Represent any point on the curve by (x, 1-x^2). The distance between (0, 0) and (x, 1-x^2) is

To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.
So minimize

Find the derivative of L and set it equal to zero.

This gives you

or

You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.

When x = 0, the second derivative is negative, indicating a relative maximum. When

, the second derivative is positive, indicating a relative MINIMUM.
The two points on the curve closest to the origin are
Answer:
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic = 1.197
Pvalue = 0.2335
There is no correlation between the two variables
Step-by-step explanation:
The null and alternative hypothesis :
H0 : No correlation exist,
H1 : Correlation exist
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic, T = r / √(1 - r²) / (n - 2)
T = 0.067 / √(1 - 0.067²) / (320 - 2)
T = 0.067 / √(0.995511 / 318)
T = 0.067 / 0.0559512
T = 1.197
The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335
α = 5% = 0.05
The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.
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ANSWER
P=8,Q=16
EXPLANATION
We can see from the table that both pattern P and Q have an initial value of 24.
Pattern P is reducing by a constant difference of 4.
The next value for pattern P is
12-4=8.
Also pattern Q is reducing by a constant value of 2.
The next value for pattern Q is,
18-2=16
Answer:
the y-intercept is 2.
Step-by-step explanation:
If you find the rate of change, which in this case is 1/-4, you can reverse the rate of change.
1 and -2
-1 (instead of adding 1) to x
+4 (instead of subtracting) to y
you get (0, 2).
Making the y-intercept 2.