Answer:
[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]
A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]
Step-by-step explanation:
Given - A tank contains 350 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t.
To find - Find the rate at which the number of grams of salt in the tank is changing at time t.
Find the number A(t) of grams of salt in the tank at time t.
Proof -
Given that,
Total fluid in the tank = 350 litres
Total salt = 40 grams
Rate in flow = 5 L/min
Rate out flow = 5 L/min
Concentration in = 0
Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)
Now,
Total solution in the tank at time t = Total fluid in the tank + (Rate in flow - Rate out flow )t
= 350 + (5 - 5)t
= 350
⇒Solution in the tank at time t = 350
⇒Concentration out = [tex]\frac{A(t)}{350}[/tex]
Now,
Rate of change in the tank at time t = [tex]\frac{dA}{dt}[/tex]
= (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)
= 5(0) - 5([tex]\frac{A(t)}{350}[/tex])
= 0 - [tex]\frac{A(t)}{70}[/tex]
= [tex]-\frac{A(t)}{70}[/tex]
⇒[tex]\frac{dA}{dt}[/tex] = [tex]-\frac{A(t)}{70}[/tex]
⇒[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]
Integrate both sides , we get
ln(A) = [tex]-\frac{1}{70}t + C[/tex]
⇒A(t) = [tex]e^{-\frac{t}{70}+ C}[/tex]
= [tex]e^{-\frac{t}{70}}*e^{C}[/tex]
= [tex]C_{1} e^{-\frac{t}{70}}[/tex]
⇒A(t) = [tex]C_{1} e^{-\frac{t}{70}}[/tex]
Now,
Given that,
Initially, the tank has 40 grams of salt
⇒A(0) = 40
⇒C₁ = 40
⇒A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]
34+35? :)))) answer immediately
Answer:
69
Step-by-step explanation:
30+30=60
4+5=9
60+9=69!
Lucy has $60,000 in a savings account that earns simple interest of 14% per year. How much will she have in her account after 5 years?
Answer:
$42,000
Step-by-step explanation:
60,000 × .14 × 5 = 42,000
Need help plz and thank u
Answer:
20%
Step-by-step explanation:
12/60 (divided) makes 0.2, converted to a percent is 20%
6) Solve:
5x + 12 + 3x = 8x - 5
Answer: −17
Step-by-step explanation: ez
1) f(x) = 3*
f(x)
x
-1
0
1
2 3
1)f(×)=3*=f(×)=×-1 0 1=0.23
How many joules of gravitational potential energy are stored in an object that has a mass of 8.5 kilograms and is held 2 meters above the surface of earth?
Answer:
I believe the answer is 166.6 Joules or (if rounding to the nearest whole number) 167 Joules.
Step-by-step explanation:
Here is the formula to find the gravitational potential energy of an object:
U = m * g * h (potential energy equals mass times gravitational acceleration * the height)
The mass is 8.5 kilograms, the height is 2 meters, and Earth's gravitational acceleration is always, no matter the other values or earthly situations, 9.8 m/s.
Now we solve:
8.5 * 9.8 * 2 = 166.6 which is rounded to 167 Joules.
How is math used in making murals?(subject:Collage and Career readiness)
An electronics store is having a 15% off sale. Suppose the sale price(p) of a laptop is $495. Which statement are true for this stuation
A. P+ 0.15p represents the sales price
B. P- 0.15p represent the sales price
C. 0.85p represents the sales price
D. The sale price is 420.75
E. The sale price is 569.25
Answer:
The answer to the Question is D
Answer:
B, C, D
Step-by-step explanation:
If the sales price is 15% off, then the the price is .85(100-15%) of the price so c is true
this also makes b true. (100-15%) is p-.15
495 x .85 (100-15%)=420.75 so d is true
Graph the inequality.
x > 4
Answer:
Step-by-step explanation:
I need help sooo please HELP ME :’) ill give good points because its my last question:
When is the multiplicative relationship used? Select all that apply.
options (more than 1):
1.When multiplying the same amount to an x-value.
