Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of0.5ft3/s. Initially, the balloon contains2ft3of hydrogen. (a) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (b) If the balloon has a capacity of15ft3, how long does it take to completely fill the balloon?

(a)

(b) It takes 26 seconds to completely fill the balloon.

Step-by-step explanation:

Let the time for which balloon is filled be 't' seconds.

(a)

Given:

Rate of filling (r) = 0.5 ft³/s

Initial volume of hydrogen in the balloon (V₀) = 2 ft³

The filling of hydrogen is a linear function of time.

So, Volume of hydrogen filled in the balloon at any time 't' is given as:

Volume = Initial volume + Rate of fill × time taken

⇒

⇒

Therefore, the linear function 'V' that models the volume of hydrogen in the balloon at any time 't' is

(b)

Given:

Balloon has a capacity of 15 ft³. This means the total volume of hydrogen that can be filled is 15 ft³.

So,

Plugging 'V' value in the above equation and solving for 't', we have:

Therefore, it takes 26 seconds to completely fill the balloon.

5x+2x=49

7x=49

x=7. 35 apples

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.