I need help with this

What is the correct order of these numbers ... 5/6, 12/13, 0.8

Ratling [72]

0.8 4/6 12/13 I think

6 0

3 years ago

Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $500 item is $30, what is the s

Archy [21]

30 / 500 = x / 900....$ 30 tax / 500 item = $ x tax on 900 item
cross multiply
(500)(x) = (900)(30)
500x = 27000
x = 27000/500
x = 54 <===

6 0

3 years ago

Read 2 more answers

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

During an Apollo moon landing, reflecting panels were placed on the moon. This allowed Earth-based astronomers to shoot laser be

rusak2 [61]

Answer:

The distance between the astronomers and the moon was $7.56*10^{8]$ meters.

Step-by-step explanation:

We have that the speed is the distance divided by the time, so:

$v = \frac{d}{t}$

In this problem, we have that:

The reflected laser beam was observed by the astronomers 2.52 s after the laser pulse was sent. This means that $t = 2.52$ .

If the speed of light is 3.00 times 10^8 m/s, what was the distance between the astronomers and the moon?

We have that $v = 3*10^{8}$ m/s.

We have to find d. So:

$v = \frac{d}{t}$

$d = vt$

$d = 3*10^{8}*2.52$

$7.56*10^{8]$

The distance between the astronomers and the moon was $7.56*10^{8]$ meters.

7 0

3 years ago

4. Determine whether the statement is true or false. Prove the statement directly from the definition if it is true, and give a

natta225 [31]

Answer:

The statement is false.

Step-by-step explanation:

Let a and b represent two odd integers.

The average (A) is defined by:

A= $\frac{a+b}{2}$

In order to prove the statement, you have to show that it's true for all odd integers. But, to disprove it, you just have to find a counterexample where the statement is false.

Notice that it is easier to try to find a counterexample.

For example, a=3 and b=5

A= $\frac{3+5}{2} = \frac{8}{2} = 4$

The result of the average is even, therefore the statement is false.

The previous calculation is a counterexample.

3 0

3 years ago