You need to repaint the floor and inside wall of your circular swimming pool. It has a diameter of 16 feet and a depth of 5 feet. What is the surface area that needs to be repainted? (Use 3.14 for π.)

1,055.04 ft 2

251.2 ft 2

401.92 ft 2

452.16 ft 2

Answers

Answer 1

Answer:

452.16 ft²

Step-by-step explanation:

The surface area is the area of the cylindrical wall plus the area of the circular floor.

A = 2πrh + πr²

h = 5.  The radius is half the diameter, so r = 8.

A = 2π(8)(5) + π(8)²

A = 144π

A ≈ 452.16 ft²

Answer 2

Answer:

A ≈ 452.16 ft mark me brainy plz!

Step-by-step explanation:

The surface area is the area of the cylindrical wall plus the area of the circular floor.

A = 2πrh + πr²

h = 5.  The radius is half the diameter, so r = 8.

A = 2π(8)(5) + π(8)²

A = 144π

A ≈ 452.16 ft²


Related Questions

what times what gives me -48 but adds to be -32?

Answers

Answer:

a couple of irrational numbers: -16±4√19, approximately {1.436, -33.436}

Step-by-step explanation:

Your question can be cast as the quadratic equation

  x² +32x -48 = 0

The solutions can be found using the quadratic formula:

  x = (-32 ±√(32² -4(1)(-48)))/(2(1)) = -16±√304 = -16±4√19

_____

Comment on the equation we used

We notice that when p and q are roots, the equation can be written ...

  (x -p)(x -q) = 0 = x² -(p+q)x +pq

You want p+q = -32, pq = -48, so the equation is ...

  x² -(-32)x +(-48) = 0

  x² +32x -48 = 0 . . . . . . with parentheses eliminated

The Earth completely rotates on its axis once every 24 hours.

A) How long does it take for it to rotate 310 degrees?

B) How long does it take to rotate 5 radians?

C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?

Show all work. Give answers to the nearest hundredth. Include the units in your response.

Answers

Answer:

Part A). 20 hours 42 minutes taken by earth to rotate 310°.

Part B). 19 hours 6 minutes taken by earth to rotate 5 radians.

Part C). 2072.4 miles a point on the equator rotate in 2 hours.

Step-by-step explanation:

Given : Earth rotate 360° in 24 hours.

Part A).

Time taken by earth to rotate 360° = 24 hours.

Time taken by earth to rotate 1° = [tex]\frac{24}{360}[/tex] hours.

Time taken by earth to rotate 310° = [tex]\frac{24}{360}\times310[/tex] hours.

                                                   = 20.7 hours = 20 hours 42 minutes (approx.)

Part B).

Time taken by earth to rotate 360° = 24 hours.

We know that 360° = 2π radian

Time taken by earth to rotate 2π radian = 24 hours.

Time taken by earth to rotate 1 radian = [tex]\frac{24}{2\pi}[/tex] hours.

Time taken by earth to rotate 5 = [tex]\frac{24}{2\pi}\times5[/tex] hours.

                                                  = 19.098 hours = 19 hours 6 minutes (approx.)

Part C).

Diameter of Earth = 7920 miles

Radius of Earth, r  = 7920/2 = 3960 miles.

Degree of rotation in 24 hour = 360°

Degree of rotation in 2 hour, [tex]\theta\:=\frac{360}{24}\times2=30^{\circ}[/tex]

Now use Formula used to calculate Length of the arc of the circle.

Length of the Arc = [tex]\frac{\theta}{360}\times2\pi r[/tex]

Length a point on equator moves in 2 hour =  [tex]\frac{\theta}{360}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]

A playing field is rectangular with a length of 100 yards and a width of 53 ​yards, 1 foot. If a player runs diagonally across this​ rectangle, how far will he​ run? [Hint: Use units of feet to perform your​ calculations.]
How far has the player​ run?

Answers

First convert yards to feet.

1 yard = 3 feet.

100 x 3 = 300 feet long.

53 x 3 = 159 + 1 = 160 feet wide.

Now use the Pythagorean theorem to find the diagonal.

x^2 = 300^3 + 160^2

x^2 = 90000 + 25600

x^2 = 115600

x = √115600

x = 340 feet

plz help I'm lost!!!!!​

Answers

Answer:

D.

Step-by-step explanation:

A linear function is one that has a constant rate of change.

On table D, we can see that it has a constant rate of +2 as every time x increases by 1, y increases by 2.

Answer:

D

Explanation:

Because linear function is having the same difference or in another way it’s having the same rate of change.

Good luck,!~s

The lengths of trout in a lake are normally distributed with a mean of 30 inches and a standard deviation of 4.5 inches.



Enter the z-score of a trout with a length of 28.2 inches.

Answers

Answer:

-0.4

Step-by-step explanation:

z score is:

z = (x - μ) / σ

For x = 28.2, μ = 30, and σ = 4.5:

z = (28.2 - 30) / 4.5

z = -0.4

Answer: -0.4

Step-by-step explanation:

Given: Mean : [tex]\mu=30\text{ inches}[/tex]

Standard deviation : [tex]\sigma=4.5\text{ inches}[/tex]

The formula to calculate z-score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X = 28.2 inches, we have

[tex]z=\dfrac{28.2-30}{4.5}\\\\\Rigahtarrow\ z=-0.4[/tex]

Hence, the z-score of a trout with a length of 28.2 inches.= -0.4

This rectangular prism is intersected by a plane that contains points D, E, K, and L.




What is the perimeter of the cross section?


Enter your answer in the box. Round only your final answer to the nearest tenth.



m


A rectangular prism with height 5 meters, length 12 meters, and width 4 meters. The vertices are labeled as G, D, H, L, E, F, J, and K.

Answers

The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m

 

Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)

The perimeter of the cross-section is 36.8 m.

Calculations and Parameters:

Given that the length of diagonal EK is

[tex]\sqrt{(5^2 + 4^2) }[/tex]

6.403m

Thus, the perimeter would be

2*(12 + 6.403)

36.8 m.

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Which graph shows a car traveling at 50 miles per hour?

Answers

Answer: The answer to your question would be the third graph to your left

Step-by-step explanation: because when you calculate the rate of change from these points:

(50,1)

(100,2)

(150,3)

(200,4)

The rate of change would be 50 miles/ km per hour

Finding the slope formula: [tex]m= y2-y1/ x2-x1[/tex]

And when you take any two points from the graph, for example: (50,1) and (200,4), it would look like this:

[tex]\frac{200-150}{4-1}= 50/1= 50 miles/km per hour[/tex]

The correct graph is 3rd.

What is slope?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Considering the 3rd graph, the coordinates are :-

(50,1)

(100,2)

(150,3)

(200,4)

Finding the slope = (y₂-y₁) / (x₂-x₁)

considering the points (50,1) and (200,4), slope =

slope = 4-1 / 200-50 = 1/50

Since the slope shows the rate, and the rate of change would be 50 miles/ km per hour

Hence, the correct graph is 3rd one.

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Estimate the line of best fit using two points on the line. (10, 32) (20, 62)

A. y = 10x

B. y = 3x + 2

C. y = 10x + 10

D. y = 3x + 20

Answers

B. 3x+2 is the correct answer

Answer:  The correct option is

(B) [tex]y=3x+2.[/tex]

Step-by-step explanation:  We are given to estimate the line of best fit using the following two points on the line.

(10, 32)  and  (20, 62).

We know that

the slope of a line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of the given line will be

[tex]m=\dfrac{62-32}{20-0}=\dfrac{30}{10}=3.[/tex]

Since the line passes through the point (10, 32), so its equation is given by

[tex]y-32=m(x-10)\\\\\Rightarrow y-32=3(x-10)\\\\\Rightarrow y=3x+30+32\\\\\Rightarrow y=3x+2.[/tex]

Thus, the required equation of the line of best fit is [tex]y=3x+2.[/tex]

Option (B) is CORRECT.

Which of the following illustrates the truth value of the given conditional statement? If 3 + 2 = 5, then 5 + 5 = 10. T F → F T T → T F T → T F F → F

Answers

Answer:

T T → T

Step-by-step explanation:

A conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 3 + 2 = 5 which is true and 5 + 5 = 10 which is also true.


Depending on the day of the week, a border guard searches every nth person coming across the border. Each Tuesday every 7th person is checked. What is the name of this method of sampling?

Convenience Sampling

Systematic Random Sampling

Stratified Random Sampling

Simple Random Sampling

Answers

the answer is "Systematic Random Sampling"

A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.251.251, point, 25 meters thick.

Answers

Answer:

S(t) = 2 - 0.25*t

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

y = 2 - 0.25x

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Please help me!




Q) Two rectangles have the same width. One is 12 units long and the other is 8 units long. The area of the first rectangle is 320 square units more than the area of the second rectangle. Find the width of each rectangle.

Answers

Answer:

80

Step-by-step explanation:

A = Area of First Rectangle

B = Area of Second Rectangle

w = Width

12(w)=320+B (1st Equation)

8(w) = B (2nd Equation)

w=B/8 (Plug this value of w into the first equation)

12B/8 = 320 +B (you get this)

12B= 2560 + 8B (Simplify)

4B = 2560

B =640 plug this value into the 2nd equation

8(w) = 640

w = 80

To Test This

12x80 = 960

8x80 = 640

960 - 640 = 320 Therefore the answer is correct the width is 80

The given tables each show the number of stories completed in the construction of four different high-rise buildings and the number of days spent working on the building. Which table best represents a linear relationship? '

A. Number of Days 140 300 520 740 960 Number of Stories 4 8 12 16 20

B. Number of Days 120 240 360 480 600 Number of Stories 5 10 15 20 25

C. Number of Days 30 60 120 240 480 Number of Stories 2 4 6 8 10

D. Number of Days 90 225 400 680 960 Number of Stories 3 6 9 12 15

Answers

Answer:

The correct answer option is B. Number of Days 120 240 360 480 600 Number of Stories 5 10 15 20 25.

Step-by-step explanation:

We are given some tables showing the number of stories completed in the construction of four different high-rise buildings and the number of days spent working on the building.

We are to determine whether which table represents a linear relationship.

Table B represents a linear relationship since its ratio of number of days to number of stories completed is constant.

Number of Days    120  240  360  480  600  

Number of Stories   5      10     15    20     25

Ratio                        24    24    24    24     24

30 points!!!!
Given the hexagon below, find the measures of angles 1 through 7.

Answers

1: 107

2: 73

3; 123

4: 62

5: 116

6: 16

7: 92

The missing angle measures in the hexagon are:

∠5 = 116°

∠4 = 62°

∠3 = 123°

∠2 = 73°

∠6 = 16°

∠7 = 92°

∠1 = 107°

What is a Hexagon?

A hexagon is a six-sided polygon, whose sum of interior angles equals 720°.

∠5 = 180 - 54 = 116° (supplementary angles)

∠4 = 180 - 118 = 62° (supplementary angles)

∠3 = 180 - 57 = 123° (supplementary angles)

∠6 = 180 - 164 = 16° (supplementary angles)

∠7 = 180 - 88 = 92° (supplementary angles)

∠1 = 720 - 116 - 118 - 123 - 164 - 92 = 107° (sum of interior angles in a hexagon )

∠2 = 180 - 107 = 73° (supplementary angles)

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Point O is the center of the circle in the diagram. What is m/_BCA

Answers

Answer:

< BCA = 70

Step-by-step explanation:

The complete central angle of a circle is 360 degrees. The given portion is 250 degrees.

What is left over? BOA = 360 - 250 = 110

Tangents always meet the radius at 90 degrees. Since there are two tangents <CAO = <BAO = 90 degrees.

So piecing it all together, the equation becomes

<BAO + CAO + BAO + ACB = 360

110 + 90 + 90 + <ACB = 360

290 + <ACB = 360

<ACB + 290 - 290 = 360 - 290

ACB = 70 degrees

Simplify Radicals
What is the difference of 25√7 - 2√63

Answers

Answer:

[tex] 19\sqrt{7} [/tex]

Step-by-step explanation:

[tex] 25\sqrt{7} - 2\sqrt{63} = [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9 \times 7} [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9} \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 2\times 3 \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 6 \sqrt{7} [/tex]

[tex] = 19\sqrt{7} [/tex]

1 litre is approximately 1.75 pints, 1 gallon = 8 pints, calculate the approcimate number of gallons that are equal to 48000cm3

Answers

Answer:

[tex]10.5\ gal[/tex]

Step-by-step explanation:

we know that

[tex]1,000\ cm^{3} =1\ l[/tex]

[tex]1\ l=1.75\ pints[/tex]

[tex]1\ gal=8\ pints[/tex]

we have

[tex]48,000\ cm^{3}[/tex]

step 1

Convert to liters

[tex]48,000\ cm^{3}=48,000/1,000=48\ l[/tex]

step 2

Convert to pints

[tex]48\ l=48*1.75=84\ pints[/tex]

step 3

Convert to gallons

[tex]84\ pints=84/8=10.5\ gal[/tex]

The approximate number of gallons that are equal to 48000cm3 is 12.67 gallons.

1 liter is approximately 1.75 pints, 1 gallon = 8 pints

To convert 48000 cm³ to gallons, first recognize that 1 liter is 1000 cm³.

Therefore, 48000 cm³ is 48 liters.

Next, knowing that 1 gallon is approximately 3.79 liters, divide 48 by 3.79 to get approximately 12.67 gallons.

Dewight is proving the sum formula for the sine function. He has started his proof, what property should he use to complete the next line?

Answers

Answer:

C) the difference identity for the cosine function

Step-by-step explanation:

The last line showing shows the cosine of the difference of two angles. The difference identity for the cosine function would seem to be indicated.

Check my answer?

The law of cosines reduces to the Pythagorean Theorem when the triangle is right.

True or False

I select False

Answers

Answer: you have the correct answer hope this helped please mark me the brainlest answer have a good day mate

Help with this question, please! I don't understand!

Answers

Answer:

  m∠LPM = 60°

Step-by-step explanation:

The measure of the angle facing the marked arcs is the average of the measures of the arcs:

  m∠LPM = (1/2)(40° +80°) = 60°

The Jeffer's company has a debt ratio (total debt to total assets) of 0.365. If their total assets are $739,000, what is their total debt?

A) $269,735
B) $469,265
C) $1,008,735
D) $2,024,657

Answers

The answer is D 2,024,657

Answer:

A

Step-by-step explanation:

0.365 x 739,000= 269,735

At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys. r + f ? 16 4r + 2f ? 40 What is the maximum number of ride tickets she can buy? 4 6 10 12

Answers

Answer:

4

Step-by-step explanation:

Here let the  number of ride tickets be r, and the number of food tickets be f.

Hence

[tex]r+f\ge16\\4r+2f\le40[/tex]

We first plot the two inequalities on graph as shown in attachment. From the graph we see that the two in-equation meet at (4,12)

Hence we can see that the maximum value of r is 4

Answer:

4

Step-by-step explanation: the maximum number of ride tickets she can buy is 4. so option a is correct

please help 80 points for 2 questions please answer all parts and show your work! due today!!!!

Answers

Part A

The scatterplot is shown the attachment.

Part B

Using a linear regression equation that models Patrick's referrals has a positive slope.

This means that, there is a positive relation between time(number of days),x and  the number of personal recommendations, y.

In other words, as the number of days increases, the number of personal recommendations also increases.

Question 2.

The given functions are:

[tex]y=x^2+3x-5[/tex]

[tex]y=4x+1[/tex]

To find the point where the graphs of these functions intersect,we solve the two equations simultaneously.

We equate the two equations to get:

[tex]x^2+3x-5=4x+1[/tex]

[tex]x^2+3x-4x-5-1=0[/tex]

[tex]x^2-x-6=0[/tex]

Factor to obtain:

[tex](x-3)(x+2)=0[/tex]

x=3 and x=-2

We put x=-2, into [tex]y=4x+1[/tex] to get;

[tex]y=4(-2)+1=-7[/tex]

when x=3 [tex]y=4(3)+1=13[/tex]

Therefore the graphs intersect at (-2,-7) and(3,13).

Yes, solution is correct.

A ball is shot into the air using a brand new super-high-tech robotic arm to help baseball players practice catch fly balls.
The ball has an initial upward velocity of 64 feet per second. The height, h, of the ball after t seconds is given by the
equation:

Answers

Answer:

69 feet

Step-by-step explanation:

we have

[tex]h(t)=-16t^{2}+64t+5[/tex]

where

h(t) is the height of the ball

t is the time in seconds

we know that the given equation is a vertical parabola open downward

The vertex is the maximum

so

the y-coordinate of the vertex represent the maximum height of the ball

Convert the quadratic equation into vertex form

The equation in vertex form is equal to

[tex]y=(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

[tex]h(t)=-16t^{2}+64t+5[/tex]

[tex]h(t)-5=-16t^{2}+64t[/tex]

[tex]h(t)-5=-16(t^{2}-4t)[/tex]

[tex]h(t)-5-64=-16(t^{2}-4t+4)[/tex]

[tex]h(t)-69=-16(t^{2}-4t+4)[/tex]

[tex]h(t)-69=-16(t-2)^{2}[/tex]

[tex]h(t)=-16(t-2)^{2}+69[/tex]

the vertex is the point (2,69)

therefore

The maximum height is 69 ft

What do a rectangle and a rhombus have in common? Select all that apply. The opposite sides are parallel. They have four right angles. Their angle measures add to 360°. They have four congruent sides. you can pick more than one so plz pick more than one be positive

Answers

Final answer:

A rectangle and a rhombus both have opposite sides that are parallel and their interior angles add up to 360 degrees. They differ in that a rectangle has four right angles and a rhombus has four congruent sides, which are not necessarily attributes they share unless they are both squares.

Explanation:

Both a rectangle and a rhombus share some properties as they are both quadrilaterals. Firstly, the opposite sides are parallel in both shapes. Secondly, the angle measures add to 360° which is a property of all quadrilaterals. However, they differ in other aspects; a rectangle has four right angles, whereas a rhombus generally does not unless it's a square. A rhombus has four congruent sides, and a rectangle does not unless it's a square. Therefore, the correct selections based on their commonalities are that the opposite sides are parallel and their angle measures add up to 360°.

I NEED THE ANSWER ASAP

Jasmin and Jarvis are going to the donut shop. They have two options, donuts or donut holes and two toppings chocolate or sprinkles. Create a tree diagram to represent the sample space.

Answers

So first do the diagram (vent) and but two and two donuts until a odd number pops I think the answer is 5.

Reposting because I seriously need help. Please, this is time sensitive!

Which ordered pair is the best estimate for the solution of the system of equations?

{y=4x−19.4 y=0.2x−4.2


(4, −3.4)

(4.9, 0)

(−3.5, 4)

(4.9, −3.5)

Answers

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 4x − 19.4      ...1

y = 0.2x−4.2      ...2

From equations 1 and 2, then we have

4x - 19.4 = 0.2x - 4.2

3.8x = 15.2

x = 4

Then the value of the variable 'y' will be calculated as,

y = 4 (4) - 19.4

y = 16 - 19.4

y = - 3.4

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

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Help me with this please don’t understand need answers please !

Answers

Answer:

see the attached for the sumsthe magic number (sums of rows, columns, diagonals) is -6

Step-by-step explanation:

The directions tell you what to do and give an example. That work is to be repeated 15 more times. The work is tedious, at best. I found it slightly less tedious to enter the 64 numbers into a spreadsheet and let it do the sums. See the attached for the result.

At the bottom of the array are the sums of columns. At the right are the sums of rows. The upper right and lower left numbers are the sums of the corresponding diagonals.

The "pattern" is that the sums are all -6, which is what you expect from a magic square.

According to Boyle’s law, PV= K, what was the volume at the time of the first measurement given the following information? Round to the nearest mL.
P1=5.42 atm
P2=8.59 atm
V2=527 mL

Answers

Hello!

The answer is:

The first measurement of volume is equal to 835.23 mL.

Why?

Boyle's Law equation can be used when the temperature is kept constant, and it establishes a relation between the pressure and volume, showing that when an ideal gas is kept constant, the pressure and volume are inversely proportional.

So, we Boyle's Law equation states that:

[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]

Where,

[tex]P_1=FirstPressure\\V_1=FirstVolume\\P_2=NewPressure\\V_2=NewVolume[/tex]

Now, if we are looking for the first volume measurement, we need to rewrite the equation as follow:

[tex]P_{1}V_{1}=P_{2}V_{2}\\\\V_{1}=\frac{P_{2}V_{2}}{P_{1}}[/tex]

So, substituting the given information and calculating, we have:

[tex]V_{1}=\frac{8.59atm*527mL}{5.42atm}[/tex]

[tex]V_{1}=\frac{4526.93atm.mL}{5.42atm}=835.23mL[/tex]

Hence, the first measurement of volume is equal 835.23 mL.

Have a nice day!

The sides of triangle ABC are 3, 4, and 5 inches long. How far is the incenter of the triangle from the circumcenter of the triangle?

Answers

Answer:

(√5)/2

Step-by-step explanation:

In the attached figure, we have labeled the circumcenter point D and the incenter point E. The points of tangency of the incircle with sides AB, BC and CA are labeled G, H, and F, respectively.

The distances from any vertex to the two points of tangency from that vertex are the same. So, AG = FA, BG = BH, and CF = CH. If we call the radius of the incircle "r", then we have ...

AG = FA = r, BG = BH = 3-r, CF = CH = 4-r

so the side length BC is ...

BC = BH +CH = (3-r) +(4-r) = 7-2r

We already know that side length BC is 5, so ...

5 = 7 -2r

r = (7 -5)/2 = 1

Of course, the circumcenter of a right triangle is the midpoint of the hypotenuse, so the circumradius "R" is 5/2 = 2.5.

The formula for the distance between the two centers is ...

d = √(R(R -2r)) = √(2.5(2.5 -2)) = √1.25 = (√5)/2

_____

Comment on this answer

We have used a formula for the center-to-center distance found using a web search. The attached diagram shows the coordinates of the two centers, so the distance can be found from those. It is the same.

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