Answer:
(a) [tex]A = 1500(1 - e^{-0.01t})[/tex]
(b) [tex]t = 0[/tex]
Step-by-step explanation:
Given
[tex]V= 300gal[/tex] --- Volume of tank
[tex]B = 5lb/gal[/tex] --- Brine solution
[tex]R_1 = 3gal/min[/tex] --- Rate in, in gallon/min
[tex]R_2 = 6gal/min[/tex] --- Rate out, in gallon/min
Required
Determine A(t)
First, calculate the rate in (R in) and (R out) in lb/min
[tex]R_{in} = B * R_1[/tex]
[tex]R_{in} = 5lb/gal * 3gal/min[/tex]
[tex]R_{in} = 15lb/min[/tex]
R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2
So, we have:
[tex]R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min[/tex]
[tex]R_{out} = \frac{3*A(t)}{300} lb/min[/tex]
[tex]R_{out} = \frac{A(t)}{100} lb/min[/tex]
The change in the amount of brin e in the tank at time t is given as:
[tex]A'(t) = R_{in} - R_{out}[/tex]
[tex]A'(t) = 15 - \frac{A(t)}{100}[/tex]
Rewrite:
[tex]\frac{dA}{dt} = 15 - \frac{A}{100}[/tex]
Multiply through by dt
[tex]dA = [15 - \frac{A}{100}]* dt[/tex]
Make dt stand alone
[tex]\frac{dA}{15 - \frac{A}{100}} = dt[/tex]
[tex]ln|15 - \frac{A}{100}| = -0.01t + ln\ c[/tex]
Express as exponents
[tex]15 - \frac{A}{100} = ce^{-\frac{t}{100}}[/tex]
Multiply through by 100
[tex]1500 - A = 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-0.01t}[/tex]
Apply initial conditions
[tex]A(0) = 0[/tex]
Substitute 0 for t in: [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]0 = 1500 - 100ce^{-0.01*0}[/tex]
[tex]0 = 1500 - 100ce^{0}[/tex]
[tex]0 = 1500 - 100c[/tex]
[tex]100c = 1500[/tex]
[tex]c = 15[/tex]
Substitute 15 for c in [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]A = 1500 - 100*15e^{-0.01t}[/tex]
[tex]A = 1500 - 1500e^{-0.01t}[/tex]
Factorize:
[tex]A = 1500(1 - e^{-0.01t})[/tex]
How long to empty the tank
Set A to 0
[tex]1500(1 - e^{-0.01t}) = 0[/tex]
Divide through by 1500
[tex]1 - e^{-0.01t} = 0[/tex]
Collect Like Terms
[tex]e^{-0.01t} = 1[/tex]
Take ln of both sides
[tex]ln\ (e^{-0.01t}) = ln\ 1[/tex]
[tex]-0.0t = 0[/tex]
[tex]t = 0[/tex]
Which equation will let you solve for jk
cos[63] = jk/8
Tan [63]= jk/8
Sin[63]=jk/8
Tan[63]= 8/jk
In a right triangle, the ratio of the opposite side of one angle to the hypotenuse is called sine.
In this problem the side JK is the opposite side of angle JLK whose value is 63 degrees. The hypotenuse is JL whose value is 8.
So the sine ratio of angle JLK would be
sin L=JK/JL
Substituting the numerical values,
sin 63°=JK/8
This implies JK=sin 63°×8 from wich we will get the value of JK
So, this equation sin 63°=JK/8 will let us solve for jk and the answer is the third one.
Answer:
C
Step-by-step explanation:
help i need the answers by tomorrow
8 inch radius:
area: 200.96
circum: 50.25
12 yd rad:
area: 452.16
circum:75.36
20 ft dia:
area: 314
circum:62.8
36 dia:
area:1017.36
circum: 113.04
What type of auto coverage is required by nearly every state in the country?
Answer: Minimum car insurance limits in each state
Step-by-step explanation: With the exception of Florida, every state requires bodily injury liability insurance (BI), while all 50 states plus Washington, D.C., require property damage liability (PD). Roughly half of the states require a type of uninsured/underinsured motorist insurance (UIM). hope this helps. Can u give me brainliest
what is the answer to this math question 5 less than c is 47
Answer:
Answer = 52
5+47= 52
done
A system of inequalities is shown below.
y < -1
2x - y < 2
In which quadrants is the solution set of the system?
Answer:
C
I may be wrong sorry if I am
Answer:
The answer is C
Step-by-step explanation:
Since they both have a negative y and Quardant 4 has a positive x
given. Round
The first three terms of a sequence are
to the nearest thousandth (if necessary).
1 , 5/4 , 25/16 find the 7th term.
