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goblinko [34]
3 years ago
8

1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.

Mathematics
1 answer:
N76 [4]3 years ago
8 0

Answer:-

Central angle , Ф/2π , A = Ф/2 r²

The ratio is 1/3 , V = 1/3 Bh

The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Step-by-step explanation:

* Lets revise the rules of the area of the sector of a circle

- The area of the sector which has a central angle Ф° is

  (Ф°/360°) × πr², where 360° is the measure of the circle and r is

  the radius of the circle

- The area of the sector which has a central angle Ф radians is

  (1/2) r²Ф

* Lets complete the missing in the 1st picture

- The ratio of the sector's area A to the circle's area is equal to the

  ratio of the <u>central angle</u> to the measure of a full rotation of the circle

- A full rotation of a circle is 2π. This proportion can written as

 A/πr² = <u>Ф/2π</u>

<em>- </em>Multiply both sides by πr² to get <u>A = Ф/2 r²</u> where Ф is the measure

 of the central angle and r is the radius of the circle

* Lets revise the rules of the volume of the prism and the volume

 of the pyramid, where they have the same base and height

- The volume of the prism = area of the base × its height

- The volume of the pyramid = 1/3 × area of the base × its height

- From them the ratio of the volume of the pyramid to the volume

 of the prism is <u>1/3</u>

- The formula of the volume of the prism is V = Bh, where B is the

  area of the base and h is the height, the formula of the volume

  of the pyramid is <u>V = 1/3 Bh</u>

<u></u>

* Lets revise the standard form of the equation of a circle with

 center (h , k) and radius r

- The equation is: (x - h)² + (y - k)² = r²

∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0

∵ x² - 8x + y² - 2y - 8 = 0

- Lets equate the two equation

∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0

∵ -2h = -8 ⇒ ÷ -2

∴ h = 4

∵ -2k = -2 ⇒ ÷ -2

∴ k = 1

∵ h² + k² - r² = -8

∴ (4)² + (1)² - r² = -8

∴ 16 + 1 - r² = -8

∴ 17 - r² = -8 ⇒ subtract 17 from both sides

∴ -r² = -15 × -1

∴ r² = 25

* Substitute the values of h , k , r in the equation of the standard

 form of the circle

∴ (x - 4)² + (k - 1)² = 25

* The equation of the circle in standard form is <u>(x - 4)² + (k - 1)² = 25</u>

<u></u>

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The rational number lies between −67/7 and−78/8
zheka24 [161]

9514 1404 393

Answer:

   -135/14

Step-by-step explanation:

There are an infinite number of rational numbers between any pair of numbers you name. These two number have the decimal values ...

  -67/7 = -9 4/7 = -9.571428... (repeating)

  -78/8 = -9 3/4 = -9.75

So, numbers like -9.6 = -48/5, or -9.7 = -97/10 are rational numbers that lie in the range you specified.

If you like, you can convert these numbers to ones with a common denominator (56).

 -67/7 = -536/56

 -78/8 = -546/56

These limits suggest several possible rational numbers with 56 as a denominator: -540/56 = -135/14, for example.

7 0
2 years ago
Which property is shown in the following statement? (46 + 17) + 3 = 46 + (17 + 3) identity property of addition associative prop
maksim [4K]

Answer: the associative property of addition

Step-by-step explanation: when adding three or more terms, you can combine the middle terms with either the first term or the last term and as you add the results, the sum will be the same either way.

3 0
2 years ago
Read 2 more answers
one days discharge at its mouth, 3 trillion gallons, could supply all of country A’s household for 5 months. how much water an a
serious [3.7K]

let's use engineering notation for the sake of brevity.

1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.

1 million is then 1E6, six zeros.

we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

\bf \begin{array}{ccll} gallons&months\\ \cline{1-2} 3E12&5\\ x&1 \end{array}\implies \cfrac{3E12}{x}=\cfrac{5}{1}\implies 3E12=5x \\\\\\ \cfrac{3E12}{5}=x\implies 6E11=x\implies 600000000000=x

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

\bf \begin{array}{ccll} gallons&households\\ \cline{1-2} 6E11&2E8\\ x&1 \end{array}\implies \cfrac{6E11}{x}=\cfrac{2E8}{1}\implies 6E11=2E8x \\\\\\ \cfrac{6E11}{2E8}=x\implies \cfrac{600000000000}{200000000}=x\implies 3000=x

5 0
3 years ago
What is 0.06x-0.18=0.12
MAXImum [283]
Hi there!

To solve this problem, we should simplify.

0.06x - 0.18 = 0.12

First, we should add 0.18 to both sides:

0.06x = 0.12 + 0.18
0.06x = 0.3

Now, we can convert 0.06 into a fraction and multiply both sides of the equation by its receprical to isolate x:

0.06 = 6/100
6/100 × 100/6 = 1
0.3 × 100/6 = 30/6
x = 30/6
x = 15/3
x = 5

So, x is 5.

Hope this helps!
7 0
2 years ago
6n&gt;6<br> Solve for inequality
kirill [66]

Answer:

n>1

Step-by-step explanation:

usually, you can solve an inequality as if it were a regular equation. Just be aware of the instances where the inequality flips.

6 0
3 years ago
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