A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wave

Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x denote the smaller number and y denote the larger number.

Part 1

The equation presented indicates that four times some number added to three times a larger number equals 31.

This translates to:

• 4x + 3y = 31

From here, solving for y yields:

• 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

This indicates the correct response for this scenario:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

The statement that seven subtracted from the larger number equals twice the smaller number translates to:

y-7= 2x

Further, solving for y yields:y-7= 2x ⇒

y= 2x+ 7

The correct answer for this equation is:

y = 2 x + 7

Let’s clarify this: the basketball moves faster, indicating the tennis ball won’t be able to catch up. Therefore, we utilize the formula:
Vr=Vb-Vt
<span>=0.5-0.25=0.25
</span>Thus, the relative speed is <span>0.25m/s.
I hope this is helpful.</span>

Response:

a)

b) From t increasing from 3 to 6, v changes from 18 gallons to 12 gallons.

Detailed explanation:

The relationship between the tank’s volume and time is given by:

Where V(0) indicates the starting volume and a denotes the hourly decrease.

a. Create a formula for v in terms of t.

The tank starts with 24 gallons of water, hence

It drains steadily at 2 gallons each hour, therefore

Then

b. When t progresses from 3 to 6, v changes from _________ to _________

So as t progresses from 3 to 6, v shifts from 18 gallons to 12 gallons.