Answer:
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
Step-by-step explanation:
Given - A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min.
To find - Find the number A(t) of pounds of salt in the tank at time t.
Proof -
Given that,
Capacity of water = 400 gallons
rate in flow = 4 gal/min
rate out flow = 8 gal/min
Concentration in = 3 lbs/gal
Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)
Now,
Let
A(t) = Amount of salt in the tank at time t
Now,
Initially tank has 400 gallons of water, So
A(0) = 0 ................(1)
Now,
Rate of change in the amount of salt = [tex]\frac{d}{dt} A(t)[/tex]
= (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)
= (4) (3) - (8) ([tex]\frac{A(t)}{400 - 4t)}[/tex]
= 12 - [tex]\frac{2A(t)}{100 - t)}[/tex]
⇒[tex]\frac{d}{dt} A(t)[/tex] + [tex]\frac{2A(t)}{100 - t)}[/tex] = 12
Now,
Integrating Factor, I.F = [tex]e^{\int {\frac{2}{100 - t} } \, dt }[/tex]
= [tex]e^{-2ln(100 - t)}[/tex]
= (100 - t)⁻²
⇒I.F = (100 - t)⁻²
The solution becomes
A (I.F) = ∫ (I.F)(12) dt + C
⇒A (100 - t)⁻² = ∫12(100 - t)⁻² dt + C
⇒A (100 - t)⁻² = -12(100 - t)⁻¹ (-1) + C
⇒A(t) = [tex]12(100 - t)+ C(100 - t)^{2}[/tex]
Now,
We have A(0) = 0
⇒C = -12/100
∴ we get
A(t) = 12(100 - t) - [tex]\frac{12}{100}[/tex] (100 - t)²
= 12(100 - t) [ 1 - [tex]\frac{100 - t}{100}[/tex] ]
= 12(100 - t) ([tex]\frac{t}{100}[/tex])
= [tex]\frac{3t(100 - t)}{25}[/tex]
⇒A(t) = [tex]\frac{3t(100 - t)}{25}[/tex]
∴ we get
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
I need help ASAP please
Answer:
x = 12.4
Step-by-step explanation:
[tex] \tan(54) = \frac{x}{9} \\ x = \tan(54) \times 9 \\ x = 12.3874 \\ to \: the \: nearest \: tenth \\ x = 12.4[/tex]
I hope that is useful for you
When you roll a number cube, there are 6 possible _____.
a.) dots
b.) sides
c.) outcomes
b.) none of these
Answer:
c. outcomes
Step-by-step explanation:
what is 5m-4-m+2 simplify
Step-by-step explanation:
5m-4-m+2
Simplifying
4m - 2
Hope it helps :)❤
The quotient of 6 and a
number (n)
Answer:
n divided by 6 (n/6)
Step-by-step explanation:
The mathematical expression for 'the quotient of 6 and a number (n)' is, 6/n or (6 ÷ n).
Used the concept of mathematical expression which can be stated that,
A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
The algebraic expression is,
''The quotient of 6 and a number (n).''
Now, the mathematical expression for 'the quotient of 6 and a
number (n)' is,
6 ÷ n
= 6 / n
So, the mathmatical notation is 6/n.
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Rosaria filled some cups with different amounts of water, as shown below.Red cup: 0.046 liters
Blue cup: 0.05 liters
Green cup: 0.20 liters
Yellow cup: 0.6 liters witch one
Answer:
Green cup: 0.20 liters
Step-by-step explanation:
6x^2 - 37x + 13 = 6
Show why this quadratic trinomial cannot be factored with an explanation.
i have been struggling with this please help
ASAP I WILL GIVE BRAINIEST IF ANSWERED ASAP!! PLEASE PLEASE HELP
Answer:
2x + 3 =84
Step-by-step explanation:
Answer:
2x + 3 = 84
Step-by-step explanation:
Find the area of sector with a radius of 4 and a central angle of 30 degrees.
Answer:
Step-by-step explanation:
[angle of sector]/360 x π x radius ² [formula to find area of a sector]
30/360 x π x 4²
Type into a calculator
4.18879
A line has a slope of
–
1
4
and passes through the point (
–
3,4). What is its equation in point-slope form?
What is 54.77 rounded to the nearest tenth ?
To decorate 6 dozen cupcakes with red hot candies, Nan needs about 550 red hots. Which two sacks of candy would be the best buy?plsss help me asap giving brainless and explain whay is that the answer. (353, 177, 255, 379)
Answer:
If the numbers at the bottom are the sack size, then the 255 and the 353.
They give enough candy but not excessive given the sizes.
If this isn't right I will continue to try to help you but ill need more info
A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is
given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie
Answer:
(c).
Step-by-step explanation:
h(t) = - 16 t² + 80 t
Coordinates of the vertex are:
t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.
h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.
A candy store in the mall orders 1000 boxes a month each box of candy weighs 45.9 grams . What is the total weight in grams of the candy in the store
Answer:
45900 grams
Step-by-step explanation:
All you need to do is multiply 45.9 grams by 1000 for the total combined weight of every box combined to get.
45.9 x 1000 = 45900
Pls someone help me with this question pls
B
280
D
C
What is the measure of angle ADB?
