Answer:
Step-by-step explanation:
The standard equation of a hyperbola is given by:
where (h, k) is the center, the vertex is at (h ± a, k), the foci is at (h ± c, k) and c² = a² + b²
Since the hyperbola is centered at the origin, hence (h, k) = (0, 0)
The vertices is (h ± a, k) = (±√61, 0). Therefore a = √61
The foci is (h ± c, k) = (±√98, 0). Therefore c = √98
Hence:
c² = a² + b²
(√98)² = (√61)² + b²
98 = 61 + b²
b² = 37
b = √37
Hence the equation of the hyperbola is:
Youssef lives 15 blocks away from his work
<em><u>Solution:</u></em>
Given that Youssef can either way from his home to his workplace or ride his bicycle
Let "x" be number of blocks away from work Youssef works
<u><em>Case 1: walking</em></u>
He walks at a pace of 1 block per min
Therefore,
1 block = 1 minute
Thus to cross "x" blocks he takes "x" minutes
<em><u>Case 2: Bicycle</u></em>
He can travel 1 block in 20 sec on his bicycle
We know that,
To convert seconds to minute, divide the time value by 60
Thus he takes 1/3 minutes for 1 block
So to cross "x" blocks he will take minutes
Given that it takes youssef 10 min longer to walk to work than to ride his bike
This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes
Thus he lives 15 blocks away from his work