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ivanzaharov [21]

2 years ago

8

At the city museum, child admission is $5.10 and adult admission is $9.60. On Monday, twice as many adult tickets as child ticke

ts were sold, for a total sales of $558.90. How many child tickets were sold that day?

1 answer:

galina1969 [7]2 years ago

8 0

Answer:

23

Step-by-step explanation:

The amount of children's tickets is x, while the amount of adults' tickets is 2x

5.1*x- the amount of money from children

9.6*2x= 19.2x- the amount of money from adults

5.1x+19.2x= 558.9

x=23 - child tickets

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Answer:

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Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

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To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

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$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

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Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

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