For each of the following maps between spheres, compute sufficiently many coordinate representations to prove that it is smooth.
(a) Pn : S1 -> S1 is the nth power map for nEz, given in complex notation by Pn^(z) = z^n
.
Answers
Pn has a smooth coordinate representation in terms of theta,Pn is a smooth map.
To show that the map Pn: S^1 -> S^1 given by Pn(z) = z^n is smooth, we need to show that it is well-defined and has smooth coordinate representations.
First, let's show that Pn is well-defined. We need to show that if z and w are two complex numbers with the same magnitude, then Pn(z) and Pn(w) also have the same magnitude. This is true because |z^n| = |z|^n = |w|^n = |w^n|, since z and w have the same magnitude. Therefore, Pn(z) and Pn(w) are both points on the unit circle, and Pn is well-defined.
Next, let's find a coordinate representation for Pn. We can represent a point on the unit circle using a complex number of magnitude 1, i.e., z = cos(theta) + isin(theta) for some angle theta. Then, Pn(z) = (cos(theta) + isin(theta))^n. Using the binomial theorem, we can expand this as a polynomial in cos(theta) and sin(theta):
Pn(z) = cos(ntheta) + isin(n*theta)
This shows that Pn has a smooth coordinate representation in terms of theta, which is a smooth coordinate on S^1. Therefore, Pn is a smooth map.
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Related Questions
oml please don’t say anything that doesn’t help,
do any of you know what 1 3/4 + 1/6 + ____= 7 1/2 is and can you tell me how you got it
Answers
Answer:
first convert mixed fraction to improper fraction then solve by taking LCM
hope the above process helps
Answer:
5 7/12
Step-by-step explanation:
1/6 can be converted to 2/12
1 3/4 can be converted to 1 9/12
Add them together, you'll get 1 11/12
7 1/2 is equal to 7 6/12
7 6/12 - 1 11/12 = 5 7/12
5 /12 is your answer
An isosceles triangle with an angle of 10 was dilated by a factor of 0.5. Which must be true about the resulting triangle?
Answers
Answer: It has a 5 degree angle
Step-by-step explanation: When you dilate it you multiply 10 and 0.5 to get an angle of 5 degrees.
Answer:
It has a 10° angle.Option B is the correct option
Step-by-step explanation:
Dilation factor doesn't change the angle. So, angle remains same.
It has 10° angle.
Hope this helps..
Best regards!!
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
m∠5 + m∠6 are linear pairs, so their sum has to be 180°.
m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).
m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.
Solve for x: 5(x + 3) = 4(x − 3) plz need help fast
Answers
Answer:
The answer is either5x+3 = 4x-3
Answer:
x = -27
Step-by-step explanation:
5 ( x + 3 ) = 4 ( x - 3 )
5 times x, 5 times 3, 4 times x, 4 times -3 =
5x +15 = 4x -12
Subtract 15
5x +15 -15 = 4x -12 -15=
5x = 4x -27
Subtract 4x
5x -4x = 4x -4x -27 =
1x = -27
Divide
1x/1 = -27/1 =
x = -27
Can someone please help solve this math problem? There are two boxes underneath the graph. I have to find the domain/range in this math problem, it is listed in the picture below, Thanks!
Domain:
Range:
Answers
Answer:
Domain: is -4 ≤ x ≤ 1
which can be expressed in interval notation as
[-4, 1]
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
Step-by-step explanation:
The domain is the set of x values from minimum to maximum
The range is the set of y values again from minimum to maximum
Minimum value of x = -4
Maximum value = 1
So range is -4 ≤ x ≤ 1 which can be expressed in interval notation as
[-4, 1]
Minimum y-value is -3 and maximum y-value is 2
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
The standard length of a piece of cloth for a bridal gown is 3.25 meters. A customer selected 35 pcs of cloth for this purpose. A mean of 3.52 meters was obtained with a variance of 0.27 m2 . Are these pieces of cloth beyond the standard at 0.05 level of significance? Assume the lengths are approximately normally distributed
Answers
The pieces of cloth are beyond the standard at 0.05 level of significance.
We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.
The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:
H0: μ = 3.25
The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:
Ha: μ > 3.25
We can calculate the test statistic as:
t = (x - μ) / (s / √n)
where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).
Plugging in the values, we get:
t = (3.52 - 3.25) / (0.52 / √35) = 3.81
Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.
Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.
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standard normal table for z-values. > Demand =100 bags / week > Order cost =$55 /order ≻ Annual holding cost =25 percent of cost > Desired cycle-service level =92 percent > Lead time =4 week(s) (20 working days) > Standard deviation of weekly demand =13 bags > Current on-hand inventory is 350 bags, with no open orders or backorders. a. What is the EOQ? Sam's optimal order quantity is bags. (Enter your response rounded to the nearest whole number.) What would be the average time between orders (in weeks)? The average time between orders is 4.46 weeks. (Enter your response rounded to one decimal place.) b. What should R be? The reorder point is bags. (Enter your response rounded to the nearest whole number.) c. An inventory withdrawal of 10 bags was just made. Is it time to reorder? It time to reorder. d. The store currently uses a lot size of 495 bags (i.e., Q = 495). What is the annual holding cost of this policy? The annual holding cost is $ (Enter your response rounded to two decimal places.) What is the annual ordering cost? The annual ordering cost is $. (Enter your response rounded to two decimal places.)
Answers
The Economic Order Quantity (EOQ) formula is used to compute the optimal quantity of an inventory to order at any given time. It is calculated by minimizing the cost of ordering and carrying inventory, and it is an important element of supply chain management.
According to the problem given, the following information is given:Demand = 100 bags / weekOrder cost = $55 / orderAnnual holding cost = 25% of costDesired cycle-service level = 92%Lead time = 4 week(s) (20 working days)Standard deviation of weekly demand = 13 bagsCurrent on-hand inventory is 350 bags, with no open orders or backorders.a. To calculate the Economic Order Quantity (EOQ), we need to use the formula:EOQ = √[(2DS)/H],whereD = Demand per periodS = Cost per orderH = Holding cost per unit per period. Substitute the given values,D = 100 bags/weekS = $55/orderH = 25% of cost = 0.25Total cost of inventory = S*D + Q/2*H*DIgnoring Q, the above expression is the annual ordering cost. Since we know the annual cost, we can divide the cost by the number of orders per year to obtain the average cost per order.Substituting the given values in the above formula,
EOQ = √[(2DS)/H] = √[(2*100*55)/0.25] = 420 bags
Sam's optimal order quantity is 420 bags. Hence, the answer to this part is 420.b. To calculate the reorder point (R), we use the formula:R = dL + SS,whereL = Lead timed = Demand per dayS = Standard deviation of demandSubstituting the given values,d = 100 bags/weekL = 4 weeksS = 13 bags/week
R = dL + SS = (100*4) + (1.75*13) = 425 bags
Therefore, the reorder point is 425 bags.c. If the inventory withdrawal of 10 bags has been made, we can calculate the new on-hand inventory using the formula:On-hand inventory = Previous on-hand inventory + Received inventory – Issued inventoryIf there are no open orders,Received inventory = 0Hence,On-hand inventory = 350 + 0 – 10 = 340Since the current on-hand inventory is more than the reorder point, it is not time to reorder. Therefore, the answer to this part is "It is not time to reorder."d. Annual holding cost of the current policy is the product of the holding cost per unit per period and the number of units being held.Annual holding cost =
(350/2) * 0.25 * 55 = $481.25
The annual holding cost is $481.25.Annual ordering cost = Total ordering cost / Number of orders per yearIf we assume 52 weeks in a year,Number of orders per year = 52/4 = 13Total ordering cost = 13 * $55 = $715Annual ordering cost = $715/13 = $55Therefore, the annual ordering cost is $55.
The Economic Order Quantity (EOQ) formula is used to compute the optimal quantity of an inventory to order at any given time. Sam's optimal order quantity is 420 bags. The reorder point is 425 bags. If there is an inventory withdrawal of 10 bags, then it is not time to reorder. The annual holding cost is $481.25. The annual ordering cost is $55. The average time between orders is 4.46 weeks.
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i asked my class what they had for breakfast. 10 students had cereal, 5 students had eggs, and 3 students had no breakfast. what kind of data do i have?
Answers
The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.
There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.
A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.
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____ is standard deviation a measure of center or a measure of variation
Answers
Standard deviation is a measure of variation.
The degree of variance or dispersion in a set of data values is measured statistically using the standard deviation. It reveals how far the data values differ from the data set's average. Data points tend to be close to the mean when the standard deviation is low, and are dispersed over a larger range when the standard deviation is high.
While measurements of the centre, such as mean, median, and mode, are used to describe a data set's central tendency. The median is the midway value when a data set is ordered, and the mode is the value that appears in a data set the most frequently. The mean is the sum of the data divided by the number of observations.
