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02s54mcoupe
11.01.2021 •
Mathematics
coffee maker has the shape of a cone 10cm high with a radius of 6 cm at the top. The coffee maker is filled with water, and the water is allowed to drain out the bottom of the cone. Water is flowing out of the filter at a rate of 5 cubic centimerters per second. At what rate is the water level in the cone falling when it is 5cm from the bottom of the cone.
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Ответ:
the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec
Step-by-step explanation:
Given the data in the question;
H/h = R/r
10/5 = 6/r
r 1 = 30/10 = 3
Also
10/h = 6/r
r2 = 6h/10 = 3/5 × h
Volume = 1/3πr²h
V = 1/3 × π × (3/5 × h)² × h
V = 1/3 × π × 9/25 × h³
V = 3π/25 × h³
Now
dv/dt = 3π/25 × 3 × h² × dh/dt
-5 = 3π/25 × 3 × 25 × dh/dt
-5 = 3π × 3 × dh/dt
-5 = 9π × dh/dt
dh/dt = -5/9π
dh/dt = -0.1768 cm/sec
therefore, the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec
Ответ:
x= -b±√b²-4ac/2a
Step-by-step explanation:
the / represents the beginning being the numerator and the end being the denominator of a fraction