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:
the equation of the line is 7x + y = 0 .
Step-by-step explanation:
in the standard form of the line that is Ax +By = C we can write it in the form of
By = C - Ax
which is in the form of 
where m is the slope of the line and c is y intercept made by the line.
comparing and
we get that 
and 
since it is given that slope of the line is -7 therefore m = -7 and c = 0
therefore 
and 
therefore C = 0 , A = 7 and B = 1
therefore the equation becomes 7x + y = 0
Answer:
70,000 i think
Step-by-step explanation:
Answer:
look it up mf
Step-by-step explanation:
Cross multiply.
14/12=x/18
14 x 18 = 252
252/12= 21
so x=21