Answer:
[tex] \frac{15625}{4096} [/tex]
. There are 258,890,850 number combinations possible in the Mega Millions lottery. One winning jackpot ticket will be chosen at random. Brent chooses his favorite number combination and buys one ticket. Find the probability Brent will win the jackpot. Round the decimal to the first digit that is not zero, then write the name of the decimal.
Answer:
0.000000004 = 4 hundred millionths probability Brent will win the jackpot.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
1 desired combination out of 258,890,850. So
[tex]p = \frac{1}{258890850} = 0.000000004[/tex]
9 places after the decimal point is hundred millionths
0.000000004 = 4 hundred millionths probability Brent will win the jackpot.
9(p-4)=-18 what does p equals ?
The financial officer is promoting a short-term investment with 9% return on any deposit
over $999. Tammy invest $1,800 and earns $486. How long did she invest her
money?
Answer:44
Step-by-step explanation:
Complete the explanation for how you could find the number of seconds in one full 24-hour day-
Then solve.
You would multiply 24 hours by _____ minutes and then multiply my answer by _____
Seconds.
There are ____ seconds in one full day
Answer:
Step-by-step explanation:
You would multiply 24 hours by 60 minutes and then multiply my answer by
60 Seconds.
There are 86400 seconds in one full day
Graph the line with the slope 1 passing through the point (-2,-1)
Answer:
Step-by-step explanation:
9. Find the mean of the data set: 2, 3, 4, 5, 5
Step 1:
Add up all the numbers.
Step 2:
Divide by the number of items
in your data set.
Answer: Step 1 box= 19 (2+3+4+5+5)
Step 2 box= 3.8 (19 divided by 5)
Step-by-step explanation:
You add together the numbers to get 19, the you divide the number by five because you added 5 numbers together.
You had it just right on the bottom. Your equation was perfect. It doesn't matter if you get a decimal number.
Your answers are right too, I double checked.
Hope I was helpful.
what is taxation ?...maths literacy grade 12
Can someone please help
Jenna has a maximum of $38 to spend at the movies. A ticket costs
$8.50 and she has x, dollars to spend on snacks. Which inequality
represents all of the possible values for x?
A. x ≥ 29.50
B. x ≤ 46.50
C. x ≥ 46.50
D. x ≤ 29.50
In isosceles triangle WXY, XY is 13 inches in length and WY is 10 inches. What is the length of XZ? answer asap please
=============================================================
Explanation:
Notice the double tickmarks on segments WZ and ZY. This tells us the two segments are the same length. Let's say they are m units long, where m is a placeholder for a positive number.
That would mean m+m = 2m represents the length of segment WY, but that's equal to 10 as the diagram shows. We have 2m = 10 lead to m = 5 after dividing both sides by 2.
We've shown that WZ and ZY are 5 units long each. In short, we just cut that length of 10 in half.
-----------------------------------
Let's focus on triangle XYZ. This is a right triangle with legs XZ = unknown and ZY = 5. The hypotenuse is XY = 13.
We'll use the pythagorean theorem to find XZ
a^2 + b^2 = c^2
(XZ)^2 + (ZY)^2 = (XY)^2
(XZ)^2 + (5)^2 = (13)^2
(XZ)^2 + 25 = 169
(XZ)^2 = 169-25
(XZ)^2 = 144
XZ = sqrt(144)
XZ = 12
Segment XZ is 12 inches long.
You want to order one milkshake. The Ice Cream Shop will not allow you to mix flavors. How many ways could you order a milkshake?
Answer:
15 ways
Step-by-step explanation:
3 sizes x 5 flavors = 15 combinations
Answer:
15
Step-by-step explanation:
if you can make 3 sizes for each flavor and there are 5 flavors then there are 15 ways to get a milkshake 3x5=15
Emma invested $750 in an account paying an interest rate of 1.9% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $910?
Answer:
10.2
Step-by-step explanation:
The B of years it took to the given principal to amount $910 is 3.4 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$750, rate of interest =1.9% and amount=$910.
Let the number of years be x and compounded quarterly.
Here, 910=750(1+ 1.9/100)³ˣ
910/750 =(1+0.019)³ˣ
1.213=(1.019)³ˣ
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x=ln(1.213)/3ln(1.019)
Decimal Form: 3.419
≈ 3.4 years
Therefore, the number of years it took to principal to reach $910 is 3.4 years.
To learn more about the compound interest visit:
https://brainly.com/question/14295570.
#SPJ2
find the value of each of the four remaining trigonometric functions
Answer:
tanФ = [tex]\frac{\sqrt{2}}{2}[/tex], cscФ = 3, secФ = [tex]\frac{3\sqrt{2} }{4}[/tex], cotФ = [tex]2\sqrt{2}[/tex]
Step-by-step explanation:
tanФ= [tex]\frac{1}{2\sqrt{2} } =\frac{2\sqrt{2}}{8} =\frac{\sqrt{2} }{2}[/tex]
cscФ= [tex]3[/tex]
secФ= [tex]\frac{3}{2\sqrt{2}} =\frac{6\sqrt{2}}{8} =\frac{3\sqrt{2}}{4}[/tex]
cotФ= [tex]2\sqrt{2}[/tex]
Evaluate the following expression -5+(63/9)
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
x²-12x+a=(x+b)² find a and b
Answer:
Step-by-step explanation:
x² - 12x + a = (x + b)²
x² - 12x + a = x² + 2xb + b²
-12 = 2b and a = b²
b = -6
a = b² = 36
The value of a is 36 and b = -6.
What is the quadratic equation?The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of: ax² + bx + c = 0.
The given expression is;
[tex]\rm x^2-12x+a=(x+b)^2[/tex]
The solution of the equation is determined in the folllowing steps given below.
[tex]\rm x^2-12x+a=(x+b)^2\\\\x^2-12x+a=x^2+2xb+b^2\\\\2xb + b^2 = a-12x[/tex]
On comparing the equation
[tex]\rm 2b =-12\\\\b =\dfrac{-12}{2}\\\\b=-6[/tex]
The value of a is;
[tex]\rm a=b^2\\\\b=-6\\\\a=(-6)^2\\\\a=36[/tex]
Hence, the value of a is 36 and b = -6.
Learn more about equation here;
https://brainly.com/question/15339001
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what is F (x) = -x^2 - 10x f= (−5)
Answer:
75
Step-by-step explanation:
f(x)=-x^2-10x
f(-5)=(-5)^2-10(-5)
f(-5)=(-5)(-5)+50
f(-5)=25+50
f(-5)=75
PLS ANSWER THANK YOU!!
Answer:
I think it is 145 degrees because 180- 35= 145
Step-by-step explanation:
Describe the transformations of f(x) when compared to the parent function [y = x2].
f(x) = x2+5
The transformations of f(x) when compared to the parent function is the graph of [tex]f(x)=x^2+5[/tex] is moved 5 units up
Transformation of functions
Transformation of function is transforming a function from one form to another form .
Rules of transformation :f(x)-> f(x)+a , f(x) will be moved 'a' units up
f(x)-> f(x)-a , f(x) will be moved 'a' units down
f(x)-> f(x-a) , f(x) will be moved 'a' units right
f(x)-> f(x+a) , f(x) will be moved 'a' units left
f(x)-> -f(x), f(x) will be reflected across x-axis
f(x)-> f(-x), f(x) will be reflected across y-axis
For quadratic, the parent function is [tex]f(x)=x^2[/tex]
Given that [tex]f(x)=x^2+5[/tex]
Here , 5 is added with f(x) at the end
f(x)-> f(x)+a , f(x) will be moved 'a' units up
[tex]f(x)=x^2 ------ > f(x) =x^2+5[/tex]
The graph of f(x) will be move 5 units up
the transformations of f(x) when compared to the parent function is the graph is moved 5 units up
Learn more about transformation here:
brainly.com/question/17586310
−5+6×52+56÷(−8) pllllll
Answer:
Its 300.
hope this helps:)
Answer:
3
Step-by-step explanation:
I tried 300 and i got it wrong but instead it gave me this answer :)
OMG PLEASE HELP MEEEEEEEEEEEEEEE
1.2 + 2.6 × 1.4 − 3.9
A) −5.3
B) 0.94
C) 1.42
D) 8.74
Answer:
c
Step-by-step explanation:
1.2+2.6=3.8
3.8×1.4=5.32
5.32-3.90=1.42
Find q. q-89=121 q= please help
Answer: q=210
Step-by-step explanation:
For this question you have to do the inverse to 'undo' the equation.
So, instead of taking away 89 you have to add it to 121.
q=121+89
q=210
Hope this helps :)
solve for the variable. -2x + 6 = 14
Answer:
Step-by-step explanation:
-2x + 6 = 14
-2x = 8
x = -4
Answer:
[tex]x=-4[/tex]
Step-by-step explanation:
To solve for the variable x, we're going to isolate it.
First step is: Subtracting 6 by both sides:
[tex]-2x+6-6=14-6\\[/tex]
Notice how the +6 and the -6 cancel each other out. So we get:
[tex]-2x=8[/tex]
Second step is to divide both sides by -2:
[tex]\frac{-2}{-2} x=\frac{8}{-2}[/tex]
The -2's cancel each other out to:
[tex]x=-4[/tex]
simplify the following 6(1/2+1/3)
Answer:
5
Step-by-step explanation:
use the distributive property
6 * 1/2 = 3
6 * 1/3 = 2
3 + 2 = 5
Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!
-Lil G
A line passes through the point (-8, -4) and has a slope of 5/2. Write and equation in slope intercept form for this line.
Answer:
i know this isn't the answer but this should help...
Step-by-step explanation:
