A tank contains 210 liters of fluid in which 30 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 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. Find the rate at which the number of grams of salt in the tank is changing at time t.
Answer:
[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min
Step-by-step explanation:
The mass flow rate dA(t)/dt = mass flowing in - mass flowing out
Since water is pumped in at a rate of 3 L/min, and it contains no salt, the concentration in is thus 0 g/L. the mass flow in is thus 0 g/L × 3 L/min = 0 g/min.
Let A(t) be the mass present at any time, t. The concentration at any time ,t is thus A(t)/volume = A(t)/210. Since water flows out at a rate of 3 L/min, the mass flow out is thus, A(t)/210 g/L × 3 L/min = A(t)/70 g/min.
So, dA(t)/dt = mass flowing in - mass flowing out
dA(t)/dt = 0 g/min - A(t)/70 g/min
dA(t)/dt = - A(t)/70 g/min
Since the tank initially contains 30 g of salt, the initial mass of salt in the tank is 30 g. So A(0) = 30
So, the initial value problem is thus
dA(t)/dt = - A(t)/70 , A(0) = 30
Separating the variables, we have
dA(t)/A(t) = -dt/70
Integrating both sides, we have
∫dA(t)/A(t) = ∫-dt/70
㏑A(t) = -t/70 + C
taking exponents of both sides, we have
A(t) = exp(-t/70 + C)
A(t) = exp(-t/70)expC
[tex]A(t) = e^{-t/70}e^{C}\\A(t) = Ce^{-t/70} whereC = e^{C}[/tex]
A(0) = 30, So
[tex]A(0) = Ce^{-0/70}\\30 = Ce^{0}\\C = 30[/tex]
[tex]A(t) = 30e^{-t/70}[/tex]
The rate at which the number of grams of salt in the tank is changing at time t is
[tex]dA(t)/dt = \frac{d30e^{-t/70} }{dt} \\dA(t)/dt = -\frac{30e^{-t/70} }{70}\\dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex]
So, the rate at which the number of grams of salt in the tank is changing at time t is
[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min
A helicopter flies 238 miles in 3 hours 10 minutes. Calculate the average speed.
Action game rental charges $25 membership fee at eight to rent a video game Bob’s easy game rental charge is $13 to rent a video game if you run in the same number of games from each business after running how many games with the overall cost be less for action game rental
division is 1.92307692308
multiply is 325
can you help me please
Answer:
1000 = n
Step-by-step explanation:
PLEASE HELP CHECK MY ANSWER ASAP GEOMETRY 20 POINTS REAL ANSWERS ONLY! PLEASE EXPLAIN HOW I AM CORRECT!
Answer:
√13
Yes you are right
Step-by-step explanation:
The law of cos again
BC^2 = 18 + 25 - 2 * 3√2 * 5 cos(45 degrees)
= 13
==>
BC = √13
Answer:
yes the answer is correct
Consider the non-right triangle below.
Suppose that m∠ABC=44∘, and that x=16 cm and y=13 cm. What is the area of this triangle?
cm^2
Answer:
72 cm²
Step-by-step explanation:
Given:
m<ABC = 44°
x = 16 cm
y = 13 cm
Required:
Area of the triangle
Solution:
Formula for finding area of a triangle using the Side-Angle-Side method is given as:
Area = ½*ab*sin C
where,
a = 16
b = 13
C = 44°
Plug in the values
Area = ½(16*13)*sin 44
Area = 72.2444705 ≈ 72 cm²
soooo again in meters I'm soo sorryyy
I think 710 is the answer
266+266+89+89= 710
Suppose x is any positive number.
Circle 1: center (0, 0) and radius 2x
Circle 2: center (0, 0) and radius 10x
Why is circle 1 similar to circle 2?
Answer:
Step 1: Determine why circle 1 is similar to circle 2
The reason why circle 1 is similar to circle 2 is that they both expand at the same rate. While x grows larger, both circle 1 and circle 2 grow at a proportional rate. Circle 2 grows is 5 times bigger than circle 1 given any value 5.
When x = 3: circle 1 = 6 and circle 2 = 30
When x = 10: circle 1 = 20 and circle 2 = 100
Answer:
Circle 2 is a dilation of circle 1 with a scale factor of 5.
Step-by-step explanation:
Took the quiz and got a perfect score :)
Can someone help meeeee ??
Answer:
Bottom left graph, ∠a + ∠b = 180°, ∠a + ∠b = 90°, ∠a + ∠b = 90°
Step-by-step explanation:
For the first problem, we can look at the slope. The slope of the equation is negative. The line has to be similar to the bottom slant of the letter "K".
There are two lines that are similar and have the same y-intercept, so it's just a matter of which slope matches.
The slope is -1, so that means to find a different point we go down 1 and right 1.
The only point that's the same on the two lines are (0, 3).
When go down 1 and right 1, the point should be: (1,2)
The only line that satisfy this is the bottom left graph.
For problem 2, ∠a and ∠b must add up to 180°.
So the equation for problem 2 is: ∠a + ∠b = 180°
For problem 3, ∠a and ∠b are equal because they're opposite angles.
So the equation for problem 3 is: ∠a = ∠b
For problem 4, ∠a and ∠b must add up to 90°.
So the equation for problem 4 is: ∠a + ∠b = 90°
For problem 5, ∠a and ∠b must add up to 90°, since the other angle is 90°, which is half to 180°.
So the equation for problem 5 is: ∠a + ∠b = 90°
if the mean of the numbers 2x,3x,4x and 3x is 12,then the sum of the numbers is?
a)4
b)12
c)48
d)80
Answer:
C. 48.
Step-by-step explanation:
If the mean is 12, then 12 must be 2x, 3x, 4x, and 3x divided by 4.
--> [tex]\frac{2x+3x+4x+3x}{4}=12[/tex]
--> [tex]\frac{12x}{4}=12[/tex]
--> [tex]\\3x=12[/tex]
--> x=4
Add: 2x+3x+4x+3x=8+12+16+12=48
What is .06 x .2 please answer
Answer: .012
Step-by-step explanation: 6*2 is 12, and you can simply use the number of decimal points on the smaller term to get .012
Answer:
should be .12
Step-by-step explanation:
.06 multiplied by 2 is .12
explain what is meant by balance stretching
Answer:
Balance stretching is giving equal attention to stretching all parts of your body. It is also important to stretch opposite muscles in equal amounts. For example, you need to stretch your hamstrings as much as your quads, and you need to stretch your right arm as much as your left arm.
or
Balanced stretching refers to performing stretching exercises across the entire body. Stretching the entire body balances the fitness benefits across all muscle groups instead of limiting the benefits to a single or limited number of muscle groups.
Step-by-step explanation:
just took the test on edge
Good Luck!
Balanced stretching can be defined as the process of performing physical exercises to stretch the whole body which gives the body a complete balance and fitness.
What is exercise?This means an activity which is done physically to improve health and fitness.
Many stretching exercises to help the body balance itself.
Alternating knee raises with each step as you walk.
Without using your hands, getting out of a chair and standing up.
Giving each portion of your body equal attention while stretching is known as balance stretching. Stretching opposing muscles equally is also essential. For instance, you should extend your right arm as much as your left arm and your hamstrings as much as your quads.
Learn more about physical exercise here:
brainly.com/question/1744272
#SPJ5
Need help asap!!!
Convert to exponential form
Answer:
B
Step-by-step explanation:
__________________________
Answer:
1.57
Step-by-step explanation:
Answer:
1.57
Step-by-step explanation:
Circumference = 2pi(r) = 2(3.14)1 = 6.28
1/4x6.28=1.57
porfa ayuda:
Dibuja un triángulo isósceles y se divide
su base en 4 partes iguales. Identifica los
triángulos congruentes pintándolos del
mismo color.
Answer:
Ignore los puntos.
Ignore the points.
What is the middle term of the trinomial from (3x+5) (4x-3)
Answer:
11x
Step-by-step explanation:
To find it, you can simply expand the expression
(3x + 5)(4x - 3)
= 3x(4x - 3) + 5(4x - 3)
= 12x² - 9x + 20x - 15
= 12x² + 11x - 15
Can someone help me please I don’t know if I did it right.
Answer:
1st, third and last options are correct answers
Step-by-step explanation:
e + 3 + e + 3
2e + 6
2(e + 3)
1) Solve for x
4x + 3 = 3x - 5
A) 8
C) -8
D) 2
B) -2
help me with this plssss I dont understand
Answer:
y = 18
a = -2
Step-by-step explanation:
Hello There!
For the first one we need to create an equation to solve for y
23+7=y+12
30=y+12
isolate the variable using inverse operations
subtract 12 from each side
30-12=18
we're left with y = 18
for the second one we need to create an equation to solve for a
3+15+a=8+8+8
3+15=18
8+8+8=16
16=18+a
step 1 subtract each side by 18
16-18=-2
we're left with a = -2
Jamie collected some data on students' average grades and the average number of hours they spend playing video games and found there was a weak negative correlation. Which r value is most likely for this data?
Answer:
g
Step-by-step explanation:
gggg
Answer:
r=-0.23684
Step-by-step explanation:
Graph the line with the equation y = – 1/5x-3
Answer:
Check image
Step-by-step explanation:
60 Benjamin bought 6.2 pounds of rice. Each pound cost
$0.90. How much did he spend on rice?
Answer:
.9x 6.2= $5.58
.............
i rlly need help. plssssss
Answer:
10
Step-by-step explanation:
5 x 8 / 4
40/4=10
A = ?
when r = 10 in.
(A = area of a circle)
(r = radius)
i really need helpl lol pleasehelppppppppppppplplplppplplpl ?
Answer:
1,050
Step-by-step explanation:
3.5x
12x
25
=
1,050
e^x is greater than or equal to 25
use an inequality symbol(<, > , =,< to
compare-3+7 -10 -2
25 divided by the difference of 12 and 7
Answer:
5
Step-by-step explanation:
25 / ( 12-7) = 25 / 5 = 5
I hope im right!!
help pls :)) much appreciated
Answer:
9,-7 hope this helps :))))))))
A large operator of timeshare complexes requires anyone interested in making a purchase to first visit the site of interest. Historical data indicates that 20% of all potential purchasers select a day visit, 50% choose a one-night visit, and 30% opt for a two-night visit. In addition, 30% of day visitors ultimately make a purchase, 10% of one-night visitors buy a unit, and 50% of those visiting for two nights decide to buy. Suppose a visitor is randomly selected and is found to have made a purchase. How likely is it that this person made a day visit
Answer:
0.2308 = 23.08% probability that this person made a day visit
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Visitor made a purchase
Event B: Made a day visit
Probability that a visitor made a purchase:
30% of 20%(day visitors)
10% of 50%(one-night)
50% of 30%(two-night)
So
[tex]P(A) = 0.3*0.2 + 0.1*0.5 + 0.5*0.3 = 0.26[/tex]
Probability of a purchase with a day visit:
30% of 20%. So
[tex]P(A \cap B) = 0.3*0.2 = 0.06[/tex]
How likely is it that this person made a day visit?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.26} = 0.2308[/tex]
0.2308 = 23.08% probability that this person made a day visit