Answer: 1
Step-by-step explanation:
Answer:
Option (d) is correct.
6 + 9 + 12 +15 = ![\sum_{k=1}^{4}(3k+3)](https://tex.z-dn.net/?f=%5Csum_%7Bk%3D1%7D%5E%7B4%7D%283k%2B3%29)
Step-by-step explanation:
Consider the given series expansion 6 + 9 + 12 +15.
since we have to write in series form of 3.
We first write each term of given series in term of 3k or 3k+3
6 can be written as 3(2) or 3(1)+3
9 can be written as 3(3) or 3(2)+3
12 can be written as 3(4) or 3(3)+3
15 can be written as 3(5) or 3(4)+3
Thus, we can write the given series as ,
or ![\sum_{k=1}^{4}(3k+3)](https://tex.z-dn.net/?f=%5Csum_%7Bk%3D1%7D%5E%7B4%7D%283k%2B3%29)
Since, we have options to choose.
From the given option (d) matches our result.
So, 6 + 9 + 12 +15 = ![\sum_{k=1}^{4}(3k+3)](https://tex.z-dn.net/?f=%5Csum_%7Bk%3D1%7D%5E%7B4%7D%283k%2B3%29)
Answer:
The height of the right circular cylinder is 4.55 inches ⇒ b
Step-by-step explanation:
The formula of the surface area of a right circular cylinder is
S.A = 2πrh + 2πr², where
∵ The surface area of a right circular cylinder is 300 square inches
∴ S.A = 300 in.²
∵ Its radius is 5 inches
∴ r = 5 in.
∵ π = 3.14
→ Substitute them in the rule above
∵ 300 = 2(3.14)(5)(h) + 2(3.14)(5)²
∴ 300 = 31.4h + 157
→ Subtract 157 from both sides
∵ 300 - 157 = 31.4h + 157 - 157
∴ 143 = 31.4h
→ Divide both sides by 31.4
∵ 4.554140127 = h
∴ 4.55 = h
∴ The height of the right circular cylinder is 4.55 inches
Step-by-step explanation:
In adding fractions, first you have to make the denominators the same. To do this, you need to find the GCF (greatest common factor).
3/4 + 4/8
The GCF on this would be 8, since both 4 and 8 can go into it. Next, you need to change both the denominators to the GCF, but you have to make sure the fractions are still equal to the original one. To do this, you have to multiply the numerator by the amount the original denominator is multiplied to get to the GCF.
4(2) = 8
3(2) = 6
So now you have 6/8 + 4/8. Next, you just add up the numbers normally, leaving the denominators the same.
6/8 + 4/8 = 10/8
If necessary, you simplify the fraction. To do this, you need to find the smallest number that goes into both of them, besides one. In this case, it would be 2. Then, you divide both the numerator and denominator by that number.
10/2 = 5
8/2 = 4
Then, to find the most simplified version, you need to divide the numorator by the denominator.
5/4 = 1 with a remainder of 1.
You put your answer as the whole number, and your remainder as the numorator. Leave the denominator the same.
1![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
Hope this helped with adding fractions!