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2 years ago

The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.

1 answer:

5 0

Hey

So my brother posted this on Yahoo
Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following: 

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7) 

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8° 

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram. 

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8° 
= 88.8/360*π*7² - 24.5*sin 88.8° 
≃ 13.5 cm² 
(using area of ∆ = ½.a.b.sin C for the triangle) 

b) 

volume of water = cross-sectional area * length 
≃ 13.5 * 30 cm³ 
≃ 404 cm³

Hoped it Helped

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ololo11 [35]

Answer:

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We also know that, by definition of linear pair postulate, $\angle 3$ and $\angle 1$ are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.

They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that $\angle 3$ and $\angle 1$ together are 180°, because they are on a straight angle. That is, $m \angle 3 + m \angle 1 = 180\°$

If we substitute $\angle 5$ for $\angle 1$ , we have $m \angle 3 + m \angle 5 = 180\°$ , which means that $\angle 3$ and $\angle 5$ are also supplementary by definition.

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2 years ago

Fiona has a play yard for her dog. She mows the yard in 8 equal rows. Each row has 41.75 square feet.

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Step-by-step explanation:

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This star is made up of 4 equilateral triangles of equal area and a square.

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Answer:

24 cm

Step-by-step explanation:

Given: Picture of the star is made up of 4 unshaded equilateral triangles of equal area and a shaded square.

Area of the shaded region (square) = $9\,\, cm^2$

To find: the perimeter of the star

Solution:

Area of the shaded region (square) = $9\,\, cm^2$

Area of square = $(side)^2$

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As each equilateral triangle has side lengths that are the same as the side length of the square,

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2 years ago

Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give trian

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Answer:

Rotation of triangle A across a point (1.5, -0.5) by 180°.

Step-by-step explanation:

Translation of a figure about a vector $\binom{-3}{1}$ means translation of a figure by 3 units to the left on x-axis and 1 unit in the positive direction of the y-axis.

Rule for the translation will be,

(x, y) → [(x - 3), (y + 1)]

From the figure attached,

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After translation new image points will be A'(-2, 0), B'(-2, -3), C'(0, -3).

After rotation of these image points 180° about the origin will be,

Rule for the rotation,

(x, y) → (-x, -y)

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C'(0, -3) → C"(0, 3)

Therefore, A(1, -1) → A"(2, 0) is the single transformation.

Rule for this transformation which maps triangle C to A will be defined by,

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