per month did we use

Answers

Answer:

20

Step-by-step explanation:

Because if 120 lasts 1/2 a year which is equivalent to 6 months you do 120 divided by 6 and get 20 hope this helps

Answer:

120/6 = 20 paper towels per month

Step-by-step explanation:

half a year is 6 months

120 divided by 6 is 20

Please help answer I’ll give brainliest

Answers

Answer:

ok i'll help just send me the question :)

Step-by-step explanation:

Answer:

what's wrong

Step-by-step explanation:

The sum of three consecutive integers is more than 62. Write an inequality to represent the above
situation then solve your inequality.

Answers

Given:

Sum of three consecutive integers is more than 62.

To find:

The inequality to represent the above  situation then solve your inequality.

Solution:

Let the three consecutive integers are [tex]x,x+1,x+2[/tex] respectively.

Sum of three consecutive integers is more than 62. So,

[tex]x+(x+1)+(x+2)>62[/tex]

[tex]3x+3>62[/tex]

Subtract 3 from both sides.

[tex]3x>62-3[/tex]

[tex]3x>59[/tex]

Divide both sides by 3.

[tex]x>\dfrac{59}{3}[/tex]

Therefore, the required inequality is [tex]x+(x+1)+(x+2)>62[/tex] and solution is [tex]x>\dfrac{59}{3}[/tex].

There are 52 cars in the movie theater parking lot. 12 more cars parked in the parking lot before the movie started but 3 cars left. How many cars are in the parking lot

Answers

Answer:

61

Step-by-step explanation:

52 + 12 = 64

64-3 that left is 62 cars in the parking lot

There are 61 cars in the parking lot.

52 + 12 = 64

64  -  3 = 61

I hope this helps, if it did, please mark brainliest and have an amazing rest of your day. Stay safe! xx

How many wholes are in 1/8?

Answers

Answer:

There are NO wholes in 1/8.

If it were 8/8, then it would be equal to 1 whole. Since it is only 1/8, there is non wholes.

Drag the tiles to the boxes to form correct pairs.
Match the trigonometric expressions to their solutions.

Answers

Answer:

1) cos (140°-(50°+30°)) = 1/2

2)  [tex]sin255^{\circ}=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

3)  [tex]cos150^{\circ}=-\frac{ \sqrt{3} }{2}[/tex]

4) ,  [tex]tan 240^{\circ}=\sqrt{3}[/tex]

Step-by-step explanation:

1) cos (140°-(50°+30°))

Solving:

cos (140°-(50°+30°))

=cos(140°-80°)

=cos(60°)

=1/2

So, cos (140°-(50°+30°)) = 1/2

2) sin 255°

We can write sin 255° as sin(180°+75°)

Solving sing formula sin(a+b)=sin(a)cos(y)+cos(x)sin(y)

[tex]sin(180^{\circ}+75^{\circ})\\=sin(180^{\circ})cos(75^{\circ})+cos(180^{\circ})sin(75^{\circ})\\=0(cos(75^{\circ}))+(-1)(\frac{\sqrt{2}+\sqrt{6} }{\sqrt{4} } )\\=0+(-1)(\frac{\sqrt{2}+\sqrt{6} }{\sqrt{4} } )\\\=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

So, [tex]sin255^{\circ}=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

3) cos 150°

We can solve this using the identity: cos(x)=sin(90°-x)

Solving:

cos 150°= sin(90°-150°)

=sin(-60°)

We know sin(-x)=-sin(x)

=-sin(60°)

=[tex]-\frac{ \sqrt{3} }{2}[/tex]

So, we get [tex]cos150^{\circ}=-\frac{ \sqrt{3} }{2}[/tex]

4) tan 240°

We know tan(180°+x)=tan(x)

tan 240° can be written as tan(180°+60°)

Using the above identity:

tan(180°+60°)=tan(60°) = [tex]\sqrt{3}[/tex]

So,  [tex]tan 240^{\circ}=\sqrt{3}[/tex]

Answer:

here ya go

Step-by-step explanation:

By what number must you multiply a quantity in order to increase it by 25% in a single step?

Answers

Answer:

5/4

Step-by-step explanation:

Lets suppose a quantity A that has a value of x

A = x

25% of A is = x/4

now adding this 25% to get 25% increase in the original value

A' = x+ x/4

    A' = 5x/4

    A' = 5*A/4

This means that , in order to increase the value by 25%  in a single step we must multiply the the original value by 5/4.

The sum of the measures of two exterior angles of a triangle is 257. What is the measure of the third exterior angle?

Answers

The measurement of the third exterior angle is 105°

What is a hectoliter?

1,000 liters
100 grams
1/100 of a liter
100 liters

Answers

Answer:

100 litres

Step-by-step explanation:

Answer:

It is 100 liters

Step-by-step explanation:

I hope it helps lol

53 students divided into groups of 6 students how many groups of students will there be?

Answers

Answer:

9

Step-by-step explanation:

53/6 = 8 R5

One of the groups will have only 5 students because you can only have whole students, not parts of a student.

Answer:

Step-by-step explanation:

53/6= 8 5/6

The first 6 groups will have 8 students with 5 students remaining. They can have 5 groups with 9 students and 1 with 8 students

Lisa cleans 6 apartments in 2.5 hours. If Lisa cleans 30 apartments at this same rate how long will it take her?

Answers

Answer:

12.5 hours

Step-by-step explanation:

 

Answer:

it will take Lisa 12.5 hours

Step-by-step explanation:

first figure out how many minutes it takes her per apartment.

in 2.5 hours is 150 minutes so divide 150 by 6 = 25

So, it takes her 25 minutes per apartment.

next, find out how many minutes it takes her to clean 30 apartments by:

30* 25= 750 minutes for 30 partments

divide 750 by 60 to find out how many hours

12.5 hours.

what fraction of 9hours 30minutes​

Answers

9.500, hope this help!

From data gathered in the period 2008−2012, the yearly value of U.S. exports can be modeled by the function E(x) = −228x3 + 2,252.8x2 − 6,098.5x + 11,425.8 where x is the number of years after 2008 and E(x) is the value of exports in billions of dollars. The yearly value of U.S. imports can be modeled by the function I(x) = −400.4x3 + 3,954.4x2 − 11,128.8x + 17,749.6 where x is the number of years after 2008 and I(x) is the value of imports in billions of dollars. Estimate the total value the U.S. imported and exported in 2011. Round to the nearest whole number. About billion dollars were imported and exported by the U.S. in 2011.

Answers

Answer:you got this:)

Step-by-step explanation:

4/9 x ? =1 what is the answer

Answers

Answer:

Step-by-step explanation:

X=2.25

Ur welcome

Answer:

Step-by-step explanation:

4/9*x=1

x=9/4 The reciprocal of 4/9 is 9/4 and makes 1 whole.

**reciprocal is a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity

archibald is so excited that he earned $200 but then uncle ramon reminds archibald he borrowed $210 for his last adventure. after archibald pays uncle ramon all that he made is the debt settled

Answers

Answer:

Um finish the question but if its how much does he have left, its none.

Step-by-step explanation:

Didn't finish question and the reason why it's none well (-10), is because he had $200.000 than got 200=10 taken away.

In how many different ways can five children hold hands to play "Ring Around the Rosy"?

Answers

Answer:

Step-by-step explanation:

25

There are 1082 orders that the children can hold hands in while spinning.

2. What is the thickness of the sediment along the east coast of North
America? I

Answers

The thickness of the sediment along the east coast of the the north is .2km

At noon, a tank contained 10 cm of water. After several hours, it contained 7 cm of water. What is the percent decrease of water in the tank?

Please answer with explanation.

Answers

The tank decreased from 10 cm to 7 cm, so the tank lost 3 cm of water.
So 30%.was lost

Answer:

10cm - 7cm = 3cm

this 3cm is the decrease in the depth of water, let us find the percentage decrease.

%decrease=(decrease÷original depth) × 100%

%decreas=(3cm÷10cm)×100%

therefore we get 30%

Pls help‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️‍♀️

Answers

It would be $4.05
Hope this helps
4.05 shall Be the correct answer

Mya runs around a 400 m track at a constant speed of 250 m/min. how many minutes does it take Mya to complete four laps of the track

Answers

Answer:

6.4 laps

Step-by-step explanation:

Hi , the answer I choose was wrong , what is the correct answer ? Will choose brainlest so be quick

Answers

Answer:

SAS

Step-by-step explanation:

Answer:

it’s the first one

Step-by-step explanation:

Plsss hellpppp 14 and 15 plsssssss

Answers

Answer:

14). 2nd quadrant

15). 1st quadrant

Step-by-step explanation:

14).Coordinates of a point → J(-8, -12)

    Coordinates of the new point J' after reflection of x-axis will follow the rule,

    (x, y) → (x, -y)

    Coordinates of J' → (-8, 12)

    Therefore, point J' will lie in 2nd quadrant.

15). Coordinates of a point → W(-6, 7)

    Rule for the rotation by 90°clockwise about the origin,

    (x, y) → (y, -x)

    Coordinates of point W → (-6, 7)

    Following this rule,

    W(-6, 7) → W'(7, 6)

    Therefore, point W' will lie in the first quadrant.

What is the area of the garden

Answers

Answer:

C) 1022 1/4 square feet

Step-by-step explanation:

2L+2W=134 (perimeter)

23.5*2+2L=134

L=(134-47)/2

L=87/2=43.5 feet

A=L*W

A=(43.5)*(23.5) ft squared

A=1022.25 square feet

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