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3 years ago

For the equation 3x = 15, what property do you use to solve it algebraically?

Mathematics

1 answer:

Molodets [167]3 years ago

6 0

Answer:

I believe it's "Multiplication Property of Equality"

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Please help me solve Logx-3logx=2base6

igor_vitrenko [27]

Answer:

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Step-by-step explanation:

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3 years ago

What multiples to -52 but also adds to 24

ANTONII [103]

Answer:

-2 and 26

Step-by-step explanation:

-2*26=-52

-2+26=24

6 0

2 years ago

There are 28 total students in Mr. Flynn’s class. The ratio of his students who are in the play to those who are not in the play

Vanyuwa [196]

About 18 students are in the play

3 0

3 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,

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

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

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

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

Let f(x) = 3x + 2 and g(x) = 4–5x. Find f(x) + g(x)

Vadim26 [7]

Answer:

-2x + 6

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 2

g(x) = 4 - 5x

Step 2: Find f(x) + g(x)

3x + 2 + 4 - 5x

-2x + 6

3 0

3 years ago

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