Cylinder Volume
V = hπr²
154 cm³ = 16 cm × 3.14 × r²
154 cm³ = 50.28 cm × r²
r² = 154 cm³ : 50.28 cm
r² = 3.0625 cm²
r = 1.75 cm
d = 2r
d = 2 × 1.75 cm
d = 3.5 cm
So, the diameter of the Cylinder is 3.5 cm
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This is a geometric sequence because each term is twice the value of the previous term. So this is what would be called the common ratio, which in this case is 2. Any geometric sequence can be expressed as:
a(n)=ar^(n-1), a(n)=nth value, a=initial value, r=common ratio, n=term number
In this case we have r=2 and a=1 so
a(n)=2^(n-1) so on the sixth week he will run:
a(6)=2^5=32
He will run 32 blocks by the end of the sixth week.
Now if you wanted to know the total amount he runs in the six weeks, you need the sum of the terms and the sum of a geometric sequence is:
s(n)=a(1-r^n)/(1-r) where the variables have the same values so
s(n)=(1-2^n)/(1-2)
s(n)=2^n-1 so
s(6)=2^6-1
s(6)=64-1
s(6)=63 blocks
So he would run a total of 63 blocks in the six weeks.
Answer:
14 ohms
Step-by-step explanation:
The resistance varies directly with length, so increasing the length by a factor will increase the resistance by the same factor.
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The length of the wire increased by a factor of 1.4 from 100 ft to 140 ft. That means the resistance will increase by a factor of 1.4 from 10 ohms to 14 ohms. (The diameter did not change.)
The longer wire will have a resistance of 14 ohms.
Answer:
The t-distribution is used.
Step-by-step explanation:
When we dont know the standard deviation of the population, we use the t-distribution(t-table).
Otherwise, the z-distribution(z-table) is used.
So the answer to this question is the t-distribution.
