This scatterplot and regression line below show the relationship between the average rent for a 1-bedroom apartment in New York
1 answer:
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Given:
The function is
To find:
The asymptotes and zero of the function.
Solution:
We have,
For zeroes, f(x)=0.
Therefore, zero of the function is 0.
For vertical asymptote equate the denominator of the function equal to 0.
Taking square root on both sides, we get
So, vertical asymptotes are x=-4 and x=4.
Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0.
Answer:
15 miles per hour is the speed of the slower train.
Step-by-step explanation:
As given in the figure attached,
Let the speed of train 1 is v and train 2 is u.
Therefore, distance traveled in 2 hours by train 1 will be = 2v miles
and distance traveled by train 2 will be = 2u miles
Now we can see in the figure a right angle triangle is formed by the two trains.
AB² + BC² = AC²
(2v)² + (2u)²= (65.30)²
4v² + 4u² = 4264.09
Now we divide this equation by 4
v² + u² = 1066.02
If speed of the slower train is v miles per hour then as per statement of the question.
u = v - 14
v = u + 14
By putting the value of v in the equation
(u + 14)² + u² = 1066
u² + 196 + 28u + u² = 1066
2u² + 28u + 196 = 1066
2u² + 28u + 196 - 1066 = 0
2u² + 28u - 870 = 0
By diving this equation by 2
u² + 14u - 435 = 0
u² + 29u - 15u - 435 = 0
u(u + 29) - 15(u + 29) = 0
(u + 29)(u - 15) = 0
u = -29, 15
Since speed can not be with negative notation so u = 15 miles per hour will be the speed.
Therefore, 15 miles per hour is the speed of the slower train.
