Answer:
The first term of the geometric series is 