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rosijanka [135]

2 years ago

11

Mark and his friends ordered 2 pizzas. The same size

1 answer:

disa [49]2 years ago

5 0

We know that

<span>They cut the first pizza into 6 equal slice---> each slice is 1/6 of a whole pizza

</span><span>They cut the second pizza into 4 equal slices---> each slice is 1/4 of a whole pizza

</span><span>Each person plans to get 2 slices

case 1) one slide pizza 1 and one slide pizza 2
total pizza=(1/6)+(1/4)----> (4+6)/24----> 10/24----> 5/12 of a whole pizza

case 2) two slides pizza 1
total pizza=2*(1/6)-----> 2/6----> multiply by 2-----> (2/2)*2/6---> 4/12
so
4/12 < 5/12-------> Mark is correct</span>

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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

2 years ago

GE = 3x - 11 FD = 2.x Find GE<br>Can someone help me??

11Alexandr11 [23.1K]

Answer:

22

Step-by-step explanation:

Given the following

GE = 3x - 11 FD = 2x

Let us assume GE is parallel to FD, hence GE = FD

3x - 11 = 2x

3x - 2x = 0+11

x = 11

Get GE

GE = 3x - 11

GE = 3(11)-11

GE= 33 - 11

GE = 22

Hence the length of GE is 22

3 0

2 years ago

(3/4)3 write as improper fraction and mixed number

matrenka [14]

15/4, 3 3/4, and 3.75

5 0

3 years ago

ASAP HELP 20 POINTS PLS HELP

Elenna [48]

Answer: they are not the same, the difference is 28

Step-by-step explanation:

6 0

2 years ago

Explain how to fin 4 x 80. show your work

algol [13]

4x80=320

Work:

4x8 = 32
(4+4+4+4+4+4+4+4)
Now carry the 0 and you get 320

5 0

2 years ago