Answer:
60mph
Step-by-step explanation:
Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. (The same conditions as in the previous problem). After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank.
(a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote thenumber of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A = rate of input - rate of exit.
(b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank. What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops?
Answer:
(a) 0.288 kg/liter
(b) 0.061408 kg/liter
Step-by-step explanation:
(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute
The mass of salt exiting the tank per minute = 5 × (5 + x)/500
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
Δ/dt = x - 5 × (5 + x)/500
The increase, in mass, Δ, after an increase in time, dt, is therefore;
Δ = (x - 5 × (5 + x)/500)·dt
Integrating with a graphing calculator, with limits 0, 10, gives;
Δ = (99·x - 5)/10
Substituting x = 1 gives
(99 × 1 - 5)/10 = 9.4 kg
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)
∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter
(b) With the added leak, we now have;
Δ/dt = x - 6 × (14.4 + x)/500
Δ = x - 6 × (14.4 + x)/500·dt
Integrating with a graphing calculator, with limits 0, 20, gives;
Δ = 19.76·x -3.456 = 16.304
Where x = 1
The increase in mass after an increase in = 16.304 kg
The total mass = 16.304 + 14.4 = 30.704 kg
The concentration of the salt in the tank then becomes;
Concentration = 30.704/500 = 0.061408 kg/liter.
Calculating the salt concentration per liter of water we will find:
(a) [tex]0.288 kg/liter[/tex]
(b) [tex]0.061408 kg/liter[/tex]
The mass of salt entering the tank per minute:
[tex]X= (0.2)( 5) = 1 kg/minute[/tex]
The mass of salt exiting the tank per minute:
[tex]\frac{5 * (5 + x)}{500}[/tex]
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
[tex]\frac{\Delta}{dt} = \frac{x - 5 * (5 + x)}{500}[/tex]
The increase, in mass, Δ, after an increase in time, dt, is therefore;
[tex]\Delta = (x - 5 * (5 + x)/500)dt[/tex]
Integrating with a graphing calculator, with limits 0 at 10, gives;
[tex]\Delta = (99X - 5)/10[/tex]
Substituting x = 1 gives:
[tex](99)( 1 - 5)/10 = 9.4 kg[/tex]
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank). The concentration of the salt and water in the tank after 10 minutes:
[tex](5 + 9.4)/500 = (14.4)/500 = 0.288[/tex]
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter.
(b) With the added leak, we now have;
[tex]\frac{\Delta}{dt} = \frac{ (x - 6 ) (14.4 + x}{500} \\\Delta = \frac{(x - 6)(14.4 + x)}{500} dt[/tex]
Integrating with a graphing calculator, with limits 0 at 20, gives;
[tex]\int\limits^{20} _0 {\frac{(x - 6)(14.4 + x)}{500} dt}[/tex]
Where x = 1:
[tex]\Delta = 19.76(1) -3.456 = 16.304[/tex]
The increase in mass after an increase in = 16.304 kg. The total mass:
[tex]16.304 + 14.4 = 30.704 kg[/tex]
The concentration of the salt in the tank then becomes;
[tex]30.704/500 = 0.061408 kg/liter[/tex]
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Covert 45 1/2 % to a fraction
A nursery owner buys 9 panes of glass to fix some damage to his greenhouse. The 9 panes cost $22.05 Unfortunately, he breaks 4 more panes while repairing the damage. What is the cost of another 4 panes of glass?
Answer: $9.80
Step-by-step explanation:22.05/9=2.45x4= 9.80
Answer:
$4.30
Step-by-step explanation:
Two panes of glass cost $4.30.
Explanation
First find the cost of one pane of glass (the "unit cost")
7 panes of glass cost
$
15.05
, so one pane of glass costs
15.05
÷7∩
$2.15 ← cost of one pane of glass
Then use that answer to find the cost of two panes of glass
If one pane of glass costs $2.15, then 2 panes cost 2× $2.15 $4.30 ← cost of two panes of glass
Answer:
Two panes of glass cost $4.30.
Exit ticket help please
Answer:
The answer is B
Step-by-step explanation:
I am learning the same thing somehow
Write sec 325° in terms of the secant of'a positive acute angle.
Answer:
sec35°
Step-by-step explanation:
sec325° = sec(360 - 325)° = sec35°
The secant of a positive acute angle of sec 325° = sec 35° = 1.22077
What are Trigonometric Ratios?
