Answer:
The answer is 6 6/12
Step-by-step explanation:
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
A car travels 1295 feet in 5 seconds. How far can the car travel in 50 seconds?
Answer:
12950
Step-by-step explanation:
evaluate the expression when x=4/5 and y=-2/9: 3y-x
Answer:
-2/15
Step-by-step explanation:
The equation below describes a proportional relationship between x and y. What is the constant of proportionality? y=3/5x The constant of proportionality is______
Answer:inversely proportional
Step-by-step explanation:
As the value of x increase the value of y decrease
please help this is so confusing!!!
Answer:
$16.50 on 3 bags of dog food
Step-by-step explanation:
First you would do 27.50/5 to find out how much one bag costs.
The symbol / mean to divide. So 27.50 divided by 5 is 5.50. We need to know the ammount of 3 bags. Hence, we evaluate 3 times 5.50 which equals to our answer, $16.50 on 3 bags of dog food. I hope this will help you succeed!
One number is four times the other number. The larger number is also 87 more than the smaller number.
Find the larger number.
Answer:
116Step-by-step explanation:
Let numbers be x and y
Then we have equations:
x = 4yx = y + 87Comparing
4y = y + 874y - y = 873y = 87y = 87/3y = 29Then, the larger number is
x = 4*29 = 11688) 4 times a number decreased by 8 equals 40
A) x=80 B) x = 40 C) x=8
D) x = 12
juanito has a rope 1.75 meters long. He needs to cut it into shorter ropes each 0.1 meter long
Answer:
17.5
Step-by-step explanation:
[tex]1.75 \div 0.1 = 17.5[/tex]
14. (01.04)
On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?
-9
-6
6
9
Answer:
6
Step-by-step explanation:
U divide 18 by 3.
Answer:
9
Step-by-step explanation:
In slope-intercept form of linear equation y = mx + b , value of "b" is y-intercept.
Let solve 3x + 2y = 18 for "y"
2y = - 3x + 18
y = [tex]-\frac{3}{2}[/tex] x + 9 ⇒ 9 is y-intercept.
===========
There is another way to solve this kind of problems:
Coordinates of y-intercept are (0, y) .
3(0) + 2y = 18
2y = 18
y = 9
(0, 9)
the number in unit form is all mixed up convert it tostandard form
Answer:
Step-by-step explanation:
What number?
Which expression represents 4 less than twice a number, n?
Answer:
x = 2n - 4
Step-by-step explanation:
hope this helped have a great day
How to solve (10 points)
Answer:
side 1: 10 = 15
side 2: 6 = 11
im not 100% sure this is correct
Step-by-step explanation:
13-8 = 5
so we add 5 on each side
10 + 5 = 15
6 + 5 = 11
Find the whole, given the part and the percent. 50% of what number is 60
Answer:
50% of 120 is 60
Step-by-step explanation:
So 60 is half of 120, and 60 times 2 is 50 :)
(Brainliest?)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Let x as that number ,
So :
[tex] \frac{50}{100} x = 60 \\ [/tex]
[tex] \frac{1}{2} x = 60 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{1}{2} x = 2 \times 60 \\ [/tex]
[tex]x = 120[/tex]
Thus that number is 120 .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Use a half-angle identity to find the exact value of sin 3pi/8
The above answer is correct! The correct response is A.
Just got it right on edge 2020, hope this helps!! Good luck, and have a great day! :)
The solution is, Using a half-angle identity we get the exact value of
sin 3pi/8 is ±√[(2 + √2) / 4].
Here, we have,
The half angle formula of sin in trigonometry is
sin A/2 = ±√[(1 - cos A) / 2].
If 0 < x < π/2 , then cos x > 0.
now, we have,
sin 3pi/8
here, A/2 = 3pi/8 so, A = 3pi/4 = 6π/8
applying this half angle formula of sin in trigonometry
we get,
sin 3π/8 = ±√[(1 - cos 6π/8) / 2]
= ±√[(1 + 1/√2) / 2]
= ±√[(2 + √2) / 4]
so, we get,
sin 3π/8 = ±√[(2 + √2) / 4]
Hence, The solution is, Using a half-angle identity we get the exact value of sin 3pi/8 is ±√[(2 + √2) / 4].
For more such question on sin in trigonometry visit:
brainly.com/question/26098092
#SPJ6
The product of two consecutive even integers is 2208. What is their sum?
Answer:
±94
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0Solving Quadratic EquationsConsecutive IntegersStep-by-step explanation:
Step 1: Define
x (1st consecutive term)
x + 2 (2nd consecutive term)
Step 2: Set up equation
x(x + 2) = 2208
Step 3: Solve for x
Distribute x: x² + 2x = 2208Rewrite in Standard Form: x² + 2x - 2208 = 0Factor quadratic: (x - 46)(x + 48) = 0Find roots: x = -48, 46Step 4: Identify Consecutive Integers
Possibility 1: x = -48
1st Consecutive Even Term: -48
2nd Consecutive Even Term: -48 + 2 = -46
Possibility 2: x = 46
1st Consecutive Even Term: 46
2nd Consecutive Even Term: 46 + 2 = 48
Step 5: Find sums
Possibility 1: x = -48
-48 + -46 = -94
Possibility 2: x = 46
46 + 48 = 94
i Wnte 2x2x3x3x5 using exponents.
Harry recently had a birthday. He was given $150 dollars from his parents and $75 from his grandparents. Harry wants to purchase movie tickets and video games with is money. Movie tickets cost $11 each and video games cost $45 each. Write an inequality that represents this situation. Let x represent the number of movie tickets and let y represent the number of video games.
Answer:
11x + 45y ≤ 225
Step-by-step explanation:
So he has 150 + 75 = 225. you then would do
11x + 45y ≤ 225
Answer:
225 ≥ 11x + 45y
Step-by-step explanation:
150 + 75 = 225, so $225 is what Harry has to work with.
Harry can't spend more than $225, hence the "more than or equal to" sign.
"x" represents the number of movie tickets, which cost $11 each. "y" represents the number of video games, which are $45 each.
You must combine these terms to equal a number less than or equal to 225.
Which of the following is a postulate or theorem used to prove two triangles are congruent? ASA SSS AAA SAS
9514 1404 393
Answer:
ASA, SSS, SAS
Step-by-step explanation:
AAA is a postulate used to prove similarity. Congruence cannot be proved without including at least one side.
ASA, SSS, SAS postulates can be used to prove congruence
Which steps can be done to both sides of the equation to determine the value of x? 3.2 x - 9.6= 38.4
Answer:
add both sides ny 9.6 and divide both sides by 3.2, hope this helps!
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
A.) 2 1/8
B.) 2 4/9
C.) 8/17
D.) 3 1/8
Note: there hours and miles, but you have to give two answers, one for miles one for hours THANKS XD lolol <3
Answer:
b
Step-by-step explanation:
the range of what function include-4
Give two reasons why it's impossible to draw triangle PQR m angle Q=103^ m angle R=47^ p = 44 q = 12 , and f = 31
Answer:
It is impossible becuase it would not eqaul the numbers a regular triangles would have. A triangle has to equal a certain number and this number does not make a traingle.
Reason 1: The hypotenuse is invalid, because 44^2 does not equal 12^2 + 31^2.
Reason 2: The angles measures do not correlate properly to their assigned letter sides (at least to me). Additionally, 30 degrees just doesn't make any sense from a logical standpoint.
Select the correct answer.
Which system of equations is satisfied by the solution shown in the graph?
Answer:
i think letter D because it's same
Answer:
one solution
Step-by-step explanation:
Which phrases can be represented by the expression 60w?
The answer is 60 plz correct me
what is the constant of porportionality between 9 and 4.5
Answer:
1/2
Step-by-step explanation:
Someone please help ASAP!!!!
Answer:
3/5 = 6/10, which is 0.6 in decimal form
your class is having a car wash for a fundraiser. it costs $27.95 for supplies. your class charges $5 per car. write an expression for the profit of the car. find the profit if the class washes 34 cars.
Answer:
5x-27.95=profit
5(34)-27.95
170-27.95
$142.05
Use the tape diagram to write an equivalent ratio in simplest form. Write your ratio using a colon and no spaces.
Answer:
4:3
Step-by-step explanation:
There are 8 yellow spots and 6 blue spots
8:6
We can divide each side by 2 since they are both even
8/2: 6/2
4:3
Answer:
4:3
Step-by-step explanation:
The graph of an absolute value function opens up and has a vertex of (0, -3).
The domain of the function is
The range of the function is
Answer:
domain (-∞, ∞)
range [-3,∞)
Step-by-step explanation:
domain is the x value and range is the y value. Since its an absolute value the y value rises from both sides of the x value in a 45° angle.
Which of the following terms is described as “the ratio of two polynomial
expressions”?
a. Linear Algebraic Expression c. Rational Algebraic Expression
b. Linear Algebraic Equation d. Rational Algebraic Equation
Answer:
rational algebraic expression
Answer:
C
Step-by-step explanation: