Ask question

Ask question

All categories

3 years ago

5

A 24 inch board is cut into 3 pieces so that the second piece is twice as long as the first and the third is 3 times as long as

the first puece. If x represents the length of the first piece find the lengths of all three pieces

2 answers:

Lady_Fox [76]3 years ago

3 0

Answer:

The answer to your question is: first piece = 4 in, second piece = 8 in, third piece = 12 in

Step-by-step explanation:

Data

total length = 24 inches

first piece = x in

second piece = 2x

third piece = 3x

Equation

x + 2x + 3x = 24

6x = 24

x = 24/6

x = 4 length of the first piece

second piece = 2(4) = 8 inches

third piece = 3(4) = 12 inches

yulyashka [42]3 years ago

3 0

Answer:

4 in
8 in
12 in

Step-by-step explanation:

The total length of the three pieces is ...

x + 2x + 3x = 24 . . . . inches

6x = 24 . . . . . . . . . . . collect terms

x = 4 . . . . . the length in inches of the first piece

2x = 8 . . . . the length in inches of the second piece

3x = 12 . . . . the length in inches of the third piece

You might be interested in

The price of a plane ticket has increased from $150 to $200. By what percent has the price increased?

Maslowich

Answer:

It has increased 33%

5 0

3 years ago

Read 2 more answers

According to the New York times article in 2009, the average selling price of a LCD TV was $700. What would be the cost of the s

nevsk [136]

Answer:

$730

Step-by-step explanation:

you just put $700-70 which is for 7years

7 0

3 years ago

Which table of ordered pairs matches the following function?<br><br> y=-1/2x - 1

abruzzese [7]

Answer:

second one

Step-by-step explanation:

3 0

3 years ago

mr ogata drove 276 mies from his house to los angeles at an average speed of 62 miles per hour. how long did it take him to get

Ilia_Sergeevich [38]

About 5 hours. I did this by dividing and rounding 276 by 62. Hope this helps!

4 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