Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
Answer:
<h2><em>
a11= -11 a12=-16 a13=6 a14=-10</em></h2>
Step-by-step explanation:
I answered this question.
Answer:
12ft trim
Step-by-step explanation:
assuming that she wants to use the same size on each side (3ft) of the window, we know that the window is a square
and a square has 4 sides
3 + 3 + 3 + 3 = 12ft
She needs 12 ft trim
Answer:
81 m
Step-by-step explanation:
At take off t = 0, substitute x = 0 into h(x)
h(0) = - 3(0 - 3)² + 108 = - 3(9) + 108 = - 27 + 108 = 81 m
Answer:
The answer is -3x.
Step-by-step explanation:
Combine like terms.
Hope this helps :)