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Masteriza [31]
3 years ago
13

Please help

Mathematics
1 answer:
cricket20 [7]3 years ago
8 0

Answer:

2.50x+80>4.00

Step-by-step explanation:

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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
Two angle measures of a triangle are given what is the third angle measure 57 68 _ 90 40 __ 29 71 _
nexus9112 [7]
Sum\ of\ angles\ in\ triangle\ is\ 180^{\circ}\\\\
57^{\circ},68^{\circ},x\\
57+68+x=180\\
125+x=180\\
x=55^{\circ}\\\\
90^{\circ},40^{\circ},x\\
90+40+x=180\\
130+x=180\\
x=50^{\circ}\\\\29^{\circ},71^{\circ},x\\
29+71+x=180\\
100+x=180\\x=80^{\circ}
3 0
3 years ago
Factoring without Combining Like Terms
Alex_Xolod [135]

Answer:

(x + 3)(2x + 5)

Step-by-step explanation:

Given

2x² + 6x + 5x + 15 ← grouping the terms

= (2x² + 6x) + (5x + 15) ← factor each group

= 2x(x + 3) + 5(x + 3) ← factor out (x + 3) from each term

= (x + 3)(2x + 5) ← in factored form

8 0
3 years ago
Is 4/6 less than 5/7 which one is greater
Oksana_A [137]
5/7 is greater than 4/6 because 5/7 = 0.71 while 4/6 = 0.67
5 0
3 years ago
Read 2 more answers
Please help me with these or just the first one even ty
shepuryov [24]

Answer:

-3+15-75+375

=12-75+375

=-63+375

=302

n=8

302÷8 = 37

3 0
2 years ago
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