2.When subtracting the same amount to an x-value.
3.When dividing the same amount to an x-value.
4.When adding the same amount to an x-value.
Answer:
1 and 3
Step-by-step explanation:
Gina tosses a number cube 66 times. About how many times would you expect that Gina would toss a 6?
Answer:11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
its 11 because 66 divided by 6 = 11
What quadrant does 21pi/4 lie in?
Answer:
The angle is in the third quadrant.
PLEASE HELP!! Will give out brainliest!!! But also have to explain how you got the answers!! Please and thanks!!
1) Consider the piecewise
function shown on the graph, which is composed of exponential,
linear, and polynomial pieces.
h(x)
Complete the statements describing function h.
10
8
6
Over the interval [0, 3), function h is represented
4
2
by
function
-10
-8-6
4
02
-2
4
6
8
10
Function h
a continuous function.
As x approaches positive infinity,
h(x) approaches
As x approaches negative infinity,
-10
h(x) approaches
9514 1404 393
Answer:
exponentialis+∞-∞Step-by-step explanation:
Neither linear nor exponential functions have a "wiggle" in their graph, so the piece in the region x < 0 is polynomial.
The piece in the interval [0, 3] is concave upward and has increasing slope. It could be polynomial, but is most likely the exponential piece of the function.
For x > 3, the function is linear.
There are no gaps in function value where the transition is made from one piece to another, so the function is continuous.
The function tends upward at the right side of the graph. It tends downward at the left side of the graph. This tells you the sign of the infinity they tend toward matches the sign of the infinity x tends toward.
__
On the interval [0, 3], h(x) is represented by an exponential function.
H(x) is a continuous function.
As x approaches +∞, h(x) approaches +∞.
As x approaches -∞, h(x) approaches -∞.
A researcher studies differences in career goals between boys and girls in middle school. All of the students in the seventh grade schools in a particular county answer a list of questions. What type of study is this?
A. Experiment
B. Sample Survey
C. Observational Study
D. Random Trial
Explanation:
When asking/answering questions like this, a survey is involved. It could be multiple choice or fill in the blank. Multiple choice may be the best way because it's easier to compare data results when you have only a few options. It also gives the computer an easier time too.
We aren't conducting an experiment since the researcher is not directly affecting the people, and instead letting them answer the questions without intervention. Also, note how we don't have two groups of treatment vs control. This is another indication we don't have an experiment.
An observational study is not being done here either. Yes the researcher is observing the survey results, but s/he is not making notes on the individuals before the survey is conducted (ie before the questions are asked). An example of an observational study is having the researcher make a tally of students' hair color. The researcher simply looks at each student, marks the correct tally, and doesn't need to ask the student a question. So you can see that the interactive question/answer portion is not present in an observational study.
The phrasing "random trial" is not a study type. When you hear "random trial" in the news, maybe for a new drug being developed, the news report is implying heavily that an experimental study had been done. This is true with all drug trials. One group is the treatment group that gets the actual drug, while the control group gets a fake drug. The control group thinks they get the actual drug, which is important because if they knew it was fake, then it would invalidate the study. I recommend researching the placebo affect for more information. The two group's results are then computed to see if the drug did in fact cause a change in the subjects or not. You would see this if there's a significant difference between the treatment and control group. Anyway, the "random trial" is not a study type but rather an aspect of an experimental study. It's possible your teacher put this in here to throw off students.
ASAP will give brainliest
Question 6(Multiple Choice Worth 4 points)
(07.06) There are currently 3 people signed up for the debate club. The school will not recognize the club officially until it has more than 5 members.
Which of the following graphs includes the possible values for the number of people who still need to sign up to make the club "official?"
H>
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6
-3-2-1 0 1 2 3 4 5 6 7 8 9 10
--10-9-8-7-6
1-2-1 0 1 2 3 4 5 6 7 8 9 10
OH
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Answer:
it should be the last one
Step-by-step explanation:
Evaluate the formula for B = 9 in.2 and h = 32 in.
