Answer:
21 and 26 totaling 47sticks
Step-by-step explanation:
Th number of sticks form an arithmetic progression
1, 6, 11, 16...
The nth term of an arithmetic progression is expressed as;
Tn = a+(n-1)d
a is the first term = 1
d is the common difference
d = 6-1 = 11-6 = 5
n is the number of terms
The next two terms are the fifth and sixth term
T5 = 1+(5-1)5
T5 = 1+4(5)
T5 = 1+20
T5 = 21
T6 = 1+(6-1)5
T6 = 1+5(5)
T6 = 1+25
T6 = 26
Hence the number of sticks needed in the next two piles are 21 and 26 totaling 47sticks
To solve this problem you must apply the proccedure shown below:
1. You have that the radius and the height of the cylinder are:
![r=8 in \\ h=6 in](https://tex.z-dn.net/?f=r%3D8%20in%20%5C%5C%20h%3D6%20in)
2. So, you must calculate the area:
![A1=2 \pi (r+h)](https://tex.z-dn.net/?f=A1%3D2%20%5Cpi%20%28r%2Bh%29)
3. Substitute the values into the formula:
![A1=2 \pi (8 in)(8 in+6in) \\ A1=703.71 in^{2}](https://tex.z-dn.net/?f=A1%3D2%20%5Cpi%20%288%20in%29%288%20in%2B6in%29%20%5C%5C%20A1%3D703.71%20%20in%5E%7B2%7D%20)
4. When the radius and the height are doubled, you obtain:
![A2=2 \pi (16 in)(16 in+12 in) \\ A2=2814.86 in^{2}](https://tex.z-dn.net/?f=A2%3D2%20%5Cpi%20%2816%20in%29%2816%20in%2B12%20in%29%20%5C%5C%20A2%3D2814.86%20in%5E%7B2%7D)
5. The factor is:
The answer is: B.
To find the answer, multiply 22 1/2 by 3.
22 1/2 x 3 = 67 1/2
This can round up to 68
The answer is C. 68 mph
If you have any further questions feel free to ask.
Hope this helps.
Answer:
9.4 units.
Step-by-step explanation:
Given information: |OQ| = 9.4 units, |OQ’| = 17.1 units, and |P’Q’| = 17.1 units.
Dilated figure is similar to the original figure. It means the corresponding sides are proportional.
![\dfrac{|OQ|}{|OQ'|}=\dfrac{|PQ|}{|P'Q'|}](https://tex.z-dn.net/?f=%5Cdfrac%7B%7COQ%7C%7D%7B%7COQ%27%7C%7D%3D%5Cdfrac%7B%7CPQ%7C%7D%7B%7CP%27Q%27%7C%7D)
Substitute the given values.
![\dfrac{9.4}{17.1}=\dfrac{|PQ|}{17.1}](https://tex.z-dn.net/?f=%5Cdfrac%7B9.4%7D%7B17.1%7D%3D%5Cdfrac%7B%7CPQ%7C%7D%7B17.1%7D)
Multiply both sides by 17.1.
![\dfrac{9.4}{17.1}\times 17.1=\dfrac{|PQ|}{17.1}\times 17.1](https://tex.z-dn.net/?f=%5Cdfrac%7B9.4%7D%7B17.1%7D%5Ctimes%2017.1%3D%5Cdfrac%7B%7CPQ%7C%7D%7B17.1%7D%5Ctimes%2017.1)
![9.4=|PQ|](https://tex.z-dn.net/?f=9.4%3D%7CPQ%7C)
Hence, the measure of |PQ| is 9.4 units.