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3 years ago

The lengths in feet of three pieces of timber are

Mathematics

1 answer:

Sonbull [250]3 years ago

7 0

The equal length of the logs will be 200 feets each.

Since the lengths in feet of three pieces of timber are 144, 216, 240 and the operator wants to cut them into 3 equal sizea, this will go thus:

= (144 + 216 + 240) / 3

= 600/3

= 200 feets each

Therefore, there'll be an equal length of 200 feets each.

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An object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seco

bulgar [2K]

Answer:

$y=2\text{cos}((\frac{2\pi}{3})t)$

Step-by-step explanation:

We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.

We know that standard form of cosine function is $y = A\cdot \text{cos}(Bt-C)+D$ , where,

|A| = Amplitude,

Period = $\frac{2\pi}{|B|}$ ,

C = Phase shift,

D = Vertical shift.

Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is, $A = 2$ .

Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by $\frac{2\pi}{|B|}$ , therefore, we can write $\frac{2\pi}{|B|}=3$ , therefore, $B = \frac{2\pi}{3}$ .

We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero .

Therefore, our function required function would be $y=2\text{cos}((\frac{2\pi}{3})t)$ .

6 0

3 years ago

Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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4 0

3 years ago

Solve:<br> 4m- 4 - 8 = -2m + 12

andriy [413]

Answer:

Step-by-step explanation:

4m-4-8=-2m+12

4m-12=-2m+12

Add 2m on both sides:

4m+2m-12=-2m+2m+12

6m-12=12

Add 12 on both sides:

6m-12+12=12+12

6m=24

Divide:

m=4

3 0

3 years ago

2. Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

KATRIN_1 [288]

Answer:

The point of division is (5 , 8)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divides the line whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ at ratio $m_{1}:m_{2}$ , then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

- The directed line segment with endpoints A (3 , 2) and B (6 , 11)

- There is a point divides AB two-thirds from A to B

∵ The coordinates of the endpoints of the directed line segments

are A = (3 , 2) and B = (6 , 11)

∴ $(x_{1},y_{1})$ is (3 , 2)

∴ $(x_{2},y_{2})$ is (6 , 11)

∵ Point (x , y) divides AB two-thirds from A to B

- That means the distance from A to the point (x , y) is 2/3 from

the distance of the line AB, and the distance from the point (x , y)

to point B is 1/3 from the distance of the line AB

∴ $m_{1}:m_{2}$ = 2 : 1

∵ $x=\frac{(3)(1)+(6)(2)}{2+1}=\frac{3+12}{3}=\frac{15}{3}=5$

∴ The x-coordinate of the point of division is 5

∵ $y=\frac{(2)(1)+(11)(2)}{2+1}=\frac{2+22}{3}=\frac{24}{3}=8$

∴ The y-coordinate of the point of division is 8

∴ The point of division is (5 , 8)

6 0

3 years ago

Can u please answer this question

Paha777 [63]

One Way:
We can change the mixed number to a decimal for comparing.

$1\frac{1}{4}$ m = $\frac{5}{4}$ m = 1.25 m

1.4 m    > 1.25 m
Darren   >   Luke

Darren's jump was higher by (1.4-1.25) 0.15 m

Or another way change the decimal to a fraction and the mixed to an improper fraction too.

$1\frac{1}{4}$ = $\frac{5}{4}$ (Luke)
1.4 = $\frac{7}{5}$ (Darren)
We need a common denominator to compare
$\frac{5*5}{4*5}$ (Luke)
$\frac{7*4}{5*4}$ (Darren)
$\frac{25}{20}$ (Luke)
$\frac{28}{20}$ (Darren)

$\frac{28}{20} > \frac{25}{20}$
  Darren >    Luke

By:
$\frac{28}{20}$ - $\frac{25}{20}$ = $\frac{3}{20}$
Which is also by 0.15 m
Darren jumps higher and by 0.15 m

3 0

3 years ago