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios.The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given data ,
The trigonometric ratio is = sec 325°
Now , to express the ratio in terms of a positive acute angle , we take the four quadrants of the graph and express the angle in the first quadrant.
And , 325° lies on the 4th Quadrant , where all cosines and secants are positive.
Therefore , sec 325° = sec ( 360° - 35° )
= sec ( 35° )
=1.22077
Hence , the secant of a positive acute angle of sec 325° = sec 35° = 1.22077
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A pet store was selling 2 lizards for
$14.48. If they ended up selling 6
lizards, how much money would they
have earned?
Answer:
43.44
Step-by-step explanation:
If they are selling 2 lizards for 14.48 you would divide
14.48 by two which is 7.24.
This means the lizards are 7.24 each.
7.24x6 is 43.44
Answer:
$43.44
Step-by-step explanation:
If two lizards are worth $14.48, then you just need two multiply the cost by three.
If f(1) = 1, what is f(3)?
Answer:
would be 3
Step-by-step explanation:
if 1 is 1 ,3 would be 3 ;-;
A rectangle has a length that is 4 ft more
than its width. What are the length and
width of the rectangle if the rectangle has
a perimeter of 48 ft?
Answer:
length = 14 width = 10
Step-by-step explanation:
48/4=12
10+10+14+14=48
Time sensitive mark best as brainiest
The density of a certain material is such that it weighs 4 kilograms
per cubic foot of volume. Express this density in ounces per cubic
meter. Round your answer to the nearest whole number.
Answer:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. Without
looking, what is the probability that Fiona pulls out a marble that is not white?
Answer:
85%
Step-by-step explanation:
The probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
What is the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event.
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. The total number of marbles in the bowl is,
[tex]n=5+2+10+3\\n=20[/tex]
The number of white balls in the bowl is 3. Thus, the probability that Fiona pulls out a marble that is white, is,
[tex]P=\dfrac{3}{20}[/tex]
The probability that Fiona pulls out a marble that is not white is,
[tex]P^{-1}=1-\dfrac{3}{20}\\P^{-1}=\dfrac{20-3}{20}\\P^{-1}=\dfrac{17}{20}[/tex]
Thus, the probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
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I need some help on this problem.
Answer:
It would be <XWY & <UTW.
(-2,-4) and (6,7)
Need help show steps too
Answer:
Step-by-step explanation:
period
Solve for n 3m+2n=8 how do you do theseee?
When I graph the inequality symbol > should it be a open or closed
circle on the number line?
Answer:
It should be open.
Step-by-step explanation:
Hope this helped!
need help pease its due at 11;59pm today explian
Answer:
65
Step-by-step explanation:
you add all the numbers inside.
80+35= 115
You have to make sure it equals to 180 to find angle 1.
Therefore, 180-115=65.
2\3n = -12 what value of n makes this equation true
Answer:
-0.055555555555556
Step-by-step explanation:
What is the image of (-5, 6) after a reflection over the line y = -2
Answer:
I'm pretty sure it would be (5,6)
Step-by-step explanation:
Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate
Jimmy practices hitting baseballs every day. His first time at bat, the baseball goes 10 feet. For every day he
practices, the baseball goes 6 feet farther. Write an equation to describe this situation.
Answer:
I think it is 10 + (6x)
Step-by-step explanation:
because he starts at ten and every day it adds 6 and x represents the number of days
Find the cos of angle c
A.3/5
B.6/5
C.5/3
D.1
Give 5 reasons explaining why math is your favorite subject.
Give 5 reasons why you dont like math.
Give 5 areas that math can help you now or in the future.
Answer:Math is important
Step-by-step explanation:
It could help you get into collage and get a good job and with that you could start your life.
Answer:
1.)
I love working with numbers
I love math because of what a challenge it is
I love math because I can become a engineer
I love math because I can also become a doctor with it
I love math because it is useful
2.)
I don't like math because of the word problems
I don't like math because it sometimes gets too easy
I don't like math because I usually have to help others
I don't like math because people call me a nerd
I don't like math because it makes me explain in words
3.)
when your in the store and it helps you with knowing how much your spending
lets you know about if the discount in the store is really good or bad
helps you with becoming certain things when you grow up
it will help you with most of your jobs
Will help others if you know it, you can share your knowledge
Step-by-step explanation:
brainlist pls :>
(-16t - 2)(t - 5) is the same as 10+78t-16t^2 but in factored form. Explain how you know,
basically help me convert the factored form into the standard form
Answer:
10+78t-16t^2
Step-by-step explanation:
(-16t-2)(t-5)
-16t × t= -16t²
-16t × -5=80t
-2 × t= -2t
-2 × -5=10
-16t²+80t-2t+10= -16t^2+78+10
3b) Two pizzas are made to the same dimensions. The only difference is that
Pizza 1 is cut into pieces at 30° angles and Pizza 2 is cut at 45° angles. They are
sold by the slice. The slices for Pizza 1 sell for $1.45/slice and the slices for Pizza 2
sell for $1.75/slice. What is the difference in total sales between Pizza 2 and Pizza
1?
Step-by-step explanation:
$0.30 because they only sell 30 cents less/more than each other
2. A package delivery service has a truck that can hold 4200 pounds of cargo
and has a capacity of 480 cubic feet. The service handles two types of
packages: small, which weigh up to 25 pounds each and are no more than 3
cubic feet each; and large, which are 50 pounds each and are 5 cubic feet
each. The delivery service charges $5 for each small package and $8 for each
large package. Let x be the number of small packages and y be the number of
large packages in the truck. What is the maximum revenue per truck?
Answer:
$680
Step-by-step explanation:
Capacity of the truck: 4200 pounds and 480 cubic feet of cargo.
Small package: 25 pounds and 3 cubic feet each.
Large package: 50 pounds and 5 cubic feet each.
For x number of small packages:
25x pounds and 3x cubic feet
Let x = 8,
200 pounds and 24 cubic feet.
For y number of large packages:
50y pounds and 5y cubic feet
Let y = 80,
4000 pounds and 400 cubic feet.
Since delivery service charges $5 for each small package and $8 for each large package.
The maximum revenue per truck = ($5x + $8y)
= ( $5 x 8) + ($8 x 80)
= $680
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It’s a math question :((
Answer:
slope: 3 y-intercept: 9
Step-by-step explanation: 19-10 is 9, and 6-3 is 3 9/3 is 3.
28-19 equals 9. 19-10 is 9, so 9 fills out that blank beside 10.
Answer:
slope is 3 and in the blank goes 1. and y intercepts line at y=1
9
show questions
Carol feeds her bird the same amount of food every day. Over the past 7 days, her bag of bird
food has decreased by 1 cups.
Answer: 1/7 of a cup
Step-by-step explanation:
7x=1 x=food per day
divide 7 from both sides
7 / 7x = 1 /7
x = 1/7
Every Friday, Jesse puts $3 into his piggy bank. is it discrete or continuous?
Answer:
I would think continuous if she does it constantly every friday night
Step-by-step explanation:
Answer:
continuious
Step-by-step explanation:
Simplify the expression
Answer:
B
Step-by-step explanation:
Please help me with this equation. It’s solving systems of equations.
Moving downstream (with the current), the boat moves at a rate of (252 mi)/(12 h) = 21 mph. Upstream (against the current), it moves at a rate of (252 mi)/(84 h) = 3 mph.
When traveling downstream, the boat's speed is the sum of its own speed in still water and the speed of the current. It's the same going upstream, but the boat and current move in opposite directions. Let b and c denote these speeds, respectively. Then
downstream: b + c = 21 mph
upstream: b - c = 3 mph
Adding these equations eliminates c and lets us solve for b :
(b + c) + (b - c) = 21 mph + 3 mph
2b = 24 mph
b = 12 mph
Now solve for c :
12 mph + c = 21 mph
c = 9 mph
encuentra el numero decimal equivalente a la fracción
7/10
198/100
85/100
45/100
1/4
3/2
3/8
1/9
7/10 = 0.7
198/100 = 1.98
85/100 = 0.85
45/100 = 0.45
1/4 = 0.25
3/2 = 1.5
3/8 = 0.375
1/9 = 0.11111111 ( goes on forever) ( sigue para siempre )
Hope it Helps!
¡Espero eso ayude!
The teacher separated her group of 28 students into 2 groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
Answer:
one group has 12. one has 16. 12 + 16 = 28. 16 is 4 more than 12