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artic0203
27.08.2019 •
Mathematics
The area of a circle is increasing at the rate of pi cm^(2)/min. at what rate is the radius increasing when the area is 4pi cm^(2)?
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Ответ:
For the formula of the area of a circle, we differentiate both sides with respect to time t.
(A = πr^2) d/dt
dA/dt = 2πr (dr/dt)
Since we don't know yet the radius r, the area of a circle is given.
A = πr^2
r^2 = A/π = 4π/π
r^2 = 4
r = 2 cm
Therefore, the rate of the radius is
dA/dt = 2πr (dr/dt)
dr/dt = (dA/dt)/(2πr)
dr/dt = π/(2π*2)
dr/dt = 0.25 cm/min
Hope this helps.
Ответ:
0.2 times
Step-by-step explanation:
Saturn: 8.867 × 108 = 957.636
Uranus: 1.787 × 109 = 194.783
You take (Uranus: 194.783)
& you divide it by (Saturn: 957.636)
You should get a funky number like 0.203399830415732 but since they said approximately you only need to use the first 2 (don't forget to round)
That would make Uranus 0.2 times as far from the sun