A. 17°
Answer:
C. 62
Step-by-step explanation:
ADC is 90 degrees. 90 - 28 = 62
Find the missing side. Round to the nearest tenth.
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
1)
Hyp =40
∠48
x = Adj
use CAH since it's got these pieces in it
Cos(48) = x / 40
40* Cos(48) = x
26.76522 = x
x = 26.8 ( rounded to nearest 10th)
2)
∠29
Hyp = 35
Opp = x
use SOH since this problem has those pieces in it
Sin(29) = x / 35
35*Sin(29) = x
16.9683 = x
x = 17.0 (rounded to nearest 10th)
3)
40 = Adj
∠16
Hyp = x
use CAH again
Cos(16) = 40 / x
x = 40 / Cos(16)
x = 41.611
x = 41.6 (rounded to nearest 10th )
4)
∠55
Opp = 35
x = Adj
use TOA
Tan(55) =35/x
x = 35/Tan(55)
x = 24.5072
X = 24.5 ( rounded to nearest 10th)
Doug took 180 photos during his vacation. He took 2/3 of photos during
the first day of his vacation. Of those photos, ¼ were of landscapes and
0.3 were of people. How many photos were of landscapes and people?
Answer:
66 pictures
Step-by-step explanation:
180 ÷ 3 = 60 60 x 2 = 120
120 = 2/3. He took 120 pictures on the first day of his vacation.
120 ÷ 4 = 30 30 x 1 = 30
30 = 1/4. He took 30 pictures of landscapes
120 ÷ 10 = 12 12 x 3 = 36
0.3 = 36. He took 36 pictures of people.
36 + 30 = 66 pictures.
He took 66 pictures of landscapes and people.
Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
Is (3,6) a solution of the system of linear equations below? Justify your response. Use of the graph is optional.
-6x + y= -12
X + y= -3
Answer:
No.
Step-by-step explanation:
The given system of equations are :
-6x + y= -12 ......(1)
x + y= -3 ......(2)
Put x = 3 and y = 6 in both equations i.e.
-6(3) + (6) = -12
And
3 + 6 = 9 ≠ -3
Hence, (3,6) is not the solution of the given system of equations.
What should be placed in the box to make the equation true?
Answer:
2x^4
Step-by-step explanation:
When multiplying variables with exponents multiply the coefficients (the number before the variable) and add the exponents.
SO to solve you have to find a number that when multiplied by 32 equals 64 and a number when added to 8 gives you 12.
2*32=64
8+4=12
So the answer is 2x^4
If this helped please consider giving brainliest.
A BAG CONTAINS 10 RED BALLS AND FIVE BLUE BALLS WHAT IS TGE CHANCE OF PICKING A BLUE BALL.PLEASE EXPLAIN HOW TO SOLVE IT
Answer:
5/15
Step-by-step explanation:
there are 15 balls altogether, 5 of which are blue meaning there is a 5/15 chance of picking a blue ball which as a percentage is 33.33% chance
The graph of the function y=f(x)+35 can be obtained from the graph of y=f(x) by one of the following actions:
7. In the figure, AABC-AXYZ. What is the perimeter of AABC? Show your work.
HELP PLEASE DUE IN 4 MINUTES
What would be the volume to this equation?
Answer:
you times 11.3 by 15.1 then times it by 18.9
Plzzz help I will mark Brainlyest
Answer:
6
Explanation:
the sum of all four angles in a quadrilateral is 360°. thus, to find the angle ∠JML, we need to subtract the values of the other angles from 360° as such:
360° - 66° - 74° - 110° = 110°
the total value of angle ∠JML is 110°.
now, since ∠JML is equal to 17x + 8, we can subtract 8° from 110° to get 102°. following that, we can divide 102° by 17 which yields us the result of 6. hence, we now know that x = 6.
Nicole took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $2.90 plus $1.75 per mile. The total fare was $44.90, not including the tip.
Write and solve an equation which can be used to determine z, the number of miles
in the taxi ride
The first thing we need to do is to find the linear equation that defines the total cost of the taxi ride as a function of the number of miles traveled.
We will find that z = 24.
We know that the taxi charges a fixed fee of $2.90, plus $1.75 per mile.
So if you travel for z miles, the total cost will be:
[tex]c(z) = \$2.90 + \$1.75 \cdot z[/tex]
Now that we have this linear equation if we know that the total fare was $44.90, then we have:
[tex]c(z) = \$2.90 + \$1.75 \cdot z = \$44.90[/tex]
Now we just need to solve the above equation for z:
[tex]\$2.90 + \$1.75 \cdot z = \$44.90\\\\\$1.75 \cdot z = \$44.90 - \$2.90 = \$42.00\\\\z = \$42.00/\$1.75 = 24[/tex]
Then we can see that she traveled for 24 miles.
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How many times was the number cube rolled
The ball was rolled 50 times.
6+4+8+12+10+10 = 50
Hope this helps; have a great day!
What is the degree of the following polynomial x²y³ + z
Please answer quick and just write explanation quick pls hurry quick for brainlessly ee
Find the surface area of the figure
a. 150 square cm
b. 228.4 square cm
c. 78.4 square cm
d. 210 square cm
Answer:
c
Step-by-step explanation: