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2 years ago

Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof?

Mathematics

2 answers:

abruzzese [7]2 years ago

5 0

It is the first answer.

KonstantinChe [14]2 years ago

5 0

Answer:

Step-by-step explanation:

From the figure, it is given that AB≅ED, BC≅CD and ∠CAD≅∠CEB.

Now, from ΔACD and ΔECB, we have

Statements Reason

1. AB≅ED, BC≅CD Given

2. ∠CAD≅∠CEB. Given

3. AB=ED, BC=DC Definition of congruent segments

4. AB+BC=AC and Segment addition postulate

ED+DC=CE

5. ED+DC=AC and Substitution property

ED+DC=CE

6. AC=CE Substitution property

7. AC≅CE Definition of congruent segments

8. ∠C≅∠C Reflexive property

9. ΔACD≅ΔECB ASA rule of congruency

Hence proved.

Hence, option A is correct.

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2 years ago

A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

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Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

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The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

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Therefore, the ratio betwen the volume and the surface area of the hemisphere is

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2 years ago