Can someone plz help this is like my 5th time putting up this question!!!
1 answer:
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<h2>Hello!</h2>
The answer is:
C) They both have the same y-intercept.
<h2>Why?</h2>In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.
So,
- Finding the equation of the g(x):
Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:
Now, calculating the value of "b" using the first point (-1,8) and the slope of the function, we have:
So, the equation of g(x) is:
- Comparing the y-intercepts of f(x) and g(x):
Finding the y-intercept of f(x), by making "x" equal to 0, we have:
We have that the function f(x) has its y-intercept at "y" equal to 4.
Finding the y-intercept of g(x), by making "x" equal to 0, we have:
We have that the function g(x) has its y-intercept at "y" equal to 4.
Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:
C) They both have the same y-intercept.
Have a nice day!
If p(x) and q(x) are arbitrary polynomials of degree at most 2 then
||p||||q|| = 26() and angle between p(x) and q(x) is 0.233.
Given that
<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)
and p(x) = 2x²+ 6 , q(x)= 4x²-4x
then the values of p and q at x = -1,0,3 are given as;
x = -1,
p(-1) = 2(-1)² + 6 = 8 , q(-1) = 4(-1)² - 4(-1) = 8
x = 0,
p(0) = 2(0)² + 6 = 6 , q(0) = 4(0)² - 4(0) = 0
x = 3,
p(3) = 2(3)² + 6 = 24 , q(3) = 4(3)²- 4(3) = 24.
<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)
= (8)(8) + (6)(0) + 24(24)
= 64 + 0 + 576
<p,q> = 640
Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||
||p|| =
=
=
||p|| = 26
and
||q|| =
=
||q|| =
∴||p||||q|| = 26()
Now we have to find angle between p(x) and q(x),
∴ α = cos⁻¹
= cos ⁻¹
= cos ⁻¹
α = 13.34°
In radian
α = 0.233.
To know more about Inner product here
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