Answer:
y = (x - 5)² - 2
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (5, - 2), thus
y = a(x - 5)² - 2
To find a substitute (7, 0) into the equation
0 = a(7 - 5)² - 2
0 = 4a - 2 ( add 2 to both sides )
2 = 4a ( divide both sides by 4 )
a = =
y = (x - 5)² - 2 ← in vertex form
Answer:
6.82
Step-by-step explanation:
By congruence of triangles, the radius r of the cone base when its height is 1 meter satisfies the relation
r/1 = 2.5/6
(See picture attached)
So, r = 0.4166 meters when the water is 1 meter high.
The volume of a cone with radius of the base = R is given by
So, the volume of water when it is 1 meter high is
One minute later, the height of the water is 1 meter + 30 centimeters = 1.30 mt
The radius now satisfies
r/1.3 = 2.5/6
and now the radius of the base is
r = 0.5416 mt
and the new volume of water is
So, the water is raising at a speed of
0.3071-0.1871 = 0.12
This speed equals the difference between the water being pumped and the water leaking,
So,
<em>0.12 = Speed of water being pumped -6.8 </em>
and
Speed of water being pumped = 6.8+0.12 = 6.82