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Find the orthocenter& circumcenter of a triangle when their vertices are A(1, 2), B(2, 6), C(3,-4).
=> Please don't spam or answer Irrelevantly.
Answers
Note:
Ortho centre :a point of intersection of altitudes of a triangle meets the opposite angle.
Given:
For Orthocentre:.
A(1, 2), B(2, 6), C(3,-4). are vertices of a triangle:
Slope of AB[m1]=\( \frac{6-2}{2-1} \)=4
Since it is perpendicular to CX.
slope of CX=m2
we have for slope of perpendicular
m1m2=-1
m2=-¼
It passes through the point C(3,-4)
equation of line CX becomes;
(y-y1)=m(x-x1)
y+4=-¼(x-3)
4y+16=-x+3
x+4y+16-3=0
x+4y+13=0........[1]
again:
Slope of AC[m1]=\( \frac{-4-2}{3-1} \)=-3
Since it is perpendicular to BY
slope of BY=m2
we have for slope of perpendicular
m1m2=-1
m2=⅓
It passes through the point B(2,6)
equation of line BY becomes;
(y-y1)=m(x-x1)
y-6=⅓(x-2)
3y-18=x-2
x-3y+18-2=0
x-3y+16=0.........[2]
Subtracting equation 1&2.
x+4y+13=0
x-3y+16=0
-__________
7y-3=0
y=\( \frac{3}{7} \)
again
Substituting value of y in equation 1.
x+4*\( \frac{3}{7} \)+13=0
x=-13-\( \frac{12}{7} \)
x=\( \frac{-103}{7} \)=-14\( \frac{5}{7} \)
So
orthocenter is (-14\( \frac{5}{7} \),\( \frac{3}{7}\))
And for circumcenter.Circumcentre: a point of intersection of perpendicular bisector of the triangle.
Now
X,Y and Z are the midpoint of AB,AC and BC respectively.
X(a,b)=(\( \frac{2+1}{2} \),\( \frac{2+6}{2} \))=
(\( \frac{3}{2} \),4)
Slope of AB=4
Slope of OX=-¼
Equation of line OX passes through (\( \frac{3}{2} \),4)is
y-4=-¼(x-\( \frac{3}{2} \))
4y-16=-x+\( \frac{3}{2} \)
8y-16*2=-2x+3
2x+8y=3+32
2x+8y=35
x+4y=\( \frac{35}{2} \)........[1]
again
Y(c,d)=(\( \frac{3+1}{2} \),\( \frac{-4+2}{2} \)=(2,-1)
Slope of AC:-3
Slope of OY=⅓
Equation of line OY passes through (2,-1) is
y+1=⅓(x-2)
3y+3=x-2
x-3y=3+2
x-3y=5......[2]
Multiplying equation 2 by 3 and
Subtracting equation 1&2.
x+4y=35/2
x-3y=5
-_______
7y=\( \frac{25}{2} \)
y=\( \frac{25}{14} \)
Substituting value of y in equation 2.
x-3*\( \frac{25}{14} \)=5
x=5+\( \frac{75}{14} \)
x=\( \frac{145}{14} \)
x=10\( \frac{5}{14} \)
circumcenter of a triangle: (10\( \frac{5}{14} \),1\( \frac{11}{14} \))
Container a was filled with water to the brim. then, some of the water was poured into an empty container b until the height of the water in both containers was the same. find the new height in both water containers
Answers
After pouring some water from container A into container B, the new height of the water in both containers will be equal.
When container A is filled with water to the brim, it reaches its maximum capacity. Let's assume the initial height of the water in container A is h.
When some water is poured from container A into container B, the water level in both containers will gradually equalize until they reach the same height. Let's denote this new height as H.
The reason the water levels equalize is due to the principle of fluid equilibrium. When the containers are connected and the water is allowed to flow, the water seeks a common level. This occurs because the pressure at the same height in a fluid is equal.
Therefore, after pouring water from container A to container B, the final height of the water in both containers will be H, which indicates that the water has reached an equilibrium point where the pressure is equal in both containers.
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A toy maker finds that it costs C = 450+ 3.75x dollars to manufacture x toy trucks. If the budget allows $3600 in costs, how many trucks can be made?
Answers
Answer:
840
Step-by-step explanation:
3600=450+3.75x
3600-450=3.75x
3150=3.75x
3150/3.75=x
840=x
840
Members of a softball team raised $1158.25 to go to a tournament. They rented a bus
for $836.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine p, the number of players the team can bring to the
tournament.
Equation:
Answer: p =
Submit Answer
attempt out of
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69°F
Answers
Answer:
1518.25=836.50+24.75p;
p=(1518.25-836.50)/24.75=681.75/24.75
Step-by-step explanation:
24.75 is about 25, so 681.75 is about 700, so that's about 28 people. If you don't have an option, do the math
Answer:
Equation: 24.75p+836.5=1158.25
Answer: p = 13
Step-by-step explanation:
Cost per player = 24.75
number of players = p
cost of bus = 836.50
total raised = 1158.25
A ten pound sack of flour costs $8 how much does 40 pounds cost?
Answers
$8 = 10lb
8x4 = $32 and 40lbs
Answer:
$32
Step-by-step explanation:
If a 10 pound sack costs $8, we know that the sacks must cost $8 for 10 pounds.
With this knowledge, we have to multiply 4 and 8.
Multiply
4x8=32
32
Find the values of a,b, and c for which the quadratic equation ax^(2)+bx+c=0 has the given numbers as solutions. Then use those values to write a quadratic equation. -4,6
Answers
To find the values of a, b, and c for which the quadratic equation ax^2 + bx + c = 0 has the solutions -4 and 6, we can use the fact that the sum and product of the solutions of a quadratic equation are related to the coefficients of the equation.
Given that the solutions are -4 and 6, we know that the sum of the solutions is:
-4 + 6 = 2
The quadratic equation with solutions -4 and 6 is:
a(x^2 - 2x - 24) = 0
The sum of the solutions is also related to the coefficient b. Therefore, we have:
2 = -b/a (Equation 1)
Similarly, the product of the solutions is:
-4 * 6 = -24
The product of the solutions is related to the coefficient c. Therefore, we have:
-24 = c/a (Equation 2)
To write the quadratic equation using the values of a, b, and c, we substitute the values obtained from Equations 1 and 2.
From Equation 1, we have:
2 = -b/a
Multiplying both sides by -a, we get:
-2a = b
Substituting this into the quadratic equation, we have:
ax^2 + (-2a)x + c = 0
Now, let's substitute the value of c from Equation 2:
ax^2 + (-2a)x + (-24a) = 0
Simplifying further, we have:
ax^2 - 2ax - 24a = 0
Factoring out 'a' from the equation, we get:
a(x^2 - 2x - 24) = 0
Finally, the quadratic equation with solutions -4 and 6 is:
a(x^2 - 2x - 24) = 0
Note that the value of 'a' can be any non-zero real number, as long as it satisfies the condition.
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Linda made $24 for making 8 baskets . If she made 12, baskets, how much money would she make? Use a model to explain your answer. Upload your model below.
Answers
1+2+3+4+5+6+7+8+9+10+11+!2+13=?
Answers
Answer:
91
Step-by-step explanation:
1+2+3+4+5+6+7+8+9+10+11+12+13 = (14 * 6) + 7 = 91
Point M is the midpoint of the segment RS. If M is located at the point (5, 1) and S is located at the point (8, -3), find the coordinates for point R.
Answers
Answer:
(2, 5)
Step-by-step explanation:
I plugged into a graphing calculator and just did it by looking at how many spots it was down or over from the midpoint and then did the opposite. I really don't know how to explain it so I am sorry for that, but I hope this helps.
Which of the following shows a translation of figure A which takes P to P
Answers
The image of a figure under the translation that takes P to \($P^{\prime}$\) is shown. Find the original figure. Note again, that the given figure is the image after translation.
If a translation is taking p to p' then for such transformation option (a) is correct.
Reason:- look closely during translation from p to p' . A point from p first travels 2 units down and then 3 units towards right to reach p'.
Using same analogy we trace back any point of the figure in an opposite way .i.e. from p' to p.
Like two units up and 3 units towards left.
If any confusion use comment box.
Now we have to move the figure parallel to P'-P and moving towards P. So option B and D becomes incorrect because the figure should be somewhere on top left portion.
Now, option C becomes incorrect because the image orientation doesn't change on translation while in image C , the image has changed.
Option A is a correct image.
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The sum of 4 consecutive integers is -54. What is the greatest integer?
Answers
9514 1404 393
Answer:
-12
Step-by-step explanation:
The number halfway between the middle two is the average of the four numbers: -54/4 = -13.5. Then the middle two numbers are -14 and -13. The greatest of the four consecutive integers is -12.
__
Those integers are -15, -14, -13, -12.
What is the volume of this entire prism
Answers
Answer:
520 cubic centimeters (cm^3)
Step-by-step explanation:
volume = length * width * height
length = 13
width = 5
height = 4 + 4, so height = 8
volume = (13) * (5) * (8)
volume = 520 units
Since the given measurements are in centimeters and the answer is the volume of the prism, the answer must be in cubic centimeters
So, the final answer is 520 cubic centimeters (cm^3)
I would appreciate Brainliest, but no worries.
Which two expressions are equivalent?
O z
7 (6+z)
7.6+7.2
O
3 (9+y)
3.9+ y
O
t +(4.5)
(t + 4).5
X + 12 : 4
(4+12) = x
Answers
Answer:
First option
Step-by-step explanation:
The result of first expression:
7(6+z) multiply 7 with inside the parenthesis
7(6+z) = 42 + 7z
the result of second expression:
since we need to do multiplying first,
7*6 = 42 and 7*z = 7z
then we add them
42 + 7z this is the same result we found for the first equation
Please help!!! i need this done by tonight!! 50 points!!
Answers
The equation of best fit is y = (-22/5)x + 10.
What is an equation of a line?
The equation of a line is given by:
y = mx + c where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The following coordinates are given:
Pick two coordinates.
(0, 10) and (25, -100)
The equation of best fit.
y = mx + c
Now,
m = (-100 - 10) / (25 - 0)
m = -110 / 25
m = -22/5
Now,
(0, 10) = (x, y)
10 = (-22/5) x 0 + c
c = 10
Now,
y = mx + c
y = (-22/5)x + 10
Thus,
Using the coordinates the equation of best fit is y = (-22/5)x + 10.
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g=A/4
fous on a please
Answers
G = A/4
Solve for A by multiplying both sides by 4:
A = 4G
I know this is super easy but i'm stupid please help!! (3/4)^3= ???
Answers
\( \huge\sf {\dag Question} \)
\( \large\sf { {\dfrac{3}{4}}^{3}} \)
\( \huge\sf {\dag Solution } \)
\( \large\sf { \leadsto \dfrac{3 \times 3 \times 3}{4 \times 4 \times 4}} \)
\( \large\sf { \leadsto \dfrac{27}{64} (Ans) } \)
In a run chart, the variable being measured is typically placed on what axis?
(A) X axis
(B) Y axis
(C) Either axis
(D) Neither axis;
Answers
during the worst periods of hyperinflation in a certain country the price of food increased at a rate of 30% per month.if your food bill was $120 in one month during this period,what was it three months later ?
Answers
The rate of inflating is r=30% per month.
The bill of food after three months can be determined as,
\(\begin{gathered} C=120(1+\frac{30}{100})^3 \\ C=263.64 \end{gathered}\)Thus, the bill after three months will be $263.64.
what is thissssssssssssssssss pls help
Answers
Answer:
add 5 to both sides
Step-by-step explanation:
thats it the reason why
Answer:
1st option will be the answer.
PLEASE HELP!!! If logb 6 = 1.79, then log6 b =
Answers
Step-by-step explanation:
\( log_{b}(6) = 1.79\)
Change of Base Formula,
\( \frac{ log(6) }{ log(b) } = 1.79\)
\( \frac{ log_{}(b) }{ log(6) } = \frac{1}{1.79} \)
\( log_{6}(b) = \frac{1}{1.79} \)
or
0.55865.... round if neededd
The radius of a circular swimming pool is 25. 48 ft in length. What is the diameter of the swimming pool?
Answers
To find the diameter of a circular swimming pool with a given radius, we need to use the formula: diameter = 2 x radius. In this case, the radius is given as 25.48 ft. Therefore, the diameter of the pool can be calculated as follows: diameter = 2 x 25.48 = 50.96 ft.
It's important to note that the length of the pool is not directly relevant to finding its diameter. The length usually refers to the distance between the two ends of the pool, while the diameter is the distance across the widest part of the pool. However, the length can be useful in determining the surface area and volume of the pool, which are important for maintenance and chemical treatment.
In summary, the diameter of the circular swimming pool with a radius of 25.48 ft is approximately 50.96 ft.
To find the diameter of a circular swimming pool, you need to use the given radius. The radius is the distance from the center of the circle to its edge. In this case, the radius of the swimming pool is 25 feet.
The diameter is simply twice the radius, as it is the distance across the entire circle, passing through the center.
To find the diameter, you can use the following formula:
Diameter = 2 * Radius
Substitute the given radius (25 feet) into the formula:
Diameter = 2 * 25 ft
Diameter = 50 ft
So, the diameter of the circular swimming pool is 50 feet.
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