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Answer: 120 ft
<u>Step-by-step explanation:</u>
The Ellipse equation is: where
- (h, k) is the center
- "a" is the horizontal radius
- "b" is the vertical radius
- c is the distance from the center to the foci: |a² - b²| = c²
Given: horizontal diameter = 122 → horizontal radius = 61 = a
vertical diameter = 22 → vertical radius = 11 = b
Foci (c): 61² - 11² = c²
3721 - 121 = c²
3600 = c²
±60 = c
Let (h, k) = (0, 0)
Then the foci are located at -60 and +60.
The distance between them is 60 + 60 = 120
<span><u><em>Answer:</em></u>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
<span>;
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>
Answer:
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Step-by-step explanation:
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