alice has eight good behavior stars and earns a new one each week. Mack has two good behavior stars and earns two new ones each
2 answers:
Answer:
In 14 weeks will they have the same number of good behavior stars
Step-by-step explanation:
Let
x ----> the number of weeks
y ----> the number of good behavior stars
we know that
<em>Alice</em>
----> equation A
<em>Mack</em>
----> equation B
To find out in how many weeks will they have the same number of good behavior stars, equate equation A and equation B
Solve for x
<u><em>Verify</em></u>
For x=6 weeks
<em>Alice</em>
<em>Mack</em>
therefore
In 14 weeks will they have the same number of good behavior stars
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Answer:
a) distance halfway = 16.49 [m], displacement halfway = 10.5 [m]
b) distrance traveled increases when the child completes one circuit of the track.
Step-by-step explanation:
a) Distance is a scalar quantity that tells you how much space a body has covered when moving. Displacement is a vector quantity that tells you how far from its initial position and object is after moving.
In this case, the child goes around the track only halfway from point 1 to point 2. We know the circunference or perimeter of a circle to be 2*PI*radius. We also know the child only when halfway, so we need to divide the perimeter by 2, thus we get distance = PI*radius
- distance halfway = (PI)*(5.25) = 16.49 [m]
And now that we know the definition of displacement, we can easily see that the child went from point 1 to point 2 which is located at a distance of 1 diameter from point 1:
- displacement halfway = D = 2*radius = 2(5.25) = 10.5 [m]
b)What happens to the distance when the child completes one circuit? The distance will increase beause he is now completing the circuit so he is covering more ground in his movement:
- distance circuit = 2*(PI)*radius = 2(PI)(5.25) = 32.99 [m]
32.99 is more than 16.49 so we are certain that the distance increases.
