9514 1404 393
Answer:
16
Step-by-step explanation:
48 = 16·3
112 = 16·7
80 = 16·5
3, 5, 7 have no common factors. The GCF of {48, 112, 80} is 16.
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It can be helpful to recognize 48 = 16·3 and 80 = 16·5. A simple check shows 112 = 16·7, so 16 is the GCF.
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You can find GCF(48,112) using Euclid's algorithm:
112 mod 48 = 16
48 mod 16 = 0 ⇒ GCF(48, 112) = 16
and the GCF(16, 80) is ...
80 mod 16 = 0 ⇒ GCF(16, 80) = 16
So, GCF(48, 80, 112) is 16.
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Answer: 66 yards of fence
Step-by-step explanation:
This is a circular enclosure so the length of the fence must be the circumference of the circular enclosure.
The fence was built 10.5 yards from the centre which would mean that 10.5 yards is the radius of the circle.
The circumference will therefore be:
= 2 * Pie * radius
= 2 * 22/7 * 10.5
= 66 yards of fence
Answer:
dV/dt = 40π
Step-by-step explanation:
We are told that The radius r(t) of the base of a cone is increasing at a rate of 10 meters per second. Thus;
dr/dt = 10 m
Height: h = 6 m
Volume of cone is given by the formula;
V = ⅓πr²h
dV/dr = ⅔πrh
We want to find the rate at which the volume is changing at radius of 1m.
Thus;
dV/dt = (dV/dr) × (dr/dt)
dV/dt = ⅔π(1 × 6) × (10)
dV/dt = 40π
Answer:
32t
Step-by-step explanation:
(-4t x 4t) + (-4t x 12)
= -16t + (-4t x 12)
= -16t+48t
= 32t
