Answer:
1-4
2-5
3-6
4-7
Step-by-step explanation:
Answer:
1 ) 5 - 82 ) -9 + 63 ) 6 ÷ -24 ) 1 × -3Step-by-step explanation:
5 - 8 = -3
-9 + 6 = -3
6 ÷ -2 = -3
1 × -3 = -3
You can check the calculator if you don't believe me!
Hope this helps! <3
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]
Learn more: brainly.com/question/11762787
Express the number 0.00001038 in scientific notation
Harper Hospital treated 423 patients last week who were children, out of a total of 931 patients. The administrator calculates that they had 408 adult patients. Is the administrator's calculation reasonable? Estimate the number of adult patients by rounding the numbers to check the administrator's calculation.
Answer:
No, the administrator is wrong.
[tex]Adult = 500[/tex]
Step-by-step explanation:
Given
[tex]Total = 931[/tex]
[tex]Children = 423[/tex]
[tex]Adult = 408[/tex]
Solving (a): Is the administrator correct?
No, the administrator is wrong.
This is so because: when the number of children is subtracted from the total patient, the remaining number is not 408
Solving (b): Estimate the number of adults
By rounding up:
[tex]Adult = Total - Children[/tex]
Actual Figures
[tex]Adult = 931 - 423[/tex]
Round up
[tex]Adult = 900 - 400[/tex]
[tex]Adult = 500[/tex] -- approximately
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
What is the solution to the equation?
132+x=74
-
O X=-6
O
O X=-6
.
O
X= 20
X= 21
Answer:
The second one is right!
x= -6 1/2
20 POINTS PLS ANSWER
Aaron has made a mistake in his work. Circle Aaron’s mistake in the image below.
Answer: 24 h/ 1 day needs to be circled
Step-by-step explanation:
To cross out the first 1 day and the second, you need to have the last 1 day at the top and 24 hour needs to be on the bottom. (You can see that the h in the answer is at the bottom too.) Good Luck!
Find the cos of angle c
A.3/5
B.6/5
C.5/3
D.1
What is the largest multiple of 7?
Answer:
175
Step-by-step explanation:
BRAINLIEST PLEASE JELP
What is the slope of a line perpendicular to the given line?
Answer:
4
Step-by-step explanation:
The perpendicular slope means opposite reciprocal
opposite: 1/4
reciprocal: 4
Answer:
The slope is undefined
Step-by-step explanation:
Rate me please
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!
Given the points below, find
XY
XY
.
X(-9, 2)
X(−9,2)
and
Y(5, -4)
Y(5,−4)
Answer:
XY=(-45,-8)
Step-by-step explanation:
XY=(-9,2)(5,-4)
What is the measure of angle a
Answer:
48
Step-by-step explanation:
42 + 90 = 132
180 - 132 = 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 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.
What the solution for x is in 14+x=3a+ab?
Answer: a= x+14 /b+3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplifying
14 + x = 3a + ab
Solving
14 + x = 3a + ab
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + x = 3a + -14 + ab
Combine like terms: 14 + -14 = 0
0 + x = 3a + -14 + ab
x = 3a + -14 + ab
Reorder the terms:
x = -14 + 3a + ab
Simplifying
x = -14 + 3a + ab
Solve for n 3m+2n=8 how do you do theseee?
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 :>
Simplify.
9(y + 7) plzzzz answer fastt
Answer:
y=7
Step-by-step explanation:
9y+63
63/9=7
Which of the following ratios is not 4:9
8 : 18
12 : 36
20 : 45
16 : 36
Answer:
I think 12 : 36 I not so sure though
Given h(x) = 5x - 3. Find h(a + 1).
Given h(x}
Answer:
5a + 2
Step-by-step explanation:
To find h(a + 1), substitute x = a + 1 into h(x), that is
h(a + 1) = 5(a + 1) - 3
= 5a + 5 - 3
= 5a + 2
⚠️⚠️marking brainliest⚠️⚠️
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
Six more than the product of a number and -2 is 4.
(-2,-4) and (6,7)
Need help show steps too
Answer:
Step-by-step explanation:
period
If f(1) = 1, what is f(3)?
Answer:
would be 3
Step-by-step explanation:
if 1 is 1 ,3 would be 3 ;-;
Exit ticket help please
Answer:
The answer is B
Step-by-step explanation:
I am learning the same thing somehow
f(x) = 3x - 8 and g(x) = -x - 4. Find (f + g)(x) and (f + g)(5).
Answer:
(f+g)(x) = 3x - 8 -x -4
(f+g)(x) = 2x-12
(f+g)(5) - substitute 5 into x
(f+g)(5) = 2(5)-12
(f+g)(5) = 10-12
(f+g)(5) = -2
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
Which statements are correct interpretations of this graph?
Select each correct answer. (multiple choice question)
A. 3 boxes are filled every 4 min.
B. 4 boxes are filled every 3 min.
C. 1.3 boxes are filled per minute.
D. 0.75 boxes are filled per minute.
(Graph down below)
Answer:
A
Step-by-step explanation:
[tex]\boxed{~ Hello!\; here's\; your \;answer!}[/tex]
___________________________________________________________
[tex]\huge\boxed{A.}[/tex]
___________________________________________________________
A's Explanation...
The first point given is at 3 and 4. 3 is at "Boxes Filled" While 4 is at "Time (Min)". Therefore, your answer is A, 3 boxes are filled every 4 min.
___________________________________________________________
[tex]\boxed{Hope\;I\;helped!}\\\\\\\boxed{May\;I\;Have\;Brainliest?}\\\\\\\\\huge\boxed{Thanks,\;Plip.}[/tex]
___________________________________________________________
PLease help with this question? I also need an explanation on how you got the answer
Answer:
25%
Step-by-step explanation:
1. there are 8 triangles
2. 2 twos
3. 2/8
4. 2/8=25%
4. T-Bone's Math teacher requires 6 book
reports the 1st semester. T-Bone has 4
more reports to complete. How many
book reports has T-Bone already
finished?
x - 4 = 6
x + 4 = 6
Answer:
2
Step-by-step explanation:
6-4=2