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
Hello! :)
543,982 rounded to the nearest hundred thousand would be 500,000. Because the digit 4 is less than 5, it would be 600,000. If the digit where the 4 is was 5 or more, it would round to 600,000,
543,982 to the nearest hundred is 500,000.
Hope this helped you!
THEDIPER
Answer:
b
Step-by-step explanation:
Answer:
If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is
Use following formulas to determine volumes of sphere and cylinder:
wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.
Then
Answer 1: correct choice is C.
If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So
R'=2R, r'=2r, h'=2h.
Write the new fask volume:
Then
Answer 2: correct choice is D.
Step-by-step explanation:
