- f(x) = x^5 – 8x^3 – 9x (find all zeros/roots)
1 answer:
You might be interested in
<h2>1. y-intercept</h2>
The quadratic function represents a parabola. In fact, the graph of a quadratic function is a special type of U-shaped curve called a parabola. To find the y intercept, we set
as follows:
To find the other x-intercept, we must set as follows:
Therefore, the other x-intercept is . You can see both the y-intercept and the x-intercepts in the figure below.
Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
_____
A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
_____
<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
The ladder resting against the house forms a triangle similar to the one in the image below
To answer this question you must use Pythagorean theorem
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = x
b = 4
c = 20
^^^Plug these numbers into the theorem
solve for x
+ 16 = 400
= 384
x = 8√6
or
x ≈ 19.5959....
Hope this helped!
~Just a girl in love with Shawn Mendes
