
Step-by-step explanation:
The vertex form of the equation for a parabola is given by

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

or

Therefore, the equation of the parabola is

Answer:
The probability that occurrence of 8 in ten minutes is 0.0771.
Step-by-step explanation:
Poisson Distribution:
A discrete random variable X having the enumerable set {0,1,2,.....} as the spectrum, is said to have Poisson distribution with parameter
(>0), if the p.m.f is given by
for x=0,1,2,...
= 0, elsewhere
The mean number of occurrences in ten minutes is 5.3.
Here
= 5.3 and x= 8

=0.0771
The probability that occurrence of 8 in ten minutes is 0.0771.
Answer:
The solution of the given initial value problems in explicit form is
and the solutions are defined for all real numbers.
Step-by-step explanation:
The given differential equation is

It can be written as

Use variable separable method to solve this differential equation.

Integrate both the sides.

![[\because \int x^n=\frac{x^{n+1}}{n+1}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cint%20x%5En%3D%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bn%2B1%7D%5D)
... (1)
It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.



The value of C is -2. Substitute C=-2 in equation (1).
Therefore the solution of the given initial value problems in explicit form is
.
The solution is quadratic function, so it is defined for all real values.
Therefore the solutions are defined for all real numbers.
Answer:
The skid distance to be used is 54 feet.
Step-by-step explanation:
Given:
Four skid marks on the highway.
in feet.
We have to find the skid distance.
The skid distance that will be used to further calculate the skid speed is actually the mean skid distance.
Mean skid distance (m) :
⇒ 
⇒ 
⇒ 
⇒
feet.
So the skid distance to be used is 54 feet.