3
O Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of π.
4cm
4cm
4cm
The diagram is not drawn to scale.

3O Find The Perimeter Of The Following Shape, Given Its Curves Are Made From Parts Of Circles.Give Your

Answers

Answer 1

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts.  For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

Parts of a circle

Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).

Let's call the diameters of each of our curves "[tex]d_{big}[/tex]"  "[tex]d_1[/tex]"  "[tex]d_2[/tex]"  "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle.  So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]

Substituting back into the main equation above:

[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]

Note that all terms have common factors of "one-half" and "pi" in them.  These can be factored out:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]

Substituting and simplifying (in terms of pi):

[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]

Additional Understanding

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]

[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]

[tex]P_{overall}=\pi d_{big}[/tex]

Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.  

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.


Related Questions

5. Dan is making the perfect shade of purple paint for his Nana. The perfect shade of purple mixes red and blue paint at a
ratio of 4 to 5. Accidently Dan mixed five cups of red and four cups of blue, using up all his red paint. How much blue must
he add to fix his mistake?

Answers

Answer:

2 and 1/4 cups

Step-by-step explanation:

4 cups-5 cups

5 cups-?

(5×5)÷4=6 cups and 1/4

6 and 1/4-4=2 cups and 1/4

red : blue = 4 : 5 = 1.25 x 4 : 1.25 x 5 = 5 : 6.25
Dan already added 4 cups of blue so he needs to add another 2.25 cups to get the perfect purple

Find the surface area of the composite figure
4 cm
13 cm
3 cm
4 cm
12 cm
SA = [?] cm²
5 cm
3 cm. Pls help

Answers

116 cm the composite figure

Select the correct answer from each drop-down menu.
Consider the function Ax) = 3x+ 1 and the graph of the function g(x) shown below.

Answers

Answer:

write three methods of writing set. Give one example of each methods.

Question 4tiple Choice Worth 5 points)
(07.03 MC)
Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B?
O Translate circle A using the rule (x+4y+3)
O Rotate circle A 45" about the center
O Dilate circle A by a scale factor of 4
O Reflect circle A about the origin

Answers

Answer:

Dilate circle A by a scale factor of 4.

Step-by-step explanation:

To show that two circles are similar, use transformations to map one to the other.

Step 1

Translate circle A so that its center is the same as circle B.

Center of circle A = (6, 7)Center of circle B = (2, 4)

Translate circle A using the rule (x - 4, y - 3)

Step 2

Find the scale factor needed to dilate circle A to the size of circle B using the radii of the circles.

Radius of circle A = 4Radius of circle B = 16

⇒ scale factor = 16 ÷ 4 = 4

Dilate circle A by a scale factor of 4.

Therefore, the only answer option that is correct is:

Dilate circle A by a scale factor of 4.

How do I solve this problem? It’s been awhile since I’ve done math

C=(2+y)h

solve for y

Answers

Answer:

y = C/h - 2

Step-by-step explanation:

Equation

C = (2 + y)*h

Solution

C = (2 + y)*h                          Divide by h

C/h = (2 + y)*h/h

C/h = 2 + y                            Subtract 2 from both sides

C/h-2 = 2-2+ y                      Combine

C/h - 2 = y

Add. State the sum in simplest form.

Answers

Answer:

[tex] \frac{ {3x}^{2} }{x + 5} + \frac{15x}{x + 5} [/tex]

[tex] \frac{3 {x}^{2} + 15x}{x + 5 } [/tex]

3x ( x + 5) /( x + 5).

3x, X is not equal to (-5)

Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
1. Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
2. Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)

Answers

The margin of error will be 20 and 10 respectively.

How to calculate the margin of error?

The margin of error for Robert will be:

= 1.96 × 50/✓25

= 1.96 × (50/5)

= 1.96 × 10

= 20 approximately

The margin of error for Val will be:

= 1.96 × 50/✓100

= 1.96 × 50/10

= 1.96 × 5

= 10 approximately

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Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The difference between a number and −23 − 23 is equal to the product of the number and 13 13 . Step 2 of 3 : Translate "the product of the number and 13 13 ".

Answers

The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23

What exactly is simplification?

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Given data;

z be the unknown number

Given conditions;

1. The difference between a number and −23.

2.−23 is equal to the product of the number and 13.

The mathematical form of the given phrase is;

⇒ z - (-23) = z × 13

⇒z+23 = 13z

⇒12z -23

The English phrase of the obtained equation is 12 times z subtracted by 3.

Hence the simplification of the given expressions is 12z -23.

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I need this answered fast pleasee
Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B rents for $150 and $50 an hour. Let t = the number of hours and c = cost.
Part A Write a system of equations to represent the cost at each studio.
Part B Solve the system of equations from Part A. Explain your method.
Part C Explain what the solution to the system means in terms of where your band will rent a studio.

Answers

The descriptive answer of different part is described below.

What is Linear Equation?

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

Here, Studio A rents for $75 plus $75 an hour .

Studio B rents for $150 and $50 an hour.

Let t = the number of hours and c = cost.

Part A

Studio A: c = 75 +75·t

Studio B: c = 150 +50·t

Part B

We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.

150 +50·t = 75 +75·t, subtract 75 and 50t from both sides

  150 -75 = 75t -50t, combine likes terms

          75 = 25t, divide both sides by 25

            3 = t

Now we know that t = 3 so we find c by substituting t with 3 in the second equation.

c = 150 +50·t

c = 150 +50·3

c = 300

The solution of the system of equations is c = 300 and t = 3

Part C:

The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.

The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.

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The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?

Answers

Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].

How to deal with a negative exponent?

When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:

[tex]a^{-b} = \frac{1}{a^b}[/tex]

Hence, in this problem, the equivalent expression is:

[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]

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Which statement describes how the y-intercept of the graph of f(x) = |2x − 1| compares to the y-intercept of the graph of g(x) = |2x − 5|? A. The y-intercept of g is 4 units above the y-intercept of f. B. The y-intercept of g is 4 units below the y-intercept of f. C. The y-intercept of g is 4 units to the right of the y-intercept of f. D. The y-intercept of g is 4 units to the left of the y-intercept of f.

Answers

The statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = |2x - 1|   and

g(x) = |2x - 5|

After plotting on a coordinate plane.

The y-intercept of f(x) is 1

The y-intercept of g(X) is 5

Or plug x = 0 to find the y-intercept.

The y-intercept of g is 4 units above the y-intercept of f

Thus, the statement "the y-intercept of g is 4 units above the y-intercept of f'' is true option first is correct.

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Describe the end behavior for the graph of y=-x³- ax + 3, if a is a constant.

Answers

Answer: Choice C

As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Check out the diagram below.

========================================================

Explanation:

The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.

What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]

As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]

Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]

Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".

--------------------------------

The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]

Here's a small table to give numeric examples:

[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]

As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.

This graph goes uphill when moving to the left.

Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.

calculate the median for: 5, 10, 12, 4, 6, 11, 13, 5r

Answers

Step-by-step explanation:

please mark me as brainlest

Answer:

8

Step-by-step explanation:

We need to sort your set into Least-to-Greatest order.

4, 5, 5, 6, 10, 11, 12, 13

That is your set in least to greatest order.

Which 2 numbers are in the middle?

They are 6 and 10.

Now, we find the mean of 6 and 10.

(6+10)/2 = 8

8 is your median

correct function combinations to x2-7x-18

Answers

The factors of the function after factorization f(x)=[tex]x^{2} -7x-18[/tex] is (x+2) and (x-9)

Given Function  f(x)=[tex]x^{2} -7x-18[/tex] and we have to find the factors of the given function.

The function whose factors are to be found is   f(x)=[tex]x^{2} -7x-18[/tex]

Factorization means finding various expressions which when together multiplied will give the  function itself. Correct combination can only be found by finding the factors of the function. Without finding factors no one can find the solution of an equation or expression also.

f(x)=[tex]x^{2} -9x+2x-18[/tex]

=x(x-9)+2(x-9)

=(x+2)(x-9)

Hence the  factors which when combine together gives function f(x)=[tex]x^{2} -7x-18[/tex] are (x+2)(x-9).

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(-3,-2) (x,6) m=-8/5 solve for x

Answers

Answer:

-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

-8/5=(6-(-2))/(x-(-3))

-8/5=(6+2)/(x+3)

-8/5=8/(x+3)

5=-(x+3)

5=-x-3

-x=5+3

-x=8

x=-8

Identify parallel and perpendicular lines

Answers

Parallel lines are those on a plane that do not intersect while perpendicular lines are those that intersect at an angle of 90°.

How are parallel and perpendicular lines different?

Parallel lines will never intersect with each other and will maintain the same distance from each other for as long as they are on the same plane.

Perpendicular lines on the other hand will intersect each other and will do so at a 90° angle. An example of such a line is the steps on a ladder which intersect the beam at a 90° angle.

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A city has a population of 1300. If the city’s population grows 30%, what is its new population?

Answers

Answer:

1699

Step-by-step explanation:

30/100*13000

Then add answer with 1300

eg 1300+399

I hope this explanation helps you.Also You can follow me.

Solve the inequality

Answers

Isolate c by subtracting all sides by 4

Then divide all sides by -5

You should get


5 less than or equal to c less than or equal to 4



Hope this helped :)

From this diagram, select the
pair of lines that must be
parallel if angle 2 is congruent to angle 6. If there is no pair of lines, select none

Answers

Answer:

A). O is parallel to q

if angle 2 is congruent to 6 them the slope of line o and q is equal

that is line o is parallel to q

Of the following fractions3/7, 5/8, 7/13, and 11/19 Which is the largest

Answers

Answer:

5/8

Step-by-step explanation:

5/8=0.6.25

0.625> all the other numbers

Given that the slope is 4 and (4, 6) is on the line. Write the equation of the line
in the slope-intercept
form

Answers

Answer:

y= 4x - 10

Step-by-step explanation:

y-6 = 4(x - 4)

y - 6 = 4x -16

+6. +6

y= 4x - 10


Find the domain and range of the function graphed below. Write your answers in interval notation.

Answers

Answer:

Domain: [tex][-2, 3)[/tex]Range: [tex](-5, 4][/tex]Is the relation a function? - Yes

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A relation is a function if each value of x maps onto no more than one value of y.

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.

Answers

Answer:

40.9 %

Step-by-step explanation:

8.8   is   .4 hours above the mean this is  .4/1.77 = .226 standard deviations above the mean

 Using z-score table this corresponds to ~ .5910    (59.10%)

    this percentage is LESS than 8.8 hours

      the percentage ABOVE this is 40.9%

(Not asked, but this is  40.9 (40 ) = ~ 16 of the 40 mechanics sampled)

               

Please help!!
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation
(-4,5) y=1/3x +6

Answers

Answer:

The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Multiplication of slope of two perpendicular lines is = -1

first line is  y= [tex]\frac{1}{3}[/tex]x +6

slope of this line is [tex]\frac{1}{3}[/tex]

So the slope of the second line is : [tex]\frac{-1}{3}[/tex]

Equation of line would be written by using :

(y - y1) = m(x - x1)

here the line passing through (-4,5)

put the values in equation

y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]

3y - 15 = -x -4

3y = -x +11

y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]

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A water wheel is designed in the shape of a regular octagon. What is the perimeter of the water wheel?

The graph shows an eight-sided polygon. Some major points are (0, 4), (3, 3), (4, 0), (3, minus 3), (0, minus 4), (minus 3, minus 3), (minus 4, 0), and (minus 3, 3).

A.

B.

C.

D.

Answers

Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.

What is the perimeter?

Perimeter is the sum of the length of the sides used to make the given figure.

For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,

Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58

Now, the perimeter of the octagon is 8 times of√58.

Perimeter = 8 ×√58 = 8√58

Hence, the perimeter of the regular octagon is 8√58 units.

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Cai drove 189 miles in 7 hours. If he continued at the same rate, how far would he
travel in 12 hours?

Answers

I think it is 324, I divided 189 by 7 which gave me 27 mph so I multiplied 27 by 12 which gave me 324 mph.

Find the slope and distance.
(6,-6) and (-6,+8)​

Answers

Answer:

[tex]\rm slope: -\dfrac{7}{6}[/tex]

[tex]\rm Distance: 2\sqrt{85} \ units[/tex]

Part A

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here given points are: (6, -6), (-6, 8)

Insert the values:

[tex]\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}[/tex]

[tex]\sf \rightarrow slope: \dfrac{8+ 6}{-12}[/tex]

[tex]\sf \rightarrow slope: \dfrac{14}{-12}[/tex]

[tex]\sf \rightarrow slope: -\dfrac{7}{6}[/tex]

Part B

[tex]\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Using the formula,

[tex]\sf d = \sqrt{(-6 - 6)^2 + (8-(-6))^2}[/tex]

[tex]\sf d = \sqrt{(-12)^2 + (14)^2}[/tex]

[tex]\sf d = \sqrt{144 +196}[/tex]

[tex]\sf d = \sqrt{340}[/tex]

[tex]\sf d = \sqrt{85 \times 4}[/tex]

[tex]\sf d = 2\sqrt{85}[/tex]

Hence, the distance is 2√85 units.

Hii!

___________________________________________________________

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

Slope =

Distance =

[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}[/tex]

[tex]\bullet[/tex] Let's work out the slope

[tex]\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}[/tex]

[tex]\bullet[/tex] Stickin the values

[tex]\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf \cfrac{8+6}{-12}[/tex]

[tex]\bullet[/tex] Finish simplifying

[tex]\twoheadrightarrow\sf \cfrac{14}{-12}[/tex]

[tex]\bullet[/tex] Reduce the fraction

[tex]\twoheadrightarrow\sf \cfrac{7}{-6}[/tex]

____________________________________

[tex]\bullet[/tex] Work out the distance

[tex]\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}[/tex]

[tex]\bullet[/tex] Simplify the radical expression

[tex]\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)[/tex]

[tex]\ddagger[/tex] [tex]\boldsymbol{DISTANCE=2\sqrt{85} \,Units}[/tex] [tex]\ddagger[/tex]

--

Hope that this helped! Best wishes.

--

Simplify x^2+2x+1 divided by x+1

Answers

The quotient is x+1.

What Long division method?

Long division is a method for dividing one large multi digit number into another large multi digit number.

Given:

f(x)=  x²+2x+1

g(x)= x+1

The steps to divide the polynomial is :

Divide the leading term of the dividend by the leading term of the divisor: x²/x=x.Multiply it by the divisor: x(x+1)=x²+x.Subtract the dividend from the obtained result: (x²+2x+1)−(x²+x)=x+1.Divide the leading term of the obtained remainder by the leading term of the divisor: x/x=1.Multiply it by the divisor: 1(x+1)=x+1.Subtract the remainder from the obtained result: (x+1)−(x+1)

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In Triangle XYZ, XZ = XY and m∠Y=57°. The longest side of the triangle is ______.

YZ
XZ
XY
Both XZ and XY

Answers

Answer:

I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.

The answer is YZ.
since XY=XZ, XYZ is the isosceles and naturally angle Y = angle Z = 57 degree.
so in a traingle the longest side is on the opposite side of the biggest angle.
If the congruent sides measures 57, the angle opposite the base( angle X) would mean 180-57-57 = 66. So basically the side which is opposite to X is the longest and that side being YZ.

can someone please help me?!? 25 points

please write wether each one is a function or a growth rate!!!

Answers

Answer:

See below

Step-by-step explanation:

There are 52 weeks in a year, so divide t by 52

= 120 (1.016)^(t/52)

      then the % for one week =   1.016^1/52 = 1.0003  = .03%

Other Questions
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