The line and parabola intersect at x=-1 and x=4, so your solution is C. –1 and 4
In triangle ABC,
AC = 12/ (sin30) = 12 / (1/2) = 24
DC = 24-x
DB = DC tan 30 = (24-x) tan30 <span>=(24−x)/</span><span>√3
</span>
In triangle ADB using Pythagorean Theorem<span><span>x2</span>+((24−x)/<span>√3</span><span>)2</span>=<span>12^2</span></span><span><span>x2</span>+(24−x<span>)^2</span>/3=<span>12^2</span></span><span>3<span>x2</span>+(24−x<span>)^2</span>=432</span><span>4<span>x2</span>−48x+576=432</span><span>4<span>x2</span>−48x+144=0</span><span><span><span>x2</span>−12x+36=0
x1 = x2 =6
AD = AC - DC = 24- (24-x) = 6</span></span>
Answer:
a) Depth changing rate of change is 
, When the water is 6 meters deep
b) The width of the top of the water is changing at a rate of 
, When the water is 6 meters deep
Step-by-step explanation:
As we can see in the attachment part II, there are similar triangles, so we have the following relation between them 
, then 
.
a) As we have that volume is 
, then 
, so we can derivate it 
due to the chain rule, then we clean this expression for 
and compute with the knowns 
, is the depth changing rate of change when the water is 6 meters deep.
b) As the width of the top is 
, we can derivate it and obtain 
The width of the top of the water is changing, When the water is 6 meters deep at this rate
3/4 is the simplified version of 9/12
