5f+3=28 find the value of f
2 answers:
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9514 1404 393
Answer:
a (3,-1)
Step-by-step explanation:
The number that "completes the square" is the square of half the x-coefficient, (-6/2)^2 = 9. Rearranging the given function to include the square trinomial, we have ...
f(x) = x^2 -6x +9 -1 . . . . . . . here, we have 8 = 9 - 1
f(x) = (x -3)^2 -1 . . . . . . . . . . vertex form
Comparing this to the generic vertex form ...
f(x) = (x -h)^2 +k . . . . . . . vertex at (h, k)
we see that h=3 and k=-1.
The vertex is (h, k) = (3, -1).
<h2>Answer:</h2>
4π
<h2>Step-by-step explanation:</h2>As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:
A = x b x h -------------(i)
Where;
A = 18
b = XZ = base of the triangle
h = YZ = height of the triangle = 6
<em>Substitute these values into equation(i) and solve as follows:</em>
18 =
x b x 6
18 = 3b
<em>Divide through by 3</em>
6 = b
Therefore, b = XZ = 6
<em>Now, assume that the circle is centered at O;</em>
Triangle XOZ is isosceles, therefore the following are true;
(i) |OZ| = |OX|
(ii) XZO = ZXO = 30°
(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]
=> XOZ + 30° + 30° = 180°
=> XOZ + 60° = 180°
=> XOZ = 180° - 60°
=> XOZ = 120°
Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;
|OZ| = 6
The radius of the circle is therefore 6.
<em>Now, let's calculate the length of the arc XZ</em>
The length(L) of an arc is given by;
L = θ / 360 x 2 π r ------------------(ii)
Where;
θ = angle subtended by the arc at the center.
r = radius of the circle.
In our case,
θ = ZOX = 120°
r = |OZ| = 6
Substitute these values into equation (ii) as follows;
L = 120/360 x 2π x 6
L = 4π
Therefore the length of the arc XZ is 4π