The value of f(11) for the recursive rule and an explicit rule is 149.
What is arithmetic sequence?An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed amount (referred to as the common difference). The nth term is often indicated by an, while the first term of the series is typically marked by a1. The following formula is used to determine the nth term in an arithmetic sequence:
a = a1 + (n-1)d
where d is the common distinction. In mathematics and other disciplines, arithmetic sequences are frequently employed to represent circumstances in which the pace or degree of change remains constant.
The recursive and explicit rule for the arithmetic sequence is given as:
an = a1 + (n-1)d
From the given graph f(1) = 19 and common difference = 32 - 19 = 13
The recursive rule is:
f(n) = f(n-1) + 13
The explicit rule is:
f(n) = 19 + 13(n-1)
Now, f(11) is calculated as:
f(11) = 19 + 13(11-1) = 19 + 130 = 149
Hence, the value of f(11) for the recursive rule and an explicit rule is 149.
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Manuel has 18 yards of fabric to make table runners. It takes Three-fourths of a yard to make each runner. The expression that represents the amount of fabric left after making t table runners is 18 minus three-fourths t. Which are possible numbers of table runners that Manuel could make? Select three options.
20
22
24
26
28
Manuel could make up to 24 table runners with the given amount of fabric thus all possible values are 20, 22, and 24.
What is algebraic expressions?One or more variables, integers, and mathematical operations like addition, subtraction, multiplication, and division are all included in an algebraic expression. Algebraic expressions are used to simulate events in the actual world and to represent relationships between quantities. Constants (fixed values), variables (unknown values), and coefficients can all be found in an algebraic equation (numbers multiplied by variables).
The expression for the left over fabric is:
Amount of fabric left = 18 - (3/4)t
Solving for t we have:
(3/4)t = 18
t = 24
Hence, Manuel could make up to 24 table runners with the given amount of fabric, thus all possible values are 20, 22, and 24.
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Heyyy y’all can you please help me
Answer:
Step-by-step explanation:
x + 5 < 7
x + 5 - 5 < 7 - 5
x < 2
The number line will have a open circle at 2 and be shaded to the left
completely. The solution is all numbers less than positive 2.
Verify that $\triangle ABC\sim\triangle DEF$ . Find the scale factor of $\triangle ABC$ to $\triangle DEF$ .
$\triangle ABC:\ BC\ =\ 18,\ AB\ =\ 15,\ AC\ =\ 12$
$\triangle DEF:\ EF\ =\ 12,\ DE\ =\ 10,\ DF\ =\ 8$
The scale factor of the given triangle is 3/2.
What is triangle?
Triangles are a particular form of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional image shown here. An example of a 3-sided shape is a triangle. The total of a triangle's three angles is 180 degrees.
In triangle ABC and triangle DEF;
AB= 15, BC=18, AC=12 and DE=10, EF=12, DF=8
NOW, we know that scale factors are the REDUCED FORM of corresponding sides of two similar triangles, then;
HERE;
scale factors will be....
AB/DE=15/10=3/2
BC/EF=18/12=3/2
AC/DF=12/8=3/2
Hence, scale factor is 3/2.
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The correct question is:
Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF. If △ABC: BC = 18, AB = 15, AC = 12 △DEF: EF = 12, DE = 10, DF = 8.
a permutation is any arrangement of r objects selected from n possible objects. which formula is used to calculate the number of permutations?
The following formula is used: P(n,r) = n! / (n - r)! to the calculate the number of permutations.
The formula used to calculate the number of permutations when a permutation is any arrangement of r objects
selected from n possible objects is P(n,r).
P(n,r) is the formula used to calculate the number of permutations.
Let us try to understand the concept of permutations first.
Permutations refer to the different ways of arranging elements.
It is represented as nPr called as n-permute-r.
Here, n represents the total number of elements present, and r represents the number of elements taken for each
permutation.
To calculate the number of permutations, the following formula is used:
P(n,r) = n! / (n - r)!
Where n! is equal to n-factorial that refers to the product of all numbers starting from 1 up to n.
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Nancy's new baby weighed 9.5 pounds one month after leaving the
hospital. If he gained 1.5 pounds since leaving the hospital, how many
ounces did he weigh when he left the hospital?
I need help please help me?
The graph for y = 4(1/4)ˣ is B)
Explain graphs.
A graph is a visual representation of a set of data, typically in the form of a diagram or a chart. A graph is made up of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs can be used to display various types of information, including mathematical functions, relationships between variables, and patterns in data. They are commonly used in fields such as science, engineering, economics, and social sciences to convey complex information in a simple and easy-to-understand manner.
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helloo, I need help!
Answer:
∠1 = 126°
∠4 = 54°
∠7 = 126°
Step-by-step explanation:
Since line p and line q are parallel lines we can use the angle relations to find the missing angle measures.
∠1 and ∠3 are alternate and congruent, so their measures are equal and 126° each.
∠4 and ∠3 are making a straight line and are supplementary angles, so their sum is adding up to 180°.
To find ∠4 we need to subtract 126 from 180:
180 - 126 = 54°
∠7 and ∠3 are corresponding angles and so they are equal in measurement and 126° each.
I need help I need to show my work help me please
The value of x in the tangent angle formed by the intersecting chords on the circle is 8.
What is the value of x?
The value of x is calculated by setting up equation for the sum of angles in a circle in order to obtain the value of the opposite arc angle (arc WX) as shown below.
arc WX + arc WV + arc VX = 360 ( sum of angles in a circle)
arc WX + 96⁰ + 64⁰ = 360⁰
arc WX + 160 = 360
arc WX = 360 - 160
arc WX = 200
The value of angle WVX is equal to half of arc angle WX (based on intersecting chord theorem).
m ∠WVX = ¹/₂ arc WX
12x + 4 = ¹/₂ (200)
12x + 4 = 100
12x = 100 - 4
12x = 96
x = 96/12
x = 8
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2√3 and √3 geometric mean
Answer:
Step-by-step explanation:
The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.
Example: What is the Geometric Mean of 2 and 18?
First we multiply them: 2 × 18 = 36
Then (as there are two numbers) take the square root: √36 = 6
In one line:
Geometric Mean of 2 and 18 = √(2 × 18) = 6
Solve for length of segment d.
2 cm
3 cm
6 cm
d= [?] cm
If two segments intersect inside
or outside a circle: ab = cd
Answer: 4
Step-by-step explanation:
2x6 = 3xd
12=3d
d=4
You can trust this answer because I answered it right now and it was correct. <3
The value of length of segment d is,
⇒ d = 4
What is mean by Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A circle is shown in figure.
Now, We can formulate;
⇒ 6 × 2 = d × 3
Solve for d;
⇒ 12 = 3d
⇒ 3d = 12
⇒ d = 12/3
⇒ d = 4
Thus, The value of length of segment d is,
⇒ d = 4
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Yangdon bought 50 shares of a stock that had a face value of Nu 100 but were selling at a discount of 15%. A 25% dividend rate was paid at the end of one year. She then sold the stock at a 10% premium. a) How much profit did she make? b) How much was her profit as a percentage of her investment?
Answer:
800$
Step-by-step explanation: not sure
20 points and brainlist!
show all steps pls!!
Using the area formula,
Area of the prism = 40mm².
Define area?
The word "area" designates a vacant region. The length and width of a form are used to calculate its area. The units of unidimensional length are feet (ft), yards (yd), inches (in), etc. Yet, the area of a shape is a two-dimensional quantity. Measurements like square inches (in²), square feet (ft²), square yards (yd²), etc. are used to measure anything in a square.
In the figure,
We have 2 equal rectangles and 2 equal triangles.
Now dimensions of the rectangles, l = 4mm and b = 3mm.
Area of 2 rectangles = 2 × 4 × 3
= 24mm².
Height of triangle, h = 4mm and base, b = 4mm.
Area of 2 triangles = 2 × 1/2 × b × h
= 4 × 4
= 16mm².
Therefore, total area of the prism = 24 + 16 = 40mm².
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Bradley made a house for his dog, Bowser, out of wood with a cube base and a triangular prism top. The dimensions of the dog house are a = 4 feet, b = 1 foot, and c = 2.2 feet.
If Bradley plans to paint the outside of the dog house blue, not including the bottom, how many square feet of paint will he use?
A. 101.6 square feet
B. 85.6 square feet
.
C. 117.6 square feet
Answer:
The answer to your problem is, 23.6 or 49.8
Step-by-step explanation:
Surface area of cube=4 x a²----> 4 x 2²-----> 16 ft²
Surface area of triangular prism=2*[a*c]+2*[a*b/2]---> 2*[2*1.4]+[2*1]
Surface area of triangular prism=5.6+2----> 7.6 ft²
Surface area of the figure=16 ft²+7.6 ft²----> 23.6 ft²
Thus the answer to your problem is, 23.6 or 49.8
It could be either one did the same quiz but I had different answers every time so choose which one you have :).
What is Limit of StartFraction 4 minus 3 x + x squared Over 2 x squared + 1 EndFraction as x approaches infinity? 0 One-half 2 nonexistent
The limit of the given function as x approaches infinity is 2.
What is infinity?Infinity is a concept used in mathematics to represent a quantity that is unbounded or without limits. It is often used to describe a value or set of values that increases or decreases indefinitely without ever reaching a final value.
According to question:To find the limit of the given function as x approaches infinity, we need to determine the behavior of the function as x becomes very large (positive or negative).
Let's examine the expression inside the limit as x approaches infinity:
StartFraction 4 - 3x + x² Over 2x² + 1 EndFraction
As x approaches infinity, the highest power term in the numerator and denominator dominates. In this case, the term x² dominates in the numerator and denominator. So we can simplify the expression by dividing both numerator and denominator by x²:
Start Fraction 4/x² - 3/x + 1 Over 2 + 1/x² End Fraction
As x approaches infinity, both the terms 3/x and 1/x² become very small and can be ignored. Therefore, the expression approaches:
Start Fraction 4/x² - 0 + 1 Over 2 + 0 End Fraction
which simplifies to:
Start Fraction 4 Over 2 End Fraction = 2
Therefore, the limit of the given function as x approaches infinity is 2.
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according to the national retail federation, the average shopper will spend $1,007.24 during the holiday shopping season. what is the null and alternatehypothesis?
Based on the amount predicted to be spent, the hypotheses Null Hypothesis = $1,007.24 and Alternate Hypothesis ≠ $1,007.24
The null hypothesis, or H0, in statistics science is the exact reverse of what the researcher wants to investigate. Generally, unless there is compelling proof to the contrary, the null hypothesis is taken to be correct. Another theory that will demonstrate the area one wants to investigate and be reflected by H1 must be developed.
The forecast is confirmed by the null hypothesis, which in this instance is that the typical consumer will indeed spend $1,007.24. According to the Alternate Hypothesis, the predicted occurrence won't occur, so in this instance, the shopper wouldn't spend $1,007.24. In conclusion, the variant contradicts the null hypothesis and supports it.
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Mario’s bank account has a balance of -49.25 dollars. Which of these statements must be true?
a) Mario just wrote a check for $49.25
b)The bank owes Mario a little more than $50
c)Mario owes the bank a little more than $50
d)Mario owes the bank a little less than $50
Answer: D Mario owes the bank a little less than $50
What is the surface area? 4 yd 4 yd 4 yd square yards
A 30
-foot-tall street lamp casts a 16.5
-foot-long shadow. Use the reciprocal functions and the Pythagorean Theorem, as necessary, to determine the distance from the top of the lamppost to the farthest part of the shadow. What is the angle at which the street lamp casts its shadow?
Step-by-step explanation:
See image
30 points for whoever solves
The probability that a person selected at random at this conference is a doctor or a woman is 63%.
What does probabilities means?The theory of probability is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes.
We will solve the problem using the union rule of probability. Using the given information, we can calculate the probabilities as follows:
P(doctor) = 53%
P(woman) = 41%
P(female doctor) = 31%
To find the probability that a person selected at random at this conference is a doctor or a woman, we can use the formula:
P(doctor or woman) = P(doctor) + P(woman) - P(doctor and woman)
We can calculate P(doctor and woman) by multiplying the probabilities of being a female doctor:
P(doctor and woman) = P(female doctor) = 31%
Substituting in the values, we get:
P(doctor or woman) = 53% + 41% - 31%
P(doctor or woman) = 63%.
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a school bake sale 4% of its cookies to the first customer there are 24 left how many did we begin with
The school begin with 25 cookies based on remaining 24 cookies and first selling of 4% cookies.
Let us assume the initial number of cookies be x. So, the remaining cookies percentage = 96%
Now, we are given the remaining cookies number. So, the equation will be -
96% × x = 24
Solving the equation by firstly converting the percentage into decimal
0.96x = 24
Rewriting the equation to further calculate the value of x
x = 24/0.96
Performing division on Right Hand Side of the equation
x = 25
Thus, there were total 25 cookies.
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pc is less than 50% (this can be seen by the shaded area which is less than half of the area under the graph). does this mean that the cost of overage or the cost of underage is higher?
The fact that PC is less than 50% indicates a higher probability of underage.
However, without additional information on the costs associated with overage and underage, we cannot determine which cost is higher.
From the information given in the student question, it is clear that the probability of underage (PC) is less than 50%, as indicated by the shaded area under the graph.
To determine whether the cost of overage or the cost of underage is higher, follow these steps:
1. Identify the costs associated with overage and underage in the given context. Overage cost refers to the cost incurred when the inventory is higher than demand, while underage cost refers to the cost incurred when the inventory is lower than demand.
2. Analyze the graph or data provided to compare the costs of overage and underage. Since the student question does not provide any specific data or graph, we cannot accurately determine which cost is higher based on the given information.
3. Interpret the results. If the cost of overage is higher than the cost of underage, this means that having excess inventory is more expensive than having insufficient inventory.
Conversely, if the cost of underage is higher than the cost of overage, this means that not having enough inventory is more expensive than having excess inventory.
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Write an equation that represents the line use exact numbers points (1,-4) and (3,-5)
Find the volume of the cylinder. Round your answer to the nearest tenth.
V:
11
9 ft
8 ft
Therefore , the solution of the given problem of volume comes out to be roughly 1,814.4 cubic feet.
A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, you must be aware of an object's volume in order to calculate its dimensions. It is standard practice to translate an object's weight to mass units like grams and kilograms.
Here,
V = r2h, where r is the radius and h is the height, is the expression for a cylinder's volume.
We are informed that the cylindrical has a 9-foot height and an 8-foot radius. (since the diameter is 16 ft).
When the formula's numbers are substituted, we obtain:
=> V = π(8 ft)²(9 ft)
=> V = π(64 ft²)(9 ft)
=> V = 1,814.37 ft³
We can calculate this result as V = 1,814.4 ft³ by rounding to the nearest tenth.
The cylinder's capacity is therefore roughly 1,814.4 cubic feet.
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What values of a and y satisfy the system of equations 10x = 5y - 8 15x = -5y-2 Enter your answer as an ordered pair, like this: (42, 53) If your answer includes one or more fractions, use the /symbol to separate numerators and denominators. For example, if your answer is 42 64 53' 75 If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf." %), enter it like this: (42/53, 64/75)
There are infinitely many solutions to this system.
We can solve the system of equations by elimination method:
10x = 5y - 8 (multiply both sides by 3)
15x = -5y - 2
30x = 15y - 24
15x = -5y - 2
Adding these two equations, we get:
45x = 13y - 26
Dividing both sides by 13, we get:
y = (45/13)x + 2
So any ordered pair (x, y) that satisfies this equation will also satisfy the system of equations given. There are infinitely many solutions to this system.
For example, if we let x = 13, then:
y = (45/13)(13) + 2 = 47
So one possible solution is (13, 47). Another possible solution is (26, 92/3).
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answer:
1 over 36
Step-by-step explanation:
Gavin is doing a survey to predict the results of an upcoming school election. He waits outside the lunchroom during each lunch period and surveys every tenth student leaving the lunchroom. This table shows the results of his survey.
Position - Votes
President
Henry 36
Christy 42
Celina 22
Vice President
Tristan 14
Kenny 46
Madison 40
Treasurer
Priscilla 53
Reuben 24
Erica 23
-Secretary-
Xavier 33
Ben 30
Charlie 37
Based on his survey, Gavin will predict who the 1,500 students in his school will vote for in the races for president, vice president, treasurer, and secretary. Complete the steps below to predict the outcome of the election.
Part A
Predict how many votes from the student population each candidate for president will get in the election. (Hint: Set up and solve a proportion between the sample and the population.)
Part B
Based on the survey results, who will most likely get the highest percentage of votes for the president’s position? What is that percentage?
Part C
Predict how many votes from the student population each candidate for vice president will get in the election.
Part D
Based on the survey results, who will most likely get the highest percentage of votes for the vice president’s position? What is that percentage?
Part E
Predict how many votes each candidate for treasurer will get in the election from the student population.
Part F
Based on the survey results, who will most likely get the highest percentage of votes for the treasurer’s position? What is that percentage?
Part G
Predict how many votes each candidate for secretary will get in the election from the student population.
Part H
Based on the survey results, who is most likely to get the highest percentage of votes for the secretary’s position? What is that percentage?
100 POINTS! PLEASE ANSWER ALL OF THEM OF I'LL REPORT YOUR ANSWER!!
Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.
What is probability?
Probability is a measure of the likelihood of an event occurring.
Part A:
To predict how many votes each candidate for president will get in the election, we can set up a proportion between the sample and the population
Let x be the number of votes each candidate will receive in the election.
For Henry:
36/150 = x/1500
x = (36/150) * 1500
x = 360
For Christy:
42/150 = x/1500
x = (42/150) * 1500
x = 420
For Celina:
22/150 = x/1500
x = (22/150) * 1500
x = 220
Therefore, Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.
Part B:
Based on the survey results, Christy is most likely to get the highest percentage of votes for the president’s position with 42/100 votes, which is approximately 42%.
Part C:
To predict how many votes each candidate for vice president will get in the election, we can set up a proportion between the sample and the population.
Let x be the number of votes each candidate will receive in the election.
For Tristan:
14/150 = x/1500
x = (14/150) * 1500
x = 140
For Kenny:
46/150 = x/1500
x = (46/150) * 1500
x = 460
For Madison:
40/150 = x/1500
x = (40/150) * 1500
x = 400
Therefore, Tristan is predicted to receive 140 votes, Kenny is predicted to receive 460 votes, and Madison is predicted to receive 400 votes for the vice president’s position.
Part D:
Based on the survey results, Kenny is most likely to get the highest percentage of votes for the vice president’s position with 46/100 votes, which is approximately 46%.
Part E:
To predict how many votes each candidate for treasurer will get in the election, we can set up a proportion between the sample and the population.
Let x be the number of votes each candidate will receive in the election.
For Priscilla:
53/150 = x/1500
x = (53/150) * 1500
x = 530
For Reuben:
24/150 = x/1500
x = (24/150) * 1500
x = 240
For Erica:
23/150 = x/1500
x = (23/150) * 1500
x = 230
Therefore, Priscilla is predicted to receive 530 votes, Reuben is predicted to receive 240 votes, and Erica is predicted to receive 230 votes for the treasurer’s position.
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Kimberly is admiring a statue in Newberry Park from 4 meters away. If the distance between the top of the statue to Kimberly's head is 9 meters, how much taller is the statue than Kimberly? If necessary, round to the nearest tenth.
Answer:
Step-by-step explanation:
To solve this problem, we need to use the concept of similar triangles.
Let's draw a diagram to visualize the situation:
* Statue top
|
|
| 9 m
|
|
|
/ \
/ \ 4 m
Kimberly
We can see that we have two right triangles, one formed by Kimberly, the ground, and the point where the statue touches the ground, and the other formed by the statue, the ground, and the point where Kimberly's head touches the ground.
These two triangles are similar because they have the same angles. In particular, the angle at Kimberly's eye is the same as the angle at the top of the statue. This means that the corresponding sides are proportional.
Let's call the height of the statue "h". Then, we have:
h/9 = (h+4)/4
We can solve for "h" by cross-multiplying:
4h = 9(h+4)
4h = 9h + 36
5h = 36
h = 7.2
Therefore, the height of the statue is 7.2 meters. To find out how much taller the statue is than Kimberly, we subtract their heights:
7.2 m - 1.5 m = 5.7 m
So the statue is 5.7 meters taller than Kimberly.
what is 8² + 36 vfvdscvfcfd
Answer:
100 or 10²
Step-by-step explanation:
8² = 64
36 = 6²
64 + 36 = 100
8² + 6² = 10²
Proportion word problems
ate
minutes
Nahla G
Scott likes to run long distances. He can run 20 km in 85 minutes. He
wants to know how many minutes (m) it will take him to run 52 km at
the same pace.
How long will it take Scott to run 52 km?
Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.
What does a lengthy example entail?Long-distance travel refers to a journey between two locations that are far apart. The best option for long-distance travel is the train because it is dependable and affordable. Communication that takes place over a long distance is referred to as long-distance. His lover in Colorado gave him a long-distance call.
We may construct a proportion to calculate how long it will take Scott to complete 52 kilometers at the same speed:
52 km/m at 20 km/85 min.
We can cross-multiply to find the value of m:
20 km * m equals 85 min * 52 km.
Simplifying:
20m = 4420
20 divided by both sides:
m = 221
Scott will therefore need 221 minutes to complete 52 kilometers at his current pace.
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how much total urine volume is excreted during this time period? (b) develop equations for the velocity of urine as it exits the body. assume that the urethra is 5.6 mm in diameter
(a) Total urine volume is excreted during this time period is 442.34 mL.
(b) Equations for the velocity of urine is v = (-3 x [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]
(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:
For t < 12 seconds, V = -0.306 x [tex](t-7)^2[/tex] + 15
For 12 ≤ t < 26.7 seconds, V = -3 x [tex]V_t[/tex] + 7.35
To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.
We can do this by setting the two equations equal to each other and solving for t:
-0.306 x [tex](t-7)^2[/tex] + 15 = -3 x [tex]V_t[/tex] + 7.35
0.306 x [tex](t-7)^2[/tex] + 3 x [tex]V_t[/tex] = 7.65
0.306 x [tex](t-7)^2[/tex] = 7.65 - 3 x [tex]V_t[/tex]
[tex](t-7)^2[/tex] = (7.65 - 3 x [tex]V_t[/tex] ) / 0.306
t = 7 +/- [tex]\sqrt{((7.65 - 3 \times Vt) / 0.306)}[/tex]
Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:
t = 7 + [tex]\sqrt{((7.65 - 3 \times 12) / 0.306)}[/tex]= 10.76 seconds
Now we can integrate each equation separately over their respective time ranges:
For 0 ≤ t < 10.76 seconds:
∫ V dt = ∫ (-0.306 x [tex](t-7)^2[/tex] + 15) dt
= [-0.102 x [tex](t-7)^3[/tex] + 15t] from t=0 to t=10.76
= 121.86 mL
For 10.76 ≤ t < 26.7 seconds:
∫ V dt = ∫ (-3 x [tex]V_t[/tex] + 7.35) dt
= [-1.5 x [tex]V_t^2[/tex] + 7.35t] from t=10.76 to t=26.7
= 320.48 mL
Therefore, the total urine volume excreted during this time period is:
121.86 mL + 320.48 mL = 442.34 mL
(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):
V = A x v
We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).
The cross-sectional area can be calculated using the formula for the area of a circle:
A = π x [tex]r^2[/tex]
A = 3.14 x [tex](0.0028)^2[/tex]
A = 2.46 x [tex]10^{-5}[/tex] [tex]m^2[/tex]
Now we can rearrange the continuity equation to solve for the velocity:
v = V / A
Substituting the given equations for V, we get:
For t < 12 seconds:
v = (-0.306 x [tex](t-7)^2[/tex] + 15) / 2.46 x [tex]10^{-5}[/tex]
For 12 ≤ t < 26.7 seconds:
v = (-3 x [tex]V_t[/tex] + 7.35) / 2.46 x [tex]10^{-5}[/tex]
Note that the velocity will be in units
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Question:-
The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:
V = -0.306 X (t – 7)2 + 15 Osts 12
V = -3 X Vt 12 + 7.35 12 st < 26.7
(a) How much total urine volume is excreted during this time period?
(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.