Answer:
The differential equation which describes the mixing process is [tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex].
Step-by-step explanation:
The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:
[tex]\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}[/tex]
Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:
[tex]\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}[/tex]
Given that [tex]\dot V_{water, in, 1} = 9\,\frac{L}{min}[/tex], [tex]\dot V_{water, in, 2} = 7\,\frac{L}{min}[/tex], [tex]c_{salt,in,1} = 0.04\,\frac{kg}{L}[/tex], [tex]c_{salt, in, 2} = 0.05\,\frac{kg}{L}[/tex], [tex]\dot V_{water, out} = 16\,\frac{L}{min}[/tex] and [tex]V_{tank} = 1000\,L[/tex], the differential equation that describes the system is:
[tex]0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}[/tex]
[tex]1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71[/tex]
[tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex]
What is 576 times 36?
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
JK = LM (equidistant from centre)
3x+19=6x+7
19-7=6x-3x
12 = 3x
Dividing both sides by 3
x = 4
JK = 3(4)+19
JK = 12+19
JK = 31
Answer:
31
Step-by-step explanation:
JK = LM (since they are equidistant from centre)
3x + 19 = 6x + 7
- 3x = - 12
x = 4
JK = 3 * (4) + 19
= 12 + 19
= 31
Hope this helps!
how does one convert meters to hectares?
Step-by-step explanation:
Meters measures length, hectares measures area.
1 hectare = 10,000 m²
Answer Meters measures length, hectares measures area.
1 hectare = 10,000 m²
Step-by-step explanation:
Hurry please !!!
The graph of g(x) is a translation of y = V.
Which equation represents g(x)?
ly
g(x) = - 4
5
4
g(x) = 3/X+4
3
27
900)
O g(x) = 5x +1.5
1
g(x) = -1.5
-10 -3 -6 -21
2
6
810
X
Answer:
The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]
which is the first option in your list of possible answers
Step-by-step explanation:
Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.
Recall that horizontal translations are performed by subtracting from the independent variable (x) , the number of units you move (in this case 4)
Therefore the new function should look like:
[tex]g(x)=\sqrt[3]{x-4}[/tex]
The answer is A.
did the test
The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.) Obtain P(X ≤ 5) by using the Cumulative Poisson Probabilities What is the probability that X exceeds its mean value by more than one standard deviation?
Answer:
a. P(X ≤ 5) = 0.999
b. P(X > λ+λ) = P(X > 2) = 0.080
Step-by-step explanation:
We model this randome variable with a Poisson distribution, with parameter λ=1.
We have to calculate, using this distribution, P(X ≤ 5).
The probability of k pipeline failures can be calculated with the following equation:
[tex]P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k![/tex]
Then, we can calculate P(X ≤ 5) as:
[tex]P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999[/tex]
The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:
[tex]P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080[/tex]
1. Divide $13 by 42.
O A. 12/13
B. 142
c. 13/12
D. %16
Answer:
To get your answer, you need to fix the typos, but the answer is gonna be the closest thing to 13/42 if that is the real value
Step-by-step explanation:
none of these answers are anywhere near to 13/42
The zeros of a function P(x)=x2-2x-24
Answer:
x = -4 and x = 6
Step-by-step explanation:
Factor using AC method.
1 × -24 = -24
Factors of -24 that add up to -2 are +4 and -6.
P(x) = (x + 4) (x − 6)
Therefore, zeroes of P(x) are x = -4 and 6.
What is the value of y?
Answer:
[tex] \boxed{D. \: 40\degree} [/tex]
Step-by-step explanation:
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°
So,
[tex] = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree [/tex]
99 POINTS AND BRAINLIEST! PLEASE EXPLAIN. Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side. The change in the scale factor is: A) 1/15 B) 3/5 C) 4/5 D) 5/4 The change of scale means that 1 inch represented 4 feet, but now 1 inch represents feet: A) 5 B) 10 C) 12 D) 15
Answer:
5/4 5 ft
Step-by-step explanation:
We are going from 12 to 15
We need to multiply by
15 = k *12
Divide each side by 12
15/12 = k
5/4 = k
The scale factor is 5/4
1 in = 4 ft
Multiply the 4 ft by the scale factor
1 in = 4 * 5/4 = 5 ft
1 in = 5 ft
Answer:
Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side.
The change in the scale factor is
✔ 4/5
.
The change of scale means that 1 inch represented 4 feet, but now 1 inch represents
✔ 5
feet.
A bacteria population is initially 320. After 45 minutes, they've grown in number to 700. What is the doubling time for this population? Round to the nearest second. answer choices 39 minutes 41 seconds 39 minutes 31 seconds 39 minutes 21 seconds 39 minutes 51 seconds
Answer: 39 minutes 51 seconds
Step-by-step explanation:
Nt=N0 * 2^n
N0=Initial population
n=number of times bacteria divide
700=320*2^n
log2(700/320)=1.129283017=n
45/1.129283017=39.84829252 minutes
0.84829252*60=50.89755135≈51seconds
so the answer is
39minutes and 51seconds
Brent is designing a poster that has an area of 1 sq.ft. He is going to paste a photo collage on a section of the poster that is 1⁄3 foot wide and 3⁄5 foot long. What part of a square foot will the photo collage cover?
Answer:
[tex]\dfrac{1}{5} $ square foot.[/tex]
Step-by-step explanation:
Area of the Poster =1 sq.ft.
The collage will cover a part of the poster that is [tex]\dfrac{1}{3} ft.$ wide and \dfrac{3}{5} ft.$ long.[/tex]
Area of the Photo Collage Section
=Length X Width
[tex]=\dfrac{1}{3} X \dfrac{3}{5} \\\\=\dfrac{1}{5} $ square foot.[/tex]
[tex]\text{Therefore, the photo collage will cover }\dfrac{1}{5} $ of a square foot.[/tex]
Kathleen already owns 1 hair band, and additional hair bands are priced at 3 for a dollar.
Write an equation that shows the relationship between the money spent on additional hair
bands d and the total number of hair bands h.
Write your answer as an equation with h first, followed by an equals sign.
Submit
Not feeling ready yet? These can help:
Answer:
h= 1+3d
Step-by-step explanation:
total amount of hairbands equals the 1 hairband she has + 3 times how ever many more she decides to buy
A researcher is interested in attitudes towards releasing prisoners with Alzheimer's who have a life sentence. 85 randomly selected Americans were asked, "Prisoners with Alzheimer's who have a life sentence should be released: Strongly Agree, Agree, Disagree, Strongly Disagree". Match the vocabulary word with its corresponding example.
Answer and Step-by-step explanation:
The matching of the vocabulary word with its corresponding example is shown below:-
a. Data - The list of answers that the 85 Americans give.
Data refers the information that is to be collected.
b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".
Variable refers the changes of the expression according to the context.
c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant
d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
Statistics is a field of mathematics involved in data collection, organisation and analysis.
e. Sample - The 85 Americans who participated in the survey.
A sample is the result of an experiment on randomly.
f. Population - All Americans
Population refers to the number of the public.
Answer:
a. Data - The list of answers that the 85 Americans give.
Data refers the information that is to be collected.
b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".
Variable refers the changes of the expression according to the context.
c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant
d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
Statistics is a field of mathematics involved in data collection, organisation and analysis.
e. Sample - The 85 Americans who participated in the survey.
A sample is the result of an experiment on randomly.
f. Population - All Americans
Population refers to the number of the public.
Step-by-step explanation:
After Halloween, a variety store had some costumes regularly priced at $20.50 on sale for 20% off the regular price. A few weeks later the costumes that hadn’t sold were reduced an additional 60% off the sale price. What was the final selling price of the remaining costumes? The final selling price of costumes was $
A pair of dice was rolled many times
and the results appear below. Based
upon these results, what is the
experimental probability of rolling a
multiple of 3?
7
8
9
10 11 12
Outcome 23
35 6
Frequency 3 6 8 11 14
16
15
12
9
5 1
Answer:
6%
Step-by-step explanation:
Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...
6/100 = 6%
in a survey of employee satisfaction , 60% of the employees are male and 45% of the employees are satisfied. what is the probability of randomly selecting an employee who is male and satisfied
Answer:
27%
Step-by-step explanation:
6/10*45/100=270/1000 which is 27/100 which is 27%
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3
Step-by-step explanation:
We can see that the line passes through (0,3) and (1,0)
So using rise over run we have
-3/1
or
-3
Jackie's broker charges her a commission of $8 per ten share of stock she buys or sells. If jackie buys 77 shares of Alesia insurance at 10.34 per share and 120 shares of Ergar Appliances at 8.11 per share, how much will Jackie spend on commission?
Answer:
$157.60
Step-by-step explanation:
77 shares + 120 shares = 197 total shares
197/10 = 19.7
19.7 x 8 = 157.60
Answer:
b on edge hope this helps :)
Step-by-step explanation:
Please help me.
Solve for x in the diagram below:
Answer:
x = 40
Step-by-step explanation:
The angles are vertical angles. We know that vertical angles are equal
120 = 3x
Divide each side by 3
120/3 = 3x/3
40 =x
Answer:
40
Step-by-step explanation:
I forgot what you would call this, but basically 3x = 120. both of the angles are the same. So divide both sides of the equation by 3. 3x/3 = 120/3 and your answer is 40.
It's a bad explanation but I hope it helps!
Subtract the fractions and reduce to lowest terms: 89-6 2/3
Answer:
82 1/3
Step-by-step explanation:
89 - 6 2/3
Borrow 1 from the 89 in the form of 3/3
88 + 3/3 - 6 2/3
88 3/3 - 6 2/3
Subtract the whole numbers
88-6 =82
Subtract the fractions
3/3 - 2/3 = 1/3
82 1/3
Given the point (4,5) and the slope of 6 find y when x=24
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Tammy rents a storage shed. The storage shed is in the shape of a rectangular prism with measurements
as shown
9 feet
9 feet
10 feet
Select the phrase and number from the drop-down menus to correctly complete each sentence
Tammy can find the volume of the storage unit by
Choose
To completely fill the storage shed, Tammy would need
choose
unit boxes that each
measure 1 cubic foot
9514 1404 393
Answer:
B, D
Step-by-step explanation:
The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.
To fill the volume with boxes of volume 1 ft³ would require 810 boxes.
-3(7+5)
What is the value of
+9(2)?
32
-6
O-2
0 14
O 22
Step-by-step explanation:
-3(7 + 5) + 9(2)
-3(12) + 18
-36 + 18
= - 18
In my opinion this should be the answer
Answer:
14
Step-by-step explanation:
Your welcome!
What is the domain of the function Begin equation . . . y equals . . . the square root of the quantity x minus ten . . . end equation?
Answer:
Domain: [10, ∞)
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Step 1: Write equation
f(x) = √(x - 10)
We know that if we get negatives under the square root, we would get imaginary numbers.
Our domain to include all x-values would have to be bigger than 10:
f(10) = √(10 - 10) = √0 = 0
If the number is smaller than 10, we get: f(9) = √(9 - 10) = √-1 = i
Therefore, our real numbers domain would be [10, ∞) or x ≥ 10.
1. A random sample of 64 customers at a drive-through bank window is observed, and it is found that the teller spends an average of 2.8 minutes with each customer, with a standard deviation of 1.2 minutes. Is there sufficient evidence to conclude that the teller spends less than 3 minutes with each customer slader
Answer:
[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
Step-by-step explanation:
Information given
[tex]\bar X=2.8[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =3[/tex] represent the value to verify
[tex]\alpha[/tex] represent the significance level
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 3[/tex]
Alternative hypothesis:[tex]\mu < 3[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]
The degrees of freedom are given by:
[tex]df=n-1=64-1=63[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
Bramble’s standard quantities for 1 unit of product include 2 pounds of materials and 2.5 labor hours. The standard rates are $6 per pound and $11 per hour. The standard overhead rate is $12 per direct labor hour. The total standard cost of Bramble’s product is
Answer:
The standard cost of Bramble's product is $69.5 per unit.
Step-by-step explanation:
We can calculate the standard cost per unit of Bramble's product as the sum of the material cost, direct labor cost and overhead cost.
Each unit of product uses 2 pounds of materials, that cost $6 per pound. So the material cost is:
[tex]MC=2\,lb/u\cdot6\,\$/lb=12\,\$/u[/tex]
Each unit needs 2.5 direct labor hours, and they have a cost of $11 per hour, so the direct labor cost is:
[tex]LC=2.5\,h/u\cdot11\,\$/h=27.5\,\$/u[/tex]
The overhead costs are calculated in this case as $12 per direct labor hour. As 2.5 labor hours are needed per unit, we have:
[tex]OC=2.5\,h/u\cdot 12\,\$/h=30\,\$/u[/tex]
The standard cost is then:
[tex]C=MC+LC+OC=12+27.5+30=69.5\,\$/u[/tex]
What is the circumference of the circle diameter 33 cm
Answer:
≈103.67cm
Step-by-step explanation:
Shape: Circle
Solved for circumference
Diameter: 33cm
Formula: C=πd
Answer: ≈103.67cm
Hope this helps.
Answer:
C = 33 pi
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 33 pi
We can approximate pi by 3.14
C = 33*3.14 =103.62
or by using the pi button
C =103.6725576
What is the measure of
Answer: C. 84
Step-by-step explanation:
In triangles ABD y BCD:
- AD=CD
- Angle BAD = angle BCD
- BD common side
THEN the triangles are equal because they have two sides and the angle opposite the longest side respectively equal.
CBD = ABD = 42 because the triangles ABD y BCD are equal
ABC = CBD+ABD = 42+42= 84
Answer:
C. 84 degrees
Step-by-step explanation:
what is the equation of a quadratic function p with rational coefficients that has a zero of 3-i
Answer:
p = x² − 6x + 10
Step-by-step explanation:
Complex roots come in conjugate pairs. So if 3−i is a root, then 3+i is also a root.
p = (x − (3−i)) (x − (3+i))
p = x² − (3+i)x − (3−i)x + (3−i)(3+i)
p = x² − 3x − ix − 3x + ix + (9 − i²)
p = x² − 6x + 10
You can check your answer using the quadratic formula.
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ 6 ± √(36 − 40) ] / 2
x = (6 ± 2i) / 2
x = 3 ± i
This problem models pollution effects in the Great Lakes. We assume pollutants are flowing into a lake at a constant rate of I kg/year, and that water is flowing out at a constant rate of F km3/year. We also assume that the pollutants are uniformly distributed throughout the lake. If C(t) denotes the concentration (in kg/km3) of pollutants at time t (in years), then C(t) satisfies the differential equationdC dt = −FVC + IVwhere V is the volume of the lake (in km3). We assume that (pollutant-free) rain and streams flowing into the lake keep the volume of water in the lake constant.A) Suppose that the concentration at time t = 0 is C0. Determine the concentration at any time t by solving the differential equation.B) Find lim t→[infinity] C(t) =C) For Lake Erie, V = 458 km3 and F = 175 km3/year. Suppose that one day its pollutant concentration is C0 and that all incoming pollution suddenly stopped (so I = 0). Determine the number of years it would then take for pollution levels to drop to C0/10.D) For Lake Superior, V = 12221 km3 and F = 65.2 km3/year.
SEE BELOW FOR THE CORRECT FORMAT OF THE QUESTION
Answer:
(a) [tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]
(b) [tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]
(c) T = 6.02619 years
(d) T = 431.593 years
Step-by-step explanation:
(a)
[tex]\dfrac{dC}{dt} = -\dfrac{F}{v}C + \dfrac{I}{v} \\ \\ \\ \dfrac{dC}{dt} + \dfrac{F}{v}C = \dfrac{I}{v}[/tex]
By integrating the factor of this linear differential equation ; we have :
[tex]= e \int\limits \dfrac{F}{v}t \\ \\ \\ = e \dfrac{Ft}{v}[/tex]
[tex]C* e \frac{Ft}{v}= \int\limits \dfrac{I}{v}*e \dfrac{Ft}{v} dt[/tex]
[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{e \frac{Ft}{v} }{F/v}+ K[/tex]
[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{V}{F} e \dfrac{Ft}{v} + K[/tex]
[tex]Ce \dfrac{Ft}{v} = \dfrac{I}{F} \ * \ e \dfrac{Ft}{v} + k \ \ \ \ (at \ t = 0 \ ; C = C_o)[/tex]
[tex]C_o = \dfrac{I}{F} e^o + K[/tex]
[tex]K = C_o - \dfrac{I}{F}[/tex]
[tex]C_{(t)} = [ \dfrac{I}{F}e \dfrac{Ft}{v}+ C_o - \dfrac{I}{F}] e\dfrac{-Ft}{v}[/tex]
[tex]C_{(t)} =\dfrac{I}{F} [ e \dfrac{Ft}{v} * e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} - 1* e \dfrac{-Ft}{v}][/tex]
[tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]
(b)
[tex]\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-e^{- \infty} + C_o e^{- \infty} ][/tex]
since [tex](e^{- \infty} = 0)[/tex]
[tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]
(c)
V = 458 km³ and F = 175 km³ , I = 0
[tex]\dfrac{dC}{dt} = - \dfrac{-175}{458}C[/tex]
[tex]= \int\limits \ \dfrac{dC}{C} = - \dfrac{175}{458}\int\limits dt[/tex]
[tex]In (C_{(t)}) = - \dfrac{175}{458} t + K[/tex]
[tex]C_{(t)} = e \dfrac{-175}{458}t + K[/tex]
Let at time t = 0 [tex]C_{(t)}} = C_o \to C_o = e^{0+k} = e^K[/tex]
[tex]C_{(t)} = e \dfrac{-175}{458}t[/tex]
Now at time t = T ; [tex]C_{9t)} = \dfrac{C_o}{10}[/tex]
[tex]\dfrac{C_o}{10} = C_o e \dfrac{-175}{458}T \to \dfrac{1}{10} = e \dfrac{-175}{458}T[/tex]
[tex]In ( \dfrac{1}{10}) = \dfrac{-175}{459}T[/tex]
[tex]- In (10) = \dfrac{175}{458}T[/tex]
[tex]T = \dfrac{458}{175} In (10)[/tex]
T = 6.02619 years
(d) V = 12221 km³
F = 65.2 km³/ year
[tex]\mathbf{T = \dfrac{v}{F}In (10)}[/tex]
[tex]T = \dfrac{12221}{65.2}In (10)[/tex]
T = 431.593 years
