Answer:
The number A(t) of pounds of salt in the tank at time 't' is;
[tex]{A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100[/tex]
Step-by-step explanation:
In the question, we have;
The volume of pure water initially in the tank = 700 gal
The concentration of brine pumped into the tank = 3 pounds per gallon
The rate at which the brine is pumped into the tank, = 7 gal/min
The rate at which the well mixed solution is pumped out = The same 7 gal/min
The number of pounds of salt in the tank at time 't' is found as follows;
The rate of change in A(t) with time = The rate of salt input - The rate of salt output
[tex]The \ rate \ of \ change \ in \ A(t) \ with \ time = \dfrac{dA}{dt}[/tex]
The rate of salt input = 7 gal/min × 3 lbs/gal = 21 lbs/min
The rate of salt output = (A(t)/700) lb/gal × 7 gal/min = (A(t)/100) lb/min
Therefore, we have;
[tex]\dfrac{dA}{dt} = 21 - \dfrac{A(t)}{100}[/tex]
Therefore;
[tex]\dfrac{dA}{dt} + \dfrac{A(t)}{100}= 21[/tex]
The integrating factor is [tex]e^{\int\limits {\frac{1}{100} } \, dx } = e^{\frac{x}{100} }[/tex]
[tex]e^{\dfrac{t}{100} } \times \dfrac{dA}{dt} + e^{\dfrac{t}{100} } \times\dfrac{A(t)}{100}= e^{\dfrac{t}{100} } \times21[/tex]
[tex]\dfrac{d}{dt} \left[ e^{\dfrac{t}{100} } \times{A(t)}{} \right]= e^{\dfrac{t}{100} } \times21[/tex]
Using an online tool, we get;
[tex]{A(t)}= c_1 \times e^{\dfrac{-t}{100} } + 2,100[/tex]
At time t = 0, A(t) = 0
We get;
[tex]0= c_1 \times e^{\dfrac{-0}{100} } + 2,100[/tex]
c₁ = -2,100
Therefore, the number A(t) of pounds of salt in the tank at time 't' is given as follows;
[tex]{A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100[/tex]
Helppppppp show your work
Answer:
No solution
Step-by-step explanation:
x+5x+4=3(2x-1)
First off, rearrange:
6x+4=6x-3
The '6x's cancel out (4=-3, incorrect), which means the equation has no solution.
Someone please help me answer this!!
Answer:
4
Step-by-step explanation:
because 7=3+4, so x=4 to make it 7
The sum of - 6a and 7a is - 31
Answer:
a = -31
Step-by-step explanation:
According to the question,
-6a + 7a = -31
a = -31
Trevor wants a life insurance policy with a cash feature and one he can change the death benefits of without having to get a new policy. What type of policy best fits this scenario
Answer:
un death somthing
Step-by-step explanation:
i need help. i don't understand
Answer:
The 20-count batteries have a lower unit price of $0.76 per battery
Step-by-step explanation:
Unit price means how much does it cost if you buy one of the item. To calculate this take the amount of money it cost and divide by the amount of object you have.
In the case of this question we know that you can buy 8 batteries for $6.16 and 20 batteries for $15.20. Let's find the unit cost (how much for one battery) for each of these packs. To calculate that we can take $6.16/8 batteries = $0.77 per battery for the 8 pack and $15.20/20 = $0.76 per battery for the 20 pack. Therefore, the 20-count batteries have a lower unit price of $0.76 per battery.
What does X and Y equal?
Answer:
X= 67
Y= 6
Step-by-step explanation:
Triangle TRU is an equilateral triangle which means all sides are equal.
Triangles sum up to 180°.
180/3= 60
60+7= 67
x=67
Triangle TRS is an isosceles triangle which means it has two equal sides.
Triangles sum up to 180°.
180-60= 120
TRS= 120°
60/2= 30°
RTS= 30°
RST= 30°
30/5= 6
y= 6
What is the x-coordinate of the solution to the following system of equations? Use
the graphing method:
y = 2x - 6
y = -1/2x + 4
A. x=-2
B. x=4
C. x=-4
D. x=2
Answer:
B. x=4
Step-by-step explanation:
if you're in k12
What do all rhombuses have in common
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.
All rhombuses have equal sides and diagonals that bisect each other at right angles.
We have,
All rhombuses have the following characteristics in common:
- Equal Sides:
A rhombus is a quadrilateral with all four sides of equal length.
Each side of a rhombus has the same measurement.
- Opposite Angles are Equal:
The opposite angles of a rhombus are congruent (equal in measure). This means that if we label the angles A, B, C, and D in a clockwise or counterclockwise direction, then angle A is congruent to angle C, and angle B is congruent to angle D.
- Diagonals Bisect Each Other:
The diagonals of a rhombus are perpendicular bisectors of each other. This means that the diagonals intersect at a right angle, and they divide each other into two equal halves.
- Diagonals are Equal in Length:
The two diagonals of a rhombus are of equal length. If we label the endpoints of the diagonals as E, F, G, and H, then EF = GH.
Thus,
All rhombuses have equal sides and diagonals that bisect each other at right angles.
Learn more about Rhombus here:
https://brainly.com/question/27870968
#SPJ6
At medieval lake 12% of people have red hair if there is a total of 150 people how many them do not have red hair
Answer:
132
Step-by-step explanation:
Please HELP
Which pair of functions are inverses of each other?
A. f(x) = 6 + 12 and g(x) = 9x - 12
B. f(x) = 8x – 3 and g(x) = 2*3
O c. f(x) = 77x and g(x) = (5) 3
O D. f(x) = 6 - 5 and g(x) = 275
Answer:
B
Step-by-step explanation:
To find inverse, you switch the x and y variables in the first equation and then solve for y
Factor the following: 18X - 6
6 (3x - 1)
18 (x - 1)
9 (2x - 4)
I need the answer NOW
Answer:
Answer is 6(3x-1)
Step-by-step explanation:
I hope it's helpful!
WILL MARK BRAINLIEST! Solve for X on the provided picture. Thank you!
Answer:
Step-by-step explanation:
x + (180-140) + (180-132) = 180
x = 92°
1. Noah printed a map of a walking trail. The length of the trail is 12 cm.
(a) 1 cm on the map represents 2 km on the actual trail. What is the scale factor from the map to the actual trail?
(b) What is the length of the actual trail?
Answer:
B: 24
(Sorry if this is wrong i tried my best)
Juan saved x dollers last month. This month he saved $8 more than 3 times the amount he saved last month. he saved a total of $141how much did he save last month
Answer:
39
Step-by-step explanation:
You take 141 and divide it bye 3. Then you get 47 then subtract 8. Hope this helps!
Ill give you brainliest if you answer this question!
Answer: [tex]16x^2[/tex]
Step-by-step explanation:
Help me with this question
Please I need help
Answer:
384 cm²
Step-by-step explanation:
The shape of the figure given in the question above is simply a combined shape of parallelogram and rectangle.
To obtain the area of the figure, we shall determine the area of the parallelogram and rectangle. This can be obtained as follow:
For parallelogram:
Height (H) = 7.5 cm
Base (B) = 24 cm
Area of parallelogram (A₁) =?
A₁ = B × H
A₁ = 24 × 7.5
A₁ = 180 cm²
For rectangle:
Length (L) = 24 cm
Width (W) = 8.5 cm
Area of rectangle (A₂) =?
A₂ = L × W
A₂ = 24 × 8.5
A₂ = 204 cm²
Finally, we shall determine the area of the shape.
Area of parallelogram (A₁) = 180 cm²
Area of rectangle (A₂) = 204 cm²
Area of figure (A)
A = A₁ + A₂
A = 180 + 204
A = 384 cm²
Therefore, the area of the figure is 384 cm²
if chase has 4 times as many nickels as dimes and they have a combined value of 180 cents .how many of each coin does he have ?
Retama Park offers a Superfecta bet, in which you predict the exact order of the top four finishers. If there are 8 horses, find the number of possible ways to pick the Superfecta.
Kerry went for a run on Monday and Tuesday. On Monday, Kerry ran 4.7 kilometers. On Tuesday, Kerry ran 3.9 kilometers. How many total meters did Kerry run over the two days?
meters
Answer:
he ran 8600 meters
Step-by-step explanation:
4.7+3.9=8.6
1 kilometer=1000 meters
8.6×1000=8600
SA = 2tr2 + 2trh (Use 3.14 for .) How much metal is needed to create a cylindrical can with a height of 5 inches and a base diameter of 3 inches? square inches Do NOT round your answer.
Answer:
[tex]SA=61.26\ \text{inches}^2[/tex]
Step-by-step explanation:
The surface area of a cylinder is given by :
[tex]SA=2\pi r^2+2\pi rh[/tex]
Where
r is radius and h is height of the cylinder
We have, h = 5 inches and r = 3/2 = 1.5 inches
Put all the respected values.
[tex]SA=2\pi \times (1.5)^2+2\pi \times 1.5\times 5\\\\SA=61.26\ \text{inches}^2[/tex]
So, the surface area of the cylinder is equal to [tex]61.26\ \text{inches}^2[/tex].
Answer:
Answer: 61.23 / {I'm right trust me Acellus 2022}
Step-by-step explanation:
how much metal is needed to create a cylindrical can with a height of 5 inches and a base diameter of 3 inches
eight hundred four thousand seventy-3 in standard form
Answer:
1/607645423000
Step-by-step explanation:
Answer:
804,067
Step-by-step explanation:
804,070 - 3 = 804,067
expresa en notacion cientifica 100000000000
Answer:
this is the answer
Step-by-step explanation:
10 to dip our 10
[tex]log10(3 \times 2)[/tex]
Answer:
log3 (2) = 0.630929754
Step-by-step explanation:
Marc throws a ball out of a second story window The path of the ball is shown on the graph
Answer:
I cant help you theres no graph sorry
Step-by-step explanation:
HURRY PLEASE!! I WILL GIVE BRAINLIEST
Answer:
1/64
Step-by-step explanation:
1/64=(1/8)^2
1/64=(1/4)^3
Answer:
25
Step-by-step explanation:
It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that customers' purchases are made independently, and let X represent number of customers who purchase running shoes. Find the probability distribution of X. Group of answer choices Geometric distribution None of the given distributions Binomial distribution Hypergeometric distribution Negative Binomial distribution Poisson distribution
Answer:
Binomial distribution
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they purchase a pair of running shoes, or they do not. Customers' purchases are made independently. This means that the probability distribution of X is the binomial probability distribution.
You allowed to eat 11 bananas and you have already eaten 4. Find the possible amount of bananas you can eat today
Answer:
7
Step-by-step explanation:
11-4=7
11
-
4
____
7
So 1-4 you cant do so you to the left number which is 1 take it back and now it is 11-4 you add 10 so then the left number you cant use anymore so then its 11-4 which is 7.
Two quantities are proportional if they vary and have a constant ratio or unit rate.
O True
O False
Please only answer if you know the answer
Plzz help mee!
What are the dimensions of the base of the pyramid?
A. 8ft by 6ft
B.8ft by 3ft
C.6ft by 3ft
D. 8ft by 9ft
Answer:
B. 8ft by 3ft
Step-by-step explanation:
It tells you in the picture, the 8 ft and 3 ft are on the sides of the base.
What’s the most common Multiple for 3 and 5
Answer:
should be 15...
Step-by-step explanation: