Speed is determined by dividing the distance travelled by the time taken to travel the
distance or s= d/t. Write a rational expression for speed, given the distance travelled,
is 3p^2+5p-2 and the time to travel that distance is 3p^2+2p-1. Identify any nonpermissible values.
you have the formula, so plug and chug
s = d/t = (3p^2+5p-2)/(3p^2+2p-1) = (3p-1)(p+2) / (3p-1)(p+1)
exclude values of p where the denominator is zero
Now reduce to get
s = (p+2)/(p+1)
To find the rational expression for speed, we need to divide the distance traveled by the time taken.
Given that the distance traveled is 3p^2+5p-2 and the time taken is 3p^2+2p-1, we can represent the speed as:
Speed = (Distance traveled) / (Time taken)
= (3p^2+5p-2) / (3p^2+2p-1)
Now, let's identify any nonpermissible values. Nonpermissible values occur when the denominator is equal to zero, as division by zero is undefined. Therefore, we need to find the values of p that make the denominator equal to zero.
For the denominator, we have: 3p^2+2p-1 = 0
To solve this quadratic equation, we can use factoring, quadratic formula, or completing the square. Since factoring is not straightforward for this equation, let's use the quadratic formula:
p = (-b ± sqrt(b^2-4ac)) / (2a)
Here, a = 3, b = 2, and c = -1. Plugging in these values in the quadratic formula, we have:
p = (-(2) ± sqrt((2)^2 - 4(3)(-1))) / (2(3))
p = (-2 ± sqrt(4 + 12)) / 6
p = (-2 ± sqrt(16)) / 6
p = (-2 ± 4) / 6
Simplifying further, we have two possible values for p:
1) p = (-2 + 4) / 6 = 2/6 = 1/3
2) p = (-2 - 4) / 6 = -6/6 = -1
Therefore, the nonpermissible values for p are p = 1/3 and p = -1.
In summary, the rational expression for speed is (3p^2+5p-2) / (3p^2+2p-1), and the nonpermissible values for p are p = 1/3 and p = -1.
To write a rational expression for speed, we need to divide the distance travelled by the time taken. In this case, the distance travelled is given as 3p^2 + 5p - 2 and the time taken is given as 3p^2 + 2p - 1.
So, the rational expression for speed (s) can be written as:
s = (3p^2 + 5p - 2) / (3p^2 + 2p - 1)
Now, let's identify any nonpermissible values. Nonpermissible values occur when the denominator of a rational expression becomes zero, as division by zero is undefined.
To find the nonpermissible values for the expression (3p^2 + 2p - 1), we set the denominator equal to zero and solve for p:
3p^2 + 2p - 1 = 0
Using factoring or the quadratic formula, we can determine the values of p that make the denominator zero.
After solving the equation, we find that the nonpermissible values are the values of p that satisfy the equation 3p^2 + 2p - 1 = 0.