Answers
Answer:
T = -22/r + 39
(a) y = [130 − 130e^(-0.015t)] / 3
(b) 22.9
Step-by-step explanation:
d²T/dr² + 2/r dT/dr = 0
If S = dT/dr, then:
dS/dr + 2/r S = 0
dS/dr = -2/r S
dS / S = -2/r dr
ln S = -2 ln r + C
S = e^(-2 ln r + C)
S = Ce^(-2 ln r)
S = C [e^(ln r)]^-2
S = C / r²
dT/dr = C / r²
dT = C dr / r²
T = -C / r + D
When r=1, T=17.
17 = -C + D
When r=2, T=28.
28 = -C/2 + D
Solving:
11 = C/2
C = 22
D = 39
T = -22/r + 39
We can check our answer by finding dT/dr and d²T/dr².
dT/dr = 22/r²
d²T/dr² = -44/r³
Plug into the original equation:
d²T/dr² + 2/r dT/dr = 0
-44/r³ + 2/r (22/r²) = 0
0 = 0
The total flow into the tank is 15 L/min, and the total flow out is 15 L/min, so the volume is constant at 1000 L. The amount of salt added to the tank is:
(0.05 kg/L) (5 L/min) + (0.04 kg/L) (10 L/min) = 0.65 kg/min
If y is the amount of salt in the tank at time t, and y/1000 is the concentration in the tank at time t, then the amount of salt removed from the tank is:
(y/1000 kg/L) (15 L/min) = 0.015y kg/min
The change in salt over time equals the amount of salt in minus the amount of salt out.
dy/dt = 0.65 − 0.015y
-200 dy/dt = 3y − 130
dy / (3y − 130) = -0.005 dt
3 dy / (3y − 130) = -0.015 dt
ln(3y − 130) = -0.015t + C
3y − 130 = Ce^(-0.015t)
3y = 130 + Ce^(-0.015t)
y = [130 + Ce^(-0.015t)] / 3
At t=0, y=0:
0 = (130 + C) / 3
C = -130
y = [130 − 130e^(-0.015t)] / 3
At t=50:
y = [130 − 130e^(-0.75)] / 3
y ≈ 22.9
Related Questions
Each of the four sets a1, a2, a3, and a4 contains four elements. the intersection of every i of these four sets (2 < i < 4) consisters of 5 - i elements. What is a1 U a2 U a3 U a4?
Answers
Answer:
the new year was patrick's year and the second time she had the target audience in her career as an 34696468 )/684₩¥€=÷×+)^^*,?^&££)ktuioon
The average wind speed at a local weather station is 35.3 miles per hour. The highest speed ever recorded at the station is 318.0 miles per hour. How much faster is the highest recorded wind speed than the average wind speed?
Answers
Answer:
282.7
Step-by-step explanation:
To find the answer, we use subtraction.
So, 318.0 - 35.3= 282.7
Hope this helps you!!
graph the image of S (7, 8) after a reflection over the x-axis
Answers
9514 1404 393
Answer:
see below
Step-by-step explanation:
Reflection over the x-axis changes the sign of the y-coordinate. Points that were above the axis are reflected to be the same distance below the axis.
What is the unit rate for 3 gallons of paint for $16.50?
Answers
Answer:
$5.50 per gallon of paint
Step-by-step explanation:
To check answer: Divide: 16.50 ÷ 3
y = 1/8 x+3
A) Slope: 8; y-intercept: 3
B) Slope: 1/3; y-intercept: 1/8
C) Slope: 1; y-intercept: 1/8
D) Slope: 1/8; y-intercept: 3
Answers
Answer:
Its D
Step-by-step explanation:
Slope intercept form is y=MX +B
if you plug it in, it would be y=1/8x+3 meaning 1/8 is the slope (m) and 3 is the y intercept (b)
PLEASE HELP! I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY! :D PLS ANSWER I AM SOOOOOO CONFUSED!
Answers
Answer/Step-by-step explanation:
7. The graph is a proportional relationship because the line passes through the point of origin, (0, 0). To find the equation the proportional relationship the graph represents, we need to find the unit rate of red paint (y) to white paint (x). The unit rate will represent the constant of proportionality, k. Then substitute the value of k in [tex] y = kx [/tex].
Unit rate or k = y/x
Using the point, (4, 1),
k = [tex] \frac{1}{4} [/tex]
Substitute k = ¼ in [tex] y = kx [/tex]
✅The equation would be:
[tex] y = \frac{1}{4}x [/tex]
8. The graph Franco made is incorrect.
The equation, [tex] y = -x [/tex], shows a negative constant of proportionality of -1. Therefore, the slope of the line descend downwards, from the left to the right. So, the graph Franco made to represent the equation, [tex] y = -x [/tex] is not correct.
9. a. Proportional relationship can be represented as [tex] y = kx [/tex]. To derive an equation that represents the graph, find k, the constant of proportionality between variable y and x.
Using the point, (2, 24), therefore:
k = y/x = 24/2 = 12.
Substitute k = 12 in [tex] y = kx [/tex]
✅The equation would be:
[tex] y = 12x [/tex]
b. We know an equation is represents a proportional relationship, when it is tales the form, [tex] y = kx [/tex]. Where k is the constant of proportionality. Thus, for if you substitute the pair of values given (x, y) into the equation, you would get the same value of k for any pair of value you substitute in the given set of values.
Also, we know a graph represents a proportional relationship when a straight line passes through the point of origin, (0, 0), and has a constant of proportionality or unit rate all through.
Help me with this question i will give braibnly if right
Answers
There are 4 lines between each number so each line would be 1/4
A is at -1 1/2
B is -3/4
C is 3/4
D is 1 3/4
Will put brainliest
What is the point of intersection for the lines y – x = 0 and 3x + 5y = 15?
Answers
In a study, a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The response and gender of the participants is shown in Table 1.
Male Female Total
Agree 372 363 735
Disagree 807 1005 1812
Don't know 34 44 78
Total 1213 1412 2625
Table 1 Is there only one true love for each person?
(a) Use the information in the table to construct a confidence interval for the difference in the proportion who agree, between males and females, using the fact that the standard error for the difference is .
Round your answers to three decimal places.
The 95% confidence interval is
to
.
(b) Is it plausible that there is no difference between males and females in the proportion who agree that each person has only one true love?
Answers
Using the information given, it is found that:
a.
The standard error for the difference is of 0.0176.
The 95% confidence interval is 0.0151 to 0.0841.
b.
Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.
What is the distribution of differences for the proportion of males and females?
For males, we have that:
[tex]n = 1213, p_M = \frac{372}{1213} = 0.3067, s_M = \sqrt{\frac{0.3067(0.6933)}{1213}} = 0.01324[/tex]
For females, we have that:
[tex]n = 1412, p_F = \frac{363}{1412} = 0.2571, s_F = \sqrt{\frac{0.2571(0.7429)}{1412}} = 0.01163[/tex]
The distribution of differences has mean and standard error given by:
[tex]p = p_M - p_F = 0.3067 - 0.2571 = 0.0496[/tex]
[tex]s = \sqrt{s_M^2 + s_F^2} = \sqrt{0.01324^2 + 0.01163^2} = 0.0176[/tex]
What is the confidence interval?It is given by:
[tex]p \pm zs[/tex]
z is the critical value, which considering that there is a 95% confidence level, it is of z = 1.96.
Then:
[tex]p - zs = 0.0496 - 1.96(0.0176) = 0.0151[/tex]
[tex]p + zs = 0.0496 + 1.96(0.0176) = 0.0841[/tex]
The 95% confidence interval is 0.0151 to 0.0841.
Item b:
Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.
More can be learned about confidence intervals at https://brainly.com/question/16162795
AA
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+
Question Progress
Homework Progress
6/43
a)
Write down, in figures, the number forty one thousand and ninety six.
Answers
Answer:
41096
Step-by-step explanation:
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.833. Can you be confident that your predicted value will be reasonably close to the actual value? Why or why not?
Answers
The correlation Coefficient gives the measure of the strength and direction of the relationship between two variables. - 0.833 depicts a strong negative relationship. Hence, one can be confident that the predicted value will be close to the actual Value.
The Correlation Coefficient, R ranges from - 1 to 1, with values closer to - 1 and 1 representing strong negative and positive relationship respectively, which is only achieved of the data is modeled very well.
Therefore, since, - 0.833 is a strong correlation Coefficient, then we can be confident in the predicted value.
Learn more : https://brainly.com/question/19805544
What are 2 ratios equivalent to 3:12
Answers
Answer:
6/24
Step-by-step explanation:
Well, this ratio would be written as 6/24. Using your knowledge of equivalent fractions, you can see that 3/12 = 6/24 (multiply the numerator and denominator of 3/12 by 2 and you get 6/24.
Hope this helps you.
Mark as Brainliest Please.!!!
Which correct variables describes the slope?
A.X/Y
B.Y/X
C.W/Z
D.Z/W
Answers
Answer:
c
Step-by-step explanation:
i took the test.
Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was his commission?
Answers
Answer:
$22.5
Step-by-step explanation:
multiply 900 by .025 to get 22.5.
When you multiply by a percentage to find an ammount, move the decimal place over to the left by 2 places and then multiply by the number (in this case 900). Whatever number you recieve is the answer.
The total commission Tyler's brother was earn is $22.5 and this can be determined by using the unitary method.
Given :
Tyler’s brother earns a commission. He makes 2.5% of the amount he sells.Last week, he sold $900 worth of shoes.The following steps can be used in order to determine the total commission Tyler's brother was earn:
Step 1 - The unitary method can be used in order to determine the total commission Tyler's brother was earn.
Step 2 - According to the given data, he sold $900 worth of shoes which is 100% value.
Step 3 - If 100% is $900 then the value of 2.5% is:
[tex]=\dfrac{2.5}{100}\times 900[/tex]
Step 4 - Simplify the above expression.
= $22.5
For more information, refer to the link given below:
https://brainly.com/question/11897796
Above is the layout of a running track and inside the track is a field. If it costs $5.00 /m2 for soil for the field,
describe how you would determine the total cost to cover the field with soil. help!
Answers
Answer:
We can think in the area as:
A rectangle of 100m by 64m
And two half circles (o a whole circle if we combine them) of diameter = 64m
Then we need to calculate the area of these two figures and then sum them.
The area of a rectangle of width W and length L is:
A = A*L
then the area of the rectangle will be:
A1 = 100m*64m = 6400m^2
The area of a circle of diameter d is:
A = pi*(d/2)^2
in this case, d = 64m
pi = 3.14
Then:
A2 = 3.14*(64m/2)^2 = 3215.35m^2
The total area of the field is:
A = A1 + A2 = 6400m^2 + 3215.35m^2 = 9615.36 m^2
Now, we know that the cost per square meter is $5.00
Then the total cost will be:
Cost = A*$5.00/m^2 = 9615.36 m^2*$5.00/m^2 = $35215.36
Activity: Which Tour Is It?
Instructions: Read the examples of tours below. Use the space provided to answer
each question.
1. If you report to work at 18.00 on a Wednesday and you get off at 02.50 on a
Thursday, which day of the pay period week are you working?
2. If you report to work at 06.00 on Friday and you get off work at 14.50 on Friday,
which Tour did you work?
3. If you report to work at 22.50 on Friday, for Week 2, and you get off of work at
07.00 on Saturday, for Week 1, your time worked is recorded for the next pay
period. Why?
Answers
Answer:
Step-by-step explanation:
hi im new im not sure what to do but yea
A machinr in a factory produces 600 units each hour. How many units does the machine produce per minute?
Answers
Answer:
10 units
Step-by-step explanation:
600 units= 1 hour
1 hour= 60 minutes
600 units= 60 minutes
1 minute=600/60
1 minutes =10 units
Hope this helped! :)
see image help me as fast as possible, please
Answers
Answer: 11.4
Step-by-step explanation:
area of rect. = 24
area of circle (half circle+half circle = full circle) = pi*r^2 = pi*(2*2) = pi*4 = about 12.57
2 = radius since 4 = diameter
24-12.57 = 11.43
round = 11.4
Answer:
11.4
Step-by-step explanation:
Area=area of rectangle-area of circle
=6*4 -pi(2^2)
=11.4
area of circle =pi (r^2)
r-radius of circle
How many quarts are in 3.75% of 20 gallons?
Answers
Answer:
3 quarts
Step-by-step explanation:
Answer:
There are 3 US Quarts in 3.75% of 20 gallons.
Toy stored 945 points playing 3 games of pinball. He scored
312 points in the first game and 356 points in the second game.
towary points did Troy score in the third game?
Show your work
Will
ten
estir
Answers
Answer:
178
Step-by-step explanation:
اسحب الإجابة الصحيحة إلى مكانها المناسب.
سر سعيد 5 كيلوجراما من وزنه خلال 4 أسابيع ، فكم كيلوجراما خير في الأسبوع الواحد؟
Answers
24. A sports medicine major wanted to conduct an experiment to determine if there is a correlation (2 between the members of the soccer team's leg strength and the time it takes for them to sprint 40 yards. He sets up the following test and records the data: Every day for a week he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The table shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions? Round any values to the nearest tenth, if necessary. 12 32 7 26 28 15 Leg Press (reps) 1 40-yard Dash (s) 8.6 14.6 7.1 8.3 11.9 19.4 9.5
Answers
Answer:
ŷ = 0.1197X + 9.2741
11.9 seconds
Step-by-step explanation:
Given the data:
Average number of leg press Repetition and average 40 yard dash line
Leg press rep (x) : 12 32 7 26 28 15 1
40 yard dash (y) : 8.6 14.6 7.1 8.3 11.9 19.4 9.5
Using the linear regression calculator :
The equation of the line of best fit obtained is :
y = 0.1197X + 9.2741
Where;
x = leg press (predictor variable)
y = 40 yard dash (predicted variable)
Slope = 0.1197
Intercept = 9.2741
How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?
