By completing the square: x²-8x+19 = (x-4)²-16+19 = (x-4)²+3 so minimum point = (4,3)
By calculus: f'(x) = 2x-8. (minimum point occurs when f'(x)=0 therefore)
2x-8 = 0 means x=4 and the corresponding y value is 3.
The minimum value of this function (y) is 3 and this occurs when x = 4.
Answer:
x = 5 , y = 5
Step-by-step explanation:
Using the sine and cosine ratios in the right triangle and exact values.
sin30° =
, cos30° =
, then
sin30°=
=
=
( cross- multiply )
2x = 10 ( divide both sides by 2 )
x = 5
and
cos30° =
=
=
( cross- multiply )
2y = 10
( divide both sides by 2 )
y = 5
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
Equating the expressions for y gives ...
-1/4x +6 = x +1
5 = 5/4x . . . . . . . add 1/4x-1
4 = x . . . . . . . . . . multiply by 4/5
y = x +1 = 4 +1
y = 5
The solution is (x, y) = (4, 5).
Hello :
-5x^2-2x^3-4x =-2x^3-5x^2-4x.....(<span> standard form.)
</span><span>the number of terms are : -2 , -5 , -4 ,0</span>
Answer:
See below.
Step-by-step explanation:
By the rational roots theorem all possible roots are:
+/-1. +/- 2, +/-4 .+/-8, +/-16 and +/-32.