We're minimizing
subject to
. Using Lagrange multipliers, we have the Lagrangian
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
and
by taking any two of the first three equations. So if
determines a critical point, then
So the smallest value for the sum of squares is
when
.
For x intercepts, plug in 0 for y.
0 = (x^2) - 2x - 35
*factoring* = (x-7)(x+5)
x intercepts = 7,-5
As for the vertex, you can use the equation -b/2a for the x-coordinate of the vertex
so,
x = -b/2a = -(-2)/2 = 1
then just find the y value by plugging it back in to the equation.
y = ((1)^2) - 2(1) - 35
= -36
so, vertex is at (1,-36)
Answer:
i think 1000
Step-by-step explanation:
if 10 to the 5th power is 100000 and 10 to the 2nd power is 100 and you divide them the answer is 1000
Answer:
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10
Step-by-step explanation:
You’re only supposed to have one number to the left of the decimal point in scientific notation.
7) 9.135x10^10
8) 3.428x10^-2
9) 2.5x10^-7
10) 4x10^10