Answer:
x(t) = 581.66 lb
Step-by-step explanation:
From the given information:
Consider the salt quantity in the tank at time t be x(t) lb.
∴ the rate of change of salt content in the tank is [tex]\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow[/tex]
where:
the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons
=21 lb/s
rate of outflow = salt conc. in the tank × flow rate
= x/250 × 9
= 9x/250 lb/s
∴
[tex]\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}[/tex]
[tex]\dfrac{dx}{dt} + \dfrac{9x}{250}= 21[/tex]
This is a 1st order linear differentiation,
The integrating factor if [tex]e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}[/tex]
∴
[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C[/tex]
[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C[/tex]
[tex]x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}[/tex] at t = (0) and x(0) = 100 lb
Hence;
[tex]100 = \dfrac{1750}{3}+C[/tex]
[tex]C = \dfrac{1750}{3} -100[/tex]
[tex]C = - \dfrac{1450}{3}[/tex]
∴[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}[/tex]
after time t = 1 minute i.e 60 s
[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}[/tex]
[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}[/tex]
x(t) = 581.66 lb
Complete the equation describing how
x and y are related.
-1
0
1
2.
3
y
-4
-4.5
-5
-5.5
-6
-6.5
y = -0.5x + [?]
Answer:
The relationship between x and y is;
y = -0.5x - 4.5
Step-by-step explanation:
When x = -1, y = -4.
Thus from y = -0.5x + [?], we have;
-4 = -0.5(-1) + [?]
Let's call the question mark m for easy identification.
-4 = 0.5 + m
m = -4 - 0.5
m = - 4.5
At x = 0, y = - 4.5. Thus;
-4.5 = - 0.5(0) + m
m = -4.5
At x = 1, y = -5. Thus;
-5 = - 0.5(1) + m
-5 = - 0.5 + m
-5 + 0.5 = m
m = -4.5
We are seeing the same patter as m = - 4.5
Thus the relationship between x and y is;
y = -0.5x - 4.5
Find value of X. write answer in simplest form
Answer:
The answer is X
Step-by-step explanation:
Which is the definition of a ray?a part of a line that has one endpoint and extends indefinitely in one direction the set of all points in a plane that are a given distance away from a given point lines that lie in the same plane and do not intersect part of a line that has two endpoints
Answer:
a part of a line that has one endpoint and extends indefinitely in one direction-by-step explanation:
The definition of a ray can be stated as: a part of a line that has one endpoint and extends indefinitely in one direction.
What is a Ray?In geometry, a ray can be defined as a line segment that has one endpoint and extends on the one direction of the line segment indefinitely.
An example of a ray is shown in the image attached below. Line segments red and blue are two rays with one endpoint that extends towards another direction indefinitely.
Therefore, the definition of a ray can be stated as: a part of a line that has one endpoint and extends indefinitely in one direction.
Learn more about a ray on:
https://brainly.com/question/1850410
What is the domain and range of the coordinates
shown below?
{(11, -3), (2,-2), (2.0), (6,2), (18,4)}
Solve equation 17=r+10
Answer:
unless I am mistaken r=7
Step-by-step explanation:
you subtract 10 from each side and boom done
While chasing its prey, a cheetah is running slowly and then increases its speed by 42.5 miles per hour to reach a top speed of 70 miles per hour. What is the cheetah's initial speed?
42.5 miles per hour
or
112.5 miles per hour
or
27.5 miles per hour
or
35.5 miles per hour
Answer: 27.5 miles per hour
Step-by-step explanation: 70 - 42.5 = 27.5
Suppose that the number of miles that an EV battery (electric vehicle) can run before its battery wears out is exponentially distributed with the average value of 100,000 miles. If a car manufacturer decides to install this type of battery to power the vehicle, do the following: 1) What percentage of the cars will fail at the end of 50,000 miles
Answer:
The value is [tex]P(X = 50,000) = 6.07*10^{-6}[/tex]
Step-by-step explanation:
From the question we are told that
The average value is [tex]E(x) = 100000 \ miles[/tex]
Generally the exponential distribution function is mathematically represented as
[tex]f(x) = \{ \left \theta* e^{-\theta * x } \ ; \ \ \theta >0} \atop {0 \ ; \ otherwise }} \right.[/tex]
Here [tex]\theta [/tex] is a constant which is mathematically represented as
[tex]\theta = \frac{1}{E(x)}[/tex]
=> [tex]\theta = \frac{1}{100000}[/tex]
=> [tex]\theta =1 *10^{-5}[/tex]
So at x = 50,000 miles (given)
[tex]f(50000) = 1 *10^{-5} * e^{-1*10^{-5} * 50000}[/tex]
[tex]f(50000) = 6.07*10^{-6}[/tex]
So the percentage of the cars will fail at the end of 50,000 miles is
[tex]P(X = 50,000) = 6.07*10^{-6}[/tex]
Which is the correct option?(attached)
Answer:
I believe it's D
Step-by-step explanation:
Joe borrowed $8,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 3 years?
Answer:
$1680
Step-by-step explanation:
make use of the simple interest formula:
PRT/100
P is the principle ($8000)
R is the rate of interest (7%)
T is the time (3)
= 8000*7*3 / 100
1680
A beverage company operates two factories. Their outputs are represented by these expressions, where b is the number of bottles produce
Factory A: 2b3 – 3b2 + b - 120
Factory B: 4b2 – 3b – 260
Which polynomial represents the company's total output?
A. 6b3 – 3b2 - 3b - 140
B. 2b3 - 7b2 + 4b + 140
C 2b3 + b2 - 2b - 380
D. 6b3 – 6b2 + b + 380
Answer:
C 2b3 + b2 - 2b - 380
Step-by-step explanation:
Given:
Factory A: 2b^3 – 3b^2 + b - 120
Factory B: 4b^2 – 3b – 260
The company's total output = factory A + factory B
= (2b^3 – 3b^2 + b - 120) + (4b^2 – 3b – 260)
= 2b^3 – 3b^2 + b - 120 + 4b^2 – 3b – 260
Collect like terms
= 2b^3 – 3b^2 + 4b^2 – 3b + b - 120 - 260
= 2b^3 + b^2 - 2b - 380
C. 2b^3 + b^2 - 2b - 380
Option C is the correct answer
Answer: C) 2b^3+b^2-2b-380
Step-by-step explanation:
I had this question on a recent test and got it right
Hope this helps! :)
1:
2
3
Deanna and Lisa are playing games at the arcade. Deanna started with $15, and the
machine she is playing costs $0.75 per game. Lisa started with $12, and the machine
she is playing costs $0.50 per game. After how many games will the two girls have
the same amount of money remaining?
Answer:
After 12 games.
Step-by-step explanation:
Deanna's money after playing 12 games =
15 - (0.75 × 12) = 6$
Lisa's money after playing 12 games =
12 - (0.50 × 12) = 6$
I need the answer to this with the steps, that’d help me out so much thank you❤️.
Answer: The dimensions of the frame:.
W= 2√10 or about 6.3245 inches
L= 4√10 or about 12.6491 inches
Step-by-step explanation:
This would be so much easier if the area of the box was 72. Then the dimensions of the frame would be 6 × 12. So just a little bit larger and more complicated.
Here the equation is w(2w)=80
2w^2 = 80 (2w is easier to work with than L/2).
w^2=40 (^2 means squared)
√w^2 = √40 square root of both sides: Factor 40. Take out√4
W = √4*10
W= 2√10
L= 2w = 4√10
6.3245 × 12.6491 = 80
Is 2 thirds times 5 greater than or less than 5
Evaluate the expression for the given variables.
-a? - (2a - 7b)
+ b for a = -2 and b = 3
A middle school has 2 girls for every 1 boy in seventh grade. The seventh-grade class
has 28 fewer students than the eighth-grade class, which has 298 students. How many
girls are in seventh grade?
Answer:
180 girls
Step-by-step explanation:
298-28=270
270 divided by 3 = 90
90+90 = 180
so there are 180 girls and only 90 boys
A square window has an area of 1,232 in2. (a) What is the length of 1 side of the window? Round your answer to the nearest tenth. Show all of your work. (1 point for the correct answer and 1 point for showing how you got your answer)
x = length of one side.
1,232in^2 = x^2
Take the sqrt of both sides.
35.1 in = x
The length of one side = 35.1 in
Step-by-step explanation:
We know that,
area of square = a²
→ 1,232 = a²
→ a = √1232
→ a = 35.0 in
Nearest 10th = 35.1 in
It takes Dariya 35 seconds to download 5 songs from the Internet. How can the number of seconds it would take Dariya to download 7 songs at this rate be determined? ( need help )
By dividing 35 by 7.
By multiplying 35 by 7.
By finding the unit rate and dividing it by 7.
By finding the unit rate and multiplying it by 7.
To determine the number of seconds it would take Dariya to download 7 songs at the same rate, we first find the unit rate and multiply it by 7.
Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.
Unit Rate = 7second/song.
Time to download 7 songs = 49 seconds.
What do we mean by unit rate?A unit rate is a quantity taken for a unit of another quantity.
How do we solve the given question?We are given that it takes Dariya 35 seconds to download 5 songs from the Internet. We are asked about the time it will take Dariya to download y songs at the same rate.
We will first determine the unit rate of the time taken for downloading a song.
5 songs take 35 seconds.
∴ 1 song takes 35/5 = 7 seconds.
∴ Unit rate is 7seconds/song.
Now to determine the time for downloading 7 songs, we multiply the unit rate by 7.
∴ Time taken to download 7 songs = 7 songs * unit rate
or, Time taken to download 7 songs = 7 songs * 7 second/song
or, Time taken to download 7 songs = 49 seconds.
∴ To determine the number of seconds it would take Dariya to download 7 songs at the same rate, we first find the unit rate and multiply it by 7.
Hence, option 4. By finding the unit rate and multiplying it by 7 is the right option.
Learn more about the unit rate at
https://brainly.com/question/620388
#SPJ2
An isosceles triangle two sides equal is placed on top of the square as shown in the picture if the two equal sides are 22 ft long and each side is 39 ft
Answer:
what we have to find , please complete the question
8p -4p =2p+6 p= Help please
Answer:
[tex]p=3[/tex]
Step-by-step explanation:
[tex]8p-4p=2p+6[/tex]
Solve the left side:
[tex]4p=2p+6[/tex]
Subtract 2p from both sides:
[tex]4p-2p=2p+6-2p[/tex]
[tex]2p=6[/tex]
Divide both sides by 2:
[tex]\frac{2p}{2}=\frac{6}{2}[/tex]
[tex]p=3[/tex]
Answer:
p=3
Step-by-step explanation:
8p-4p=2p+6
4p=2P+6
4p-2p=6
2p=6
P=6/2
p=3 ans
If angle W and angle V are supplementary angels and measure at V is 49 degrees what does measure of angle W equal?
Answer:
131
Step-by-step explanation:
supplementary angles are any two angles whode sum is 180. If v= 49 then 131 would be W. 131+49= 180
What is the formula for finding circumference given the radius?
Answer:
[tex]C = 2\pi r\\[/tex]
Step-by-step explanation:
[tex]Circumference = 2\times \pi \times r[/tex]
Point G is on line segment FH. Given FH = 5x + 2, GH = 5x – 9, and
FG = x + 5, determine the numerical length of FG.
Answer:
Step-by-step explanation:
11
4.5 = m +2.75
what is the answer?
Answer:
m=1.75
Step-by-step explanation:
4.5 = m+2.75Subtract 2.75 on both sides of the equationm = 1.758•1,000+1•1+5•100+4•10,000+8•10 standard form
Answer:
48581
Step-by-step explanation:
Answer:
48581
Step-by-step explanation:
Brainliest WILL BE MARKED I NEED HELP MATH DON'T GET IT
the temperature dropped from 44 degree to -56 degree. what was the change in tempreture
the place to the left of the tens place
Answer:
I think it's gonna be 100.
Step-by-step explanation:
Answer:
my bad didn't understand hundredth
Step-by-step explanation:
A triangle has a perimeter of 26 inches. The medium side is 6 more than the short side, and the longest side is 3
times the length of the shortest side. Find the shortest side?
Answer:
where is your formula? pliz tell me
plz hellppppp (6h + 8) - (3h + 2) = 15
Answer:
h = 3
Step-by-step explanation:
Step 1: Write out equation
(6h + 8) - (3h + 2) = 15
Step 2: Distribute negative
6h + 8 - 3h - 2 = 15
Step 3: Combine like terms
3h + 6 = 15
Step 4: Subtract 6 on both sides
3h = 9
Step 5: Divide both sides by 3
h = 3
Step 6: Check Step
(6(3) + 8) - (3(3) + 2) = 15
(18 + 8) - (9 + 2) = 15
26 - 11 = 15
15 = 15
(6h + 8) - (3h + 2) = 15
Let's distribute the - to 3h + 2
6h + 8 - 3h - 2 = 15
Combine like terms
3h + 6 = 15
Subtract 6 from both sides
3h = 9
Divide both sides by 3
h = 3
If the room had a volume of 5,184,000 cubic inches, approximately how many basketballs
did the students put in the principal's office if each basketball has a volume of 523.6 cubic inches?
Answer:
around 9900.6 balls can fit in the room
Step-by-step explanation: