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3 years ago

Pleaseeeee help, I need this now...

Mathematics

1 answer:

hoa [83]3 years ago

3 0

Answer:

7/16.

Step-by-step explanation:

The first triangle has no shading.

The second triangle has 1/4 shaded.

The third has 3/9.

The fourth has 6/16.

Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.

The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.

So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.

Hope this helps!

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Central angle , Ф/2π , A = Ф/2 r²

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

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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 central angle 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 = Ф/2π

- Multiply both sides by πr² to get A = Ф/2 r² 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 1/3

- 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 V = 1/3 Bh

* 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 (x - 4)² + (k - 1)² = 25

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