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SVEN [57.7K]
3 years ago
6

A group of seven people spent $33.50 on a movie ticket. They paid six dollars and 50 Cent for each adult ticket and $3.50 for ea

ch child ticket. What is the sum of equations can be used to find X the number of adult tickets purchased and why the number of children's tickets purchased
Mathematics
2 answers:
Reika [66]3 years ago
7 0
.5X+3.50y=33.50 Would be the equation hope this helps
Daniel [21]3 years ago
6 0
X= 3
y = 4
$6.50×3=$19.50
$3.50×4=$14.00
$19.50+$14.00=$33.50
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Step-by-step explanation:


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Answer:

8\pi\text{ square cm}

Step-by-step explanation:

Since, we know that,

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S=2\pi rh

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h = height,

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

16 = 4r^2 + h^2

16 - 4r^2 = h^2

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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}

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