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
NEEd help quickly please!!! The basketball game had 500 people in attendance. If the ratio of Pioneer fans to Lion fans is 15:5, how many MORE Pioneer fans were there? Pls use tape diagram.
Answer:
Step-by-step explanation:
15(500/20)-5(500/20)
375-125
250
There were 250 more Pioneer fans than Lion fans.
Is my Answers Correct? Very easy Question!
Answer:
Step-by-step explanation:
Correct
Step-by-step explanation:
the 5th one on the right is standard form,
the second one is perfect square form.
PLS HELP I DONT KNOW THIS ONE ITS URGENT
Answer:
A. [tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]
Step-by-step explanation:
WX, VY, and UZ are parrelel to each other, therefore, base on triangle proportional theorem, the two transversal lines are divided proportionally by the 3 parallel lines.
Thus, we would have the following equation which is true:
[tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]
They boost the economy
Answer:
I think the question is incorrect
Step-by-step explanation:
they boost the economy why is this in mathematics
♀️♀️
What is the answer to -5+(-5r)+10
Answer:
=−5r+5
Step-by-step explanation:
Let's simplify step-by-step.
−5−5r+10
=−5+−5r+10
Combine Like Terms:
=−5+−5r+10
=(−5r)+(−5+10)
=−5r+5
Answer: -5r+5
Step-by-step explanation: 1rst: Eliminate redundant parentheses
-5+(-5r)+10
-5-5r+10
2nd: Add the numbers
-5-5r+10
5-5r
3rd: Rearrange terms
5-5r
-5r+5
Use the bar graph to find the probability of the event
Not spinning a 1
10+8 you add all the data to get your answer
A bus can hold a total of 60 students. The bus is 73% full how many students are on the bus?
Answer:
44
Step-by-step explanation:
so youre looking for 73% of students rite? of means multiplication , you just times 73% by 60
73%*60=43.8
but there cant be point 8 of a person unless theyre missin a couple limbs, so you round up to 44!
hope it helps :)
Look at the image. Could someone please help me out? Only question B Thank you! WILL GIVE BRAINLYEST
Answer:
y = 3
Step-by-step explanation:
2x+6y=5x+4y if x=2
2(2)+6y=5(2)+4y
4+6y=10+4y
-4 =-4
6y=6+4y
-4y= -4y
2y=6
/2=/2
y=3
HELPPPPP PLSSSSSS !!!!!!!
Charmaine is having a party. She'll have 4 tables for every 8 guests. Complete the table below showing the number of tables and the number of guests
Answer:
Top is 18, Bottom goes 6 for 12, then 7 for 14, then 10 for 20
Step-by-step explanation:
2 guests = 1 table
Please Help. Will give Brainliest.
Answer:
translation.........
Show how you found the slope and y-intercept
Answer:
Slope: [tex]\frac{5}{2}[/tex]
y-intercept: 0
Step-by-step explanation:
First, find the slope. Use two points given to you. In this case, I will use the following:
(x₁ , y₁) = (2 , 5)
(x₂ , y₂) = (4 , 10)
Use the following equation:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the corresponding numbers to the corresponding variables:
slope (m) = [tex]\frac{10 - 5}{4 - 2}[/tex] = [tex]\frac{5}{2}[/tex]
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Plug in the slope into m for the equation:
[tex]y = \frac{5}{2} x + b[/tex]
Choose a point to use to find b. In this case, I will use (2 , 5). Plug in 2 for x, and 5 for y:
[tex]5 = \frac{5}{2}(2) + b[/tex]
Simplify. Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:
[tex]5 = \frac{5}{2}(2) + b\\5 = 5 + b\\5 (-5) = 5 (-5) + b\\b = 5 - 5\\b = 0[/tex]
Y-intercept: 0
I cut a pizza in half. Then I cut each half into 3 equal pieces and each piece into 2 equal slices. I sold 6 slices. What fraction of the pizza did I sell?
Answer:
6/12
Step-by-step explanation:
im pretty sure, i did it on a paper correct me if im wrong sorry if i am
Please help I'm confused with what to put in those boxes
Factorise
7lm - 21lmn
Answer:
7lm - 21lmn
taking common 7lm
7lm(1-3n)
Please!!!!! help!!!!!
Answer:
x = 6, x = 8, and x = 10
Step-by-step explanation:
Since 44 > 35, that means that
[tex]2x + 3 > x + 8\\x + 3 > 8\\x > 5[/tex]
so that means the ones that work are x = 6, x = 8, and x = 10
Laura had a toy robot collection. 4/7 of her 28 robots make noise. How many of Laura’s robots make noise? If you guys answer can you please do show you work.
Answer:
4/7 of 28 robots is 16.
