First, we need to transform the equation into its standard form (x - h)²=4p(y - k).
Using completing the square method:
y = -14x² - 2x - 2
y = -14(x² + 2x/14) - 2
y = -14(x² + 2x/14 + (2/28)²) -2 + (2/28)²
y = -14(x + 1/14)² - 391/196
-1/14(y + 391/196) = (x + 1/14)²
This is a vertical parabola and its focus <span>(h, k + p) is (-1/14, -391/196 + 1/56) = (-1/14, -775/392).
Or (-0.071,-1.977).</span>
The volume of a sphere is given by the equation
, where r is the radius.
We are given the diameter of the sphere, but recall that the diameter is twice the radius:
. So the radius is half of the diameter:
.
Half of 8 cm is 4 cm.
We substitute this for r in the equation and we use 3.14 for <span>π.</span>
Answer:
15 teachers
Step-by-step explanation:
Given:
number of children is c
number of teachers is t
= (rearrange)
t = x C
When C = 70,
t = x 70
t = 15 teachers