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2 years ago

5

Can someone help me? I’m not sure if -4/-12 simplified is negative or positive

1 answer:

horrorfan [7]2 years ago

6 0

Answer:

The answer is 1/3

Step-by-step explanation:

-4/-12 is the same as -4 divided by -12, and a negative divided by a negative will always be a positive; therefore, the answer comes out to be positive.

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If points A,B and C are collinear, determine the value of x in the diagram.

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3 years ago

In 1980 (before the era of in-vitro fertilization), there were 3,612,258 births in the United States (according to the U.S. Cens

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Answer:

There was a 1.93% probability of having multiples (twins or more) in 1980.

Step-by-step explanation:

There were 3,612,258 births in the US in 1980.

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68339 + 1337 = 69676 were multiplies.

So

What was the probability of having multiples (twins or more) in 1980?

$P = \frac{69676}{3612258} = 0.0193$

There was a 1.93% probability of having multiples (twins or more) in 1980.

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3 years ago

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3 years ago

Which equation has the correct sign on the product

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3 years ago

Read 2 more answers

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,

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

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

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

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

Hence largest volume,

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

3 0

3 years ago