22 leg press Repetitions = x
From the line of best fit equation :
y = 0.1197(22) + 9.2741
y = 11.9075
y = 11.9 seconds
The lines of best fit is the trend line of the dataset.
The equation of line of best fit is [tex]\mathbf{y =0.120x + 9.274}[/tex]The time for 22 leg-press reps is 11.9 seconds(a) The equation of the line of best fit
The table is given as:
(x) : 12 32 7 26 28 15 1
(y) : 8.6 14.6 7.1 8.3 11.9 19.4 9.5
To determine the equation of line of best fit, we make use of a regression calculator.
Enter the above dataset in a regression calculator, the equation is:
[tex]\mathbf{y =0.120x + 9.274}[/tex] -- approximated to three decimal places
(b) The number of seconds for 22 leg-press reps
This means that x = 22.
So, we have:
[tex]\mathbf{y =0.120 \times 22 + 9.274}[/tex]
[tex]\mathbf{y =2.64 + 9.274}[/tex]
[tex]\mathbf{y =11.914}[/tex]
Approximate to the nearest tenth
[tex]\mathbf{y =11.9}[/tex]
Hence, the time for 22 leg-press reps is 11.9 seconds
Read more about linear regressions at:
https://brainly.com/question/18405415
Estimate the total number of hairs on your head. To calculate your estimate, you must make assumptions
1. Assume head spherical and 50% covered with hair.
2. Assume a radius of 5 inches.
3. Assume 150 hairs per
A)
100,000 hairs
B)
250,000 hairs
500,000 hairs
D)
1,000,000 hairs
Answers
Answer: A 100,000 hairs
Step-by-step explanation:
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements. Triangle JKL is congruent to triangle . Side LK corresponds to sides . Angle JLK corresponds to angles
Answers
Answer:
Triangle JKL is congruent to triangle
✔ ABC
.
Side LK corresponds to sides
✔ WV and CB
.
Angle JLK corresponds to angles
✔ UWV and ACB
.
Step-by-step explanation:
just did it on edge 2020
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides BC.
Angle JLK corresponds to angles BAC.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
As per the given information,
ΔJKL ≅ ΔUVW: This means that triangle JKL is congruent to triangle UVW. Congruent triangles have the same shape and size, so their corresponding angles and sides are equal in measure and length, respectively.
ΔUVW ≅ ΔABC: This means that triangle UVW is congruent to triangle ABC.
Combining these two pieces of information, we can conclude that:
ΔJKL ≅ ΔABC: This is because if two triangles are congruent to the same triangle, then they must be congruent to each other. Therefore, triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides BC: Corresponding sides of congruent triangles are equal in length. In this case, side LK corresponds to side VW (since JKL ≅ UVW), which corresponds to side BC (since UVW ≅ ABC).
Angle JLK corresponds to angles BAC: Corresponding angles of congruent triangles are equal in measure. In this case, angle JLK corresponds to angle UVW (since JKL ≅ UVW), which corresponds to angle BAC (since UVW ≅ ABC).
So, we can say that triangle JKL is congruent to triangle ABC, side LK corresponds to sides BC, and angle JLK corresponds to angles BAC.
To learn more about the congruent;
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You spend half of your money on a movie ticket. Then you spend half of what you have left to buy a large popcorn. Then you spend half of what remains to buy a small drink. Which expression equals the fraction of money you have left?
Answers
Answer:
1/8
Step-by-step explanation:
1 divided by 2 = 1/2
1/2 divided by 2 = 1/4
1/4 divided by 2 = 1/8
Can you help me with this thanks
Answers
Answer:
no
Step-by-step explanation:
191.0
Find the number with the given prime factorization.
23. 2 X 2 X 5 X 7 X 11
Answers
Answer: 1540
Explanation: Just multiply or use a calculator. The prime factorization is all the prime factors, meaning you can multiply all of them to get the original number.
3 pound pork lion can be cut into 10 pork shots of equal weight how many ounces in each pork shop
Answers
Answer:caca
Step-by-step explanation:
poop
#1 Jo estimates that a piece of ribbon measures 8.5 inches. If it actually measures 7.8 inches, what is the percent error of Jo’s estimate? *
Answers
Answer:
8.97 %
Step-by-step explanation:
error is 8.5 - 7.8 inches = 0.7 inches
now
x % of 7.8 = 0.7
7.8x/100 = 0.7
x = 70/7.8 %
= 8.97 %
Answer:
Jo's estimate was 109% the actual answer
Step-by-step explanation:
109% of 7.8 is 8.502, round up to 8.5
May I have brainliest please? :)
The cost of 5 scarves is $63.75. What is the unit price?
Answers
Unit price = total price / total quantity
Unit price = 63.75 / 5
Unit price = $12.75