32 in.3
9.6 in.3
96 in.3
288 in.3
Answer:
is going to give you a decimal as then you divide it by 2 and then multiply that number by 4 hope this helps
Step-by-step explanation:
Answer:
is going to give you a decimal as then you divide it by 2 and then multiply that number by 4 hope this helps
Step-by-step explanation:
How can you find f(4) if f(x)=7x^(2)-5
Answer:
107
Step-by-step explanation:
f(x)=7x^(2)-5
f(4) means that x=4
f(4)=7*4^(2)-5
= 7 * 16 -5
= 112 -5
= 107
What is 3r-2 ?? Algebra is not my strong suit
What is the slope of a line of best fit if its equation is y = −2x + 3?
−2
Negative 1 over 2
1 over 3
3
Answer:
-2
Step-by-step explanation:
y=m(slope)x+b(y axis)
please help me. In the circle below, U is the center, VX is a diameter, and m VW = 110 degrees Use this information to fill in the blanks.
Answer:
Step-by-step explanation:
Inscribed angle → ∠VXY
(Angle included between two chords meeting at a point on circumference)
Minor arc → (arc VY)
(Arc measuring less than 180° is called as minor arc)
Semicircle → (arc VWX)
(Arc inscribed by the diameter)
m(arc VWX) = 180°
(Semicircle)
m(∠VUW) = 110°
(Central angle subtended by an arc)
Will Give Brainleist! Plz help me on this problem
Which equation represents a line with slope 3/5 of and y-intercept of -1 ?
Answer:
y = 3/5x - 1
i think that's what's supposed to be there...
( 3 x + 2 ) + ( − 5 x + 7 )
Answer: -2x+9
Step-by-step explanation:
(3
Answer:
It wasnt letting me answer so I put it in the comments but the answer is -2x+9
Step-by-step explanation:
Brainliest??
Tanner collected 360 cans and bottles while fundraising for his basketball team This was 40% less than what Reggie collected How many cans and bottles did Reggie collect?
Answer:
Reggie collected 504 cans and bottles.
Step-by-step explanation:
40%=.40
360*.40=144
360+144=504
honestly lost on these problems
Answer:
29
Step-by-step explanation:
Hope this helps
mark me brainlist
Answer:
27
Step-by-step explanation:
We know the missing angle for the triangle on the left is 63. And that is the same angle reflected to the other side. There is a right angle so its 63 + 90 = 157.
180 - 157 = 27
Write 8 1/5 as a fraction
Answer:
8.2
Step-by-step explanation:
let me know if its wrong
can somebody help me with this quickly I forgot how to do this and yeah ill mark you!
Answer:
4/11 i believe
Step-by-step explanation:
Select the correct comparison.
Set A
Set B
.
....
24
8 10
4 6 8 12
A. The typical value and the spread are both greater in set B.
B. The typical value and the spread are both greater in set A.
C. The typical value is greater in set A. The spread is greater in set B.
D. The typical value is greater in set B. The spread is greater in set A.
Answer:i would say C ADHAKFFA
Step-by-step explanation:
Gavin needs to buy candy for the 11 students in his class plus himself. Gavin and each student will get one bag of candy. He uses $20 to buy two different types of candy. Gavin buys x bags of gummy bears that cost $1.50 per bag and y bags of chocolates that cost $2.00 per bag. The system of equations used to represent this situation is graphed, as shown.
Answer:
20=1.50(6)+2.00(4)
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
What is the area of the shaded region?
identify the coefficeient following expression
6a+7
Answer:
6
Step-by-step explanation:
The coeffecient is the number next to the variable. Boom. Done.
Answer:
6
Step-by-step explanation:
a coefficient is a number in front (behind) the variable (ex. the coefficient in 2x is 2, and the variable is x)
i hope this helps :)