Answer:
√(p²-4q)
Step-by-step explanation:
Using the Quadratic Formula, we can say that
x = ( -p ± √(p²-4(1)(q))) / 2(1) with the 1 representing the coefficient of x². Simplifying, we get
x = ( -p ± √(p²-4q)) / 2
The roots of the function are therefore at
x = ( -p + √(p²-4q)) / 2 and x = ( -p - √(p²-4q)) / 2. The difference of the roots is thus
( -p + √(p²-4q)) / 2 - ( ( -p - √(p²-4q)) / 2)
= 0 + 2 √(p²-4q)/2
= √(p²-4q)
Answer:
The concept which best describes the change of the population is the derivative of
.
Step-by-step explanation:
Observe that the function
describes the amount of rabbits at the time t (in years) but no the rate of change of the population at a given instant. So you have to use the derivative of
to obtain that rate of change at any instant. For example, if we derivate the function
we obtain:

And if we want to find the rate of change at
years we evaluate
rabbits/year
Answer:
The zeros are 0, 4, 6.
The y-intercept is 0.
Step-by-step explanation:
f(x) = x^3 - 10x^2 + 24x
x^3 - 10x^2 + 24x = 0
x(x^2 - 10x + 24) = 0
x(x - 4)(x - 6) = 0
x = 0 or x - 4 = 0 or x - 6 = 0
x = 0 or x = 4 or x = 6
y-intercept:
Since x = 0 is a root, that means that the point (0, 0) is part of the function. That makes the y-intercept 0.
You can also solve for the y-intercept by letting x = 0 in the function and solving for f(0).
Let x = 0.
f(0) = 0^3 - 10(0^2) + 24(0)
f(0) = 0
y-intercept: 0
33. 15x10=150x9
the answer is b
34. a
Answer: 
Step-by-step explanation:
To solve this exercise you need to remember the following:
→ 
Therefore, keeping the above on mind, you can solve for x as following:


Remember that, by definition:
, then you have:

Subtract 6 from both sides of the equation.
Then the value of x is:
