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Yakvenalex [24]

3 years ago

14

Graph the equation. Identify the vertex and the axis of symmetry.

1 answer:

givi [52]3 years ago

3 0

I think B is the answer

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A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

I need help with my geometry hw

marishachu [46]

If you can pick more than one i cant read the other ones to tell you what they are but number one is one of them

7 0

3 years ago

Will give brainly! Please help...

olga55 [171]

a) Choose Z since the σ is smallest . The smaller the σ the higher the consistency. Also we can see that the fewest day the student attendance is higher than other while the highest day is the same with others. (L = 130 ,H = 180)

b) Choose W since mean in W is the highest.

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4 0

3 years ago

If f(x)=3x + 2 and g(x)=2x - 2 what is (f-g)(x)?

omeli [17]

(3x+2)-(2x-2)
3x+2-2x-2
3x-2x=x
2-2+0
X

4 0

3 years ago

A ball is tossed at a hole in a board. The ball goes into the hole 15 times and misses the hole 52 times.

Varvara68 [4.7K]

Probability (Ball goes into hole) = 0.22388 or 22.388%

Step-by-step explanation:

Given:

Ball goes into hole = 15 times

Ball miss the hole = 52 times

Find:

Probability (Ball goes into hole)

Computation:

Total number of tries = 15 + 52

Total number of tries = 67

Probability (Ball goes into hole) = 15 / 67

Probability (Ball goes into hole) = 0.22388 or 22.388%

3 0

3 years ago