Step-by-step explanation:
This is because 4/7 is equal to 16/28 when you simplify it. multiply 7 by four and you get 28 as your denominator and 16 as your numerator.
5th grade math. correct answer will be marked brainliest. what are the last 2 boxes?
Answer:
you forgot (2,28) :)
Step-by-step explanation:
A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function
Answer:
-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7
Step-by-step explanation:
[tex](x-5/2)^{2}(x-3)(x-0)^4 =0\\(2x-5)^{2}(x-3)(x)^4 =0[/tex]
Expand and get
-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7
The standard form will be [tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
What will be the standard form of the given expression?The given expression is
[tex](x-\dfrac{5}{2})^2(x-1)^2(x-0)^4=0[/tex]
[tex](x^2-5x+\frac{25}{4} )(x^2-2x+1)(x^4)=0[/tex]
[tex](x^4-2x^3+x^2-5x^3+10x^2-5x+\dfrac{25x^2}{4} -\dfrac{50}{4} x+\dfrac{25}{4} ) x^4=0[/tex]
[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
Thus the standard form will be
[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
To know more about Polynomials follow
https://brainly.com/question/15702527
Barbara charges $3.50, plus $2.25 for each hour she babysits. If Barbara charges $21.50, how many hours does she babysit?
Answer:
8 hours
Step-by-step explanation:
The equation is 2.25X + 3.50 = 21.50
X represents the unknown amount of hours she worked. 2.25 is the cost per hour. 3.50 is the fee she charges for every gig. That fee only happens once a gig so naturally it wasn't the number x was placed with.
2.25X + 3.50 = 21.50
2.25X + 3.50 - 3.50 = 21.50 - 3.50
2.25X = 18
2.25X = 18
2.25 2.25
X = 8
There are 4 oranges, 7 bananas, and 5 apples in a fruit basket.
Ignacio selects a piece of fruit at random and then Terrance
selects a piece of fruit at random.
probability of two bananas
p( two bananas )
.hnsxasy543esx nuyAtre
Which phrase best describes the relationship indicates by the scatter plotting?
Answer:B
Step-by-step explanation:
A single six-sided die is rolled. Find the probability of rolling a seven.
Answer: there is no probability to roling a 7
Step-by-step explanation: there are only 6 sides to the die that is rolled
Please Help me, what the answer
When Joe solved a system using substitution, he got 7 = 9. What can Joe
conclude? *
The solution to the system is (7.9).
The system of equations does not have a solution,
The work must be incorrect because it is not possible to get this equation
The system of equations has infinitely many solutions,
Answer:
The system of equations does not have a solution
Step-by-step explanation:
Whenever you get a number = a different number, that means there's no solution.
u={1,2,3,4,5,6,7,8,9}
a={2,4,6,8}
b={3,6,9}
What is the set AUB?
Answer:
AUB = {2,3,4,6,8,9}
Step-by-step explanation:
The set u should not be included in set AUB
in a classroom 1/6 of the students are wearing blue shirts and 2/3 of wearing white shirts there are 36 students in the class how many students are wearing blue shirts
Answer:
6 students are wearing blue shirts
Step-by-step explanation:
you divide 36 by 6 and that equals 1/6 of the students.
Can someone explain the washer method in calculus and help me solve this problem?
Answer:
Step-by-step explanation:
When 6 is added to four times a number, the result is 50
Answer:
50-6= 54
54÷4= 13.5
editing for clarity.
first you subtract the 6 from the 50 to find out what the "4 times a number" came to.
in this case, 50-6, which equals 54.
then, you divide the 54 by 4 to get 13.5.
so, the whole math problem would be
4 times 13.5 plus 6 equals 50.
Answer and explain ILL MARK BRAINLIEST I DONT UNDERSTAND
First let's reduce the feet to miles
there are 5280 feet in a mile therefore
26400 feet=5 miles
31680 feet=6 miles
Jet A(the first jet) descends 5 miles in 96 miles
Jet B(the second jet) descends 6 miles in 120 miles
We can compare these as fractions to see which is steeper. This can be viewed as slope and the origin (0,0) is the airport.
slope: 6/120=?=5/96
1/20=?=5/96
Now we know that 5/100 =1/20 so 5/96 must be bigger than 5/100 because you are dividing by a smaller number.
so 1/20<5/96
So Jet B is descending steeper than Jet A.
As for linear model, I don't exactly know what your teacher means but I think I actually used the linear model when I'm thinking of steepness as slope in the coordinate plane, I will include a picture.
In this extremely zoomed out graph, you can see the blue line is just slighly higher than the red line(slope as in explanation is way easier to tell) this could be seen as the linear model) :) Hope it helped!
What is the measure of angle A?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.
Answer: 45 degrees
Step-by-step explanation: