The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance left to travel to O
ak Glen, what does the domain represent? What is the domain?
A) time left to reach Oak Glen; x ≥ 0
B) distance left to reach Oak Glen; x ≥ 0
C) time it takes to travel to Oak Glen; x ≥ 0
Eliminate
D) distance traveled since leaving Bay Town; x ≥ 0
A) time left to reach Oak Glen; x ≥ 0
B) distance left to reach Oak Glen; x ≥ 0
C) time it takes to travel to Oak Glen; x ≥ 0
Eliminate
D) distance traveled since leaving Bay Town; x ≥ 0
1 answer:
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Answer:
Step-by-step explanation:
In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.
The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:
The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be (). Now one has this much of the function assembled
Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following:
Answer:
Step-by-step explanation:
The given differential equation is
The characteristics equation is given by
Finding the values of r
We got a repeated roots. Hence, the solution of the differential equation is given by
On differentiating, we get
Apply the initial condition y (0)= 3 in equation (i)
Now, apply the initial condition y' (0)= 13 in equation (ii)
Therefore, the solution of the differential equation is