Their distance differs by 15 miles for each hour of travel time. Thus, the travel time of interest is
.. (180 -144) miles/(15 miles/hour) = 2.4 hour
The red car's speed is 180 mi/(2.4 h) = 75 mi/h.
The blue car's speed is 144 mi/(2.4 h) = 60 mi/h.
Answer:
and as ![x->-2^{+}, p(x)->-\infty](https://tex.z-dn.net/?f=x-%3E-2%5E%7B%2B%7D%2C%20p%28x%29-%3E-%5Cinfty)
Step-by-step explanation:
Given
-- Missing from the question
Required
The behavior of the function around its vertical asymptote at ![x = -2](https://tex.z-dn.net/?f=x%20%3D%20-2)
![p(x) = \frac{x^2-2x-3}{x+2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cfrac%7Bx%5E2-2x-3%7D%7Bx%2B2%7D)
Expand the numerator
![p(x) = \frac{x^2 + x -3x - 3}{x+2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cfrac%7Bx%5E2%20%2B%20x%20-3x%20-%203%7D%7Bx%2B2%7D)
Factorize
![p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cfrac%7Bx%28x%20%2B%201%29%20-3%28x%20%2B%201%29%7D%7Bx%2B2%7D)
Factor out x + 1
![p(x) = \frac{(x -3)(x + 1)}{x+2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cfrac%7B%28x%20-3%29%28x%20%2B%201%29%7D%7Bx%2B2%7D)
We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)
We are only interested in the sign of the result
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As x approaches -2 implies that:
Say x = -3
![p(x) = \frac{(x -3)(x + 1)}{x+2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cfrac%7B%28x%20-3%29%28x%20%2B%201%29%7D%7Bx%2B2%7D)
![p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12](https://tex.z-dn.net/?f=p%28-3%29%20%3D%20%5Cfrac%7B%28-3-3%29%28-3%2B1%29%7D%7B-3%2B2%7D%20%3D%20%5Cfrac%7B-6%20%2A%20-2%7D%7B-1%7D%20%3D%20%5Cfrac%7B%2B12%7D%7B-1%7D%20%3D%20-12)
We have a negative value (-12); This will be called negative infinity
This implies that as x approaches -2, p(x) approaches negative infinity
![x->-2^{-}, p(x)->-\infty](https://tex.z-dn.net/?f=x-%3E-2%5E%7B-%7D%2C%20p%28x%29-%3E-%5Cinfty)
Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)
As x leaves -2 implies that: ![x>-2](https://tex.z-dn.net/?f=x%3E-2)
Say x = -2.1
![p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1](https://tex.z-dn.net/?f=p%28-2.1%29%20%3D%20%5Cfrac%7B%28-2.1-3%29%28-2.1%2B1%29%7D%7B-2.1%2B2%7D%20%3D%20%5Cfrac%7B-5.1%20%2A%20-1.1%7D%7B-0.1%7D%20%3D%20%5Cfrac%7B%2B5.61%7D%7B-0.1%7D%20%3D%20-56.1)
We have a negative value (-56.1); This will be called negative infinity
This implies that as x leaves -2, p(x) approaches negative infinity
![x->-2^{+}, p(x)->-\infty](https://tex.z-dn.net/?f=x-%3E-2%5E%7B%2B%7D%2C%20p%28x%29-%3E-%5Cinfty)
So, the behavior is:
and as ![x->-2^{+}, p(x)->-\infty](https://tex.z-dn.net/?f=x-%3E-2%5E%7B%2B%7D%2C%20p%28x%29-%3E-%5Cinfty)
Answer:
x= - square root 141 or x= square root 141
196 3/8 in^3. To get this, multiply all the numbers together. To find volume, the equation is length x width x height.
It would be d
because -5•-2=10
and 10+3=13