Mathematics High School

The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

Answers

Answer 1

Answer:

Area of the shaded region = 16(π - 2) in²

Perimeter of the shaded region = 4(π + [tex]2\sqrt{2}[/tex]) in

Step-by-step explanation:

Since, BDC is a quarter of the circle with radius = 8 in.

Area of the quarter of the circle = [tex]\frac{1}{4}(\pi)(r)^2[/tex]

= [tex]\frac{1}{4}(64)\pi[/tex]

= 16π in²

Area of ΔBCD = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

= [tex]\frac{1}{2}(8)(8)[/tex]

= 32 in²

Since, area of the shaded part = Area of quarter of the circle - Area of triangle BCD

= (16π - 32)

= 16(π - 2) in²

Therefore, area of the shade region = 16(π - 2) in²

Similarly, length of arc BD = [tex]\frac{1}{4}(2\pi r)[/tex]

= [tex]\frac{8\pi }{2}[/tex]

= 4π in.

Length of the diagonal of a square = (Side)√2

= 8√2 in

Perimeter of the shaded region = Length of arc BD + Length of diagonal BD

= 4π + 8√2

= 4(π + 2√2) in.

Related Questions

WILL MARK YOU BRAINLIEST

Answers

Answer: 4

Step-by-step explanation:

Answer:

PZ = 4

because P is the centre of XYWZ

=> PZ = 1/2.XZ

WP = 1/2. WY

=> PZ + WP = 1/2.(XZ + WY) = 1/2.24 = 12

=> PZ = 12 - WP = 12 - 8 = 4

please help!! ill give ten points

Answers

Answer:

its f

Step-by-step explanation:

The length of a rectangle is 5 more than the width. The perimeter is 98.
What is the length, width and area of the rectangle? Explain

Answers

Answer:

Width=22, Length=27, Area= 594

Step-by-step explanation:

Let the width if the rectangle be represented by x

If the length is 5 more than the width

Length =x+5

The perimeter is given by

2(x)+2(x+5)=98

2x+2x+10=98

4x=88

x=22

Width=22

Length=27

Area= 22*27=594

when you spin a 2D triangle, it looks like a 3D pyramid. true or false

Answers

Answer:

False

Step-by-step explanation:

False?? Sry if I’m wrong

HELP!! Mr. Posey is buying a baseball bat that normally cost $160. It is now on sale for 24% off. If sales tax is 10%, how much will he pay for the baseball bat?

Answers

Answer:

he will pay $133.10

Step-by-step explanation:

Can someone help me pleas

Answers

Answer:

2)6h+9c+6

Step-by-step explanation:

3(2h+3c+2)

3*2h=6h

3*3c=9c

3*2=6

6h+9c+6

if m=7 then what is 5m-6

Answers

Answer:

Step-by-step explanation:

5(7)-6

35-6

Answer: 29

Explanation: you substitute m with 7, so
5(7)-6
5 • 7 = 35
35 - 6 = 29

simplify 2x+1-2x/2x+1

Answers

Answer:

1 = 2+ 348/46 (56+35)

Step-by-step explanation:

You must bye one hundred eggs with 100 cents. There are three types of eggs and you will need to buy all three types of eggs.Goose eggs must be bought in multiples of twenty. 1 chicken egg costs 5 cents 1 duck egg costs 1 cent 20 goose eggs costs 1 cent How many chicken, duck and goose eggs do you need to buy?

Answers

Answer:

1 duck egg

19 chicken eggs

80 goose eggs

Step-by-step explanation:

Given that:

Goose eggs must be bought in multiples of 20

20 goose eggs = 1 cent

1 chicken egg = 5 cents

1 duck egg = 1 cent

Total amount to spend = 100 cents

Total number of eggs to purchase = 100

In other to ensure that 100 cents is spent and 100 eggs is purchased :

Using logical analysis :

1 cent is spent on duck egg, so 1 duck egg is purchased

Goose eggs (sold in multiples of 20) for 1 cent each ; 4 cents is spent on (20 * 4) = 80 goose eggs

100 - (4 + 1) = 100 - 5 = 95 cents is spent on chicken eggs ; 95 / cost per chicken egg = 95 / 5 = 19 chicken eggs

Hence,

1 duck egg = 1 cent

(20 *4) goose eggs = 80 eggs ; 4 * 1 = 4 cents

19 chicken eggs = 19 * 5cent = 95 cents

(1 + 80 + 19)eggs = (1 + 4 + 95)cents

100eggs = 100centa

Please help me ASAP !!!

Answers

Answer:

Step-by-step explanation:

the first number x in (X,Y) is the domain and the second number y is the range. Domain is the set of all x values and range is the set of all y values

Given the statement "r varies jointly as s and t". if r =16 when s = 4 and t =6, what is the constant of the variation?

Answers

Arrangements for weddings would have been with the local church. Weddings were always a religious ceremony, conducted by a minister. The religions varied but the legal process prior to the wedding was always the same. There were no Registry Office marriages or marriages conducted by a Justice of the Peace. The first stage was Crying the Bann

please help me 2/5+ -2 1/4

Answers

Answer:

-1.85

Step-by-step explanation:

write the equation of the line passing through points (2,-2) and (1,0) in the slope intercept form

Answers

Answer:

y=-2x+2

Step-by-step explanation:

Just follow the slope-intercept form formula-

Formula: y=mx+b

Key:

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

Let me know if you have any questions, hope this helps! (:

Jan 16, 3:12:20 PM
Subtract 3.x2 + 8x from 9x2 + 3x – 8.

Answers

Answer:

Step-by-step explanation:

ok so do this

9x² + 3x - 8 - (3x² + 8x)

distribute the negative sign

9x² + 3x - 8 - 3x² - 8x

simplify

6x² - 5x - 8

Answer:

x = 8 inches

Step-by-step explanation:

As the triangles are similar, their corresponding sides will have same ratio:

left short side /right short side = left long side / right long side

or simpler

s₁/s₂ = l₁/l₂

Substitute values to find the missing one:

4/x = 10/204/x = 1/2x = 4*2x = 8

The missing side is 8 inches long

Solve for n: 2n = n + 3

Answers

Answer:

Step-by-step explanation:

Here you go mate

Step 1

2n=n+3 Equation/Question

Step 2

2n=n+3 Simplify

2n=n+3

Step 3

2n=n+3 Subtract n

answer

n=3

The value of n is given by the equation n = 3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

2n = n + 3 be equation (1)

On simplifying the equation , we get

Subtracting n on both sides of the equation , we get

2n - n = 3

n = 3

Therefore , the value of n is 3

Hence , the equation is n = 3

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

h(n) = 3^n+3; Find h (3n)

Answers

Answer:

[tex] h(3n) = 27^{n}+3 [/tex]

Step-by-step explanation:

[tex]h(n) = 3^n+3 \\ \\ plug \: n = 3n \\ \\ h(3n) = 3^{3n}+3 \\ \\ \red{ \bold{ h(3n) = 27^{n}+3 }}[/tex]

please help it's due today

Answers

Answer:

one pound of meat is $3.89

Step-by-step explanation:

93.36/8=11.67

11.67/3=3.89

Answer:

it is now by this

x^2 by jai ieye play free fire boyahh

The internal measures of a cuboidal room are 9m, 5m and 6m respectively. Find the total cost of
whitewashing all four walls of a room, if the cost of white washing is ₹ 5 per sq.m. What will be the cost of white washing if the ceiling of the room is also whitewashed.

Answers

Answer:

₹ 1290

Step-by-step explanation:

The total surface area of the room = 2(LW + WH + LH)

TSA = 2(9*5 + 9*6 + 5*6)

TSA = 2(45 + 54 + 30)

TSA = 2(129)

TSA = 258

Hence the total surface area of the room is 258m²

If 1m² = ₹ 5

258m² = 5(258) = ₹ 1290

The cost of white washing if the ceiling of the room is also whitewashed is ₹ 1290

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