Which natural phenomenon is the best example of periodic behavior?

Chang made 6 identical necklaces each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces w

son4ous [18]

Answer:

One pendant costed $3.40

Step-by-step explanation:

6 0

2 years ago

A cookie company packages its cookies in rectangular prism boxes designed with square bases that have both a length and width of

maw [93]

Answer:

h³- 8h² + 16h

Step-by-step explanation:

The problem tells us that the length and width of these boxes are both 4 inches less than the height of the box.

So if we name h the height of the box, the width of the box would be h - 4 and the height of the box would be h - 4.

Now, the volume of a rectangular prism is given by V = height x width x length

So, considering the values we have in this problem we get:

V= height x width x volume

V = h (h-4)(h-4)

V= h(h-4)²

V= h (h²-8h + 16)

V = h³- 8h² + 16h

Therefore, the polynomial representing the volume of this box in terms of the height is h³- 8h² + 16h

5 0

3 years ago

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

2 years ago

2(1-x)=3(1+2x)+5 how to solve this

IrinaK [193]

Whew photo. Hope this helps.

8 0

3 years ago

Read 2 more answers

Which of the following is not an example of replication?

Vitek1552 [10]

Solution: Which of the following is not an example of replication?

Answer: Replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. Therefore option A is not an example of replication

A. Conducting different experiments on the same groups

3 0

2 years ago