If the height of candle after 10 and 26 hours are 25 cm and 17 cm then the height of candle after 21 hours is 19.5 cm.
Given height of candle after 10 hours is 25 cm , height of candle after 26 hours is 17 cm.
We have to find the height of candle after 21 hours.
We have been given two points of linear function (10,25),(26,17).
We have to first form an equation which shows the height of candle after x hours.
let the hours be x and the height be y.
Equation from two points will be as under:
(y-25)=(17-25)/(26-10)* (x-10)
y-25=-8/16 *(x-10)
16(y-25)=-8(x-10)
16y-400=-8x+80
8x+16y=480
Now we have to put x=21 to find the height of candle after 21 years.
8*21+16y=480
168+16y=480
16y=480-168
16y=312
y=312/16
y=19.5
Hence the height of candle after 21 hours is 19.5 cm.
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We could stop here and have answered the question.
Answer: 
1² + 3² + 4² + 4(n - 1)² = ¹/₃n(2n - 1)(2n + 1)
1² + 3² + 4² + (2n - 2)² = ¹/₃n(2n - 1)(2n + 1)
1 + 9 + 16 + (2n - 2)(2n - 2) = ¹/₃n(2n(2n + 1) - 1(2n + 1))
10 + 16 + (2n(2n - 2) - 2(2n - 2)) = ¹/₃n(2n(2n) + 2n(1) - 1(2n) - 1(1) 16 + (2n(2n) - 2n(2) - 2(2n) + 2(2)) = ¹/₃n(4n² + 2n - 2n - 1)
26 + (4n² - 4n - 4n + 4) = ¹/₃n(4n² - 1)
26 + (4n² - 8n + 4) = ¹/₃n(4n² - 1)
26 + 4n² - 8n + 4 = ¹/₃n(4n²) - ¹/₃n(1)
4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n
4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n
+ ¹/₃n + ¹/₃n
4n² - 7²/₃n + 30 = 1¹/₃n³
-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0
-3(-1¹/₃n³ + 4n² - 7²/₃n + 30) = -3(0)
-3(-1¹/₃n³) - 3(4n²) - 3(-7²/₃n) - 3(30) = 0
4n³ - 12n² + 23n - 90 = 0
Let's have this equation equal y first. All we have to do is add y to both sides and subtract 4 from both sides.
5x-4=y
Now, to get a parallel line, the y intercept has to change. The y intercept (the -4 in the equation) can be an infinite amount of number but -4.
Let's choose 6. We would have 5x+6=y or you could put it in the way the other equation was, 5x-y=-6.
Answer:
a) rational
b) irrational
Step-by-step explanation:
a) 36 = 6²
So sqrt(36) = 6
b) 72 = 2 × 36
sqrt(72) = sqrt(2) × sqrt(36)
Since 2 is not a perfect square, sqrt(72) is irrational
