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harkovskaia [24]

3 years ago

8

Graciela was trying to solve the quadratic equation x2+2.5x−1.5=0 "I think I need to use the Quadratic Formula because of the de

cimals," she told Walter. Walter replied, "I'm sure there's another way! Can't we rewrite this equation so there aren't any decimals?"

1 answer:

drek231 [11]3 years ago

7 0

Answer:

The answer to your question is x² + 5/2x - 3/2 = 0

Step-by-step explanation:

Data

Quadratic equation x² + 2.5x - 1.5 = 0

Process

1.- Convert the decimals into fractions

2.5 = 25/10 = 5/2

1.5 = 15/10 = 3/2

2.- Substitution

x² + 5/2x - 3/2 = 0

3.- Conclusion

I rewrite the equation, now it is expressed in fractions. It could be solve by factoring.

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On Friday it snowed 3 4/7 inches. On Saturday it snowed 2/7 inches. How much more did it snow on Friday then Saturday? A. 3 2/7

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Step-by-step explanation:

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4 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

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

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

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,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

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

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

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,

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

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

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

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

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Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

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

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Step-by-step explanation:

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3 years ago

Read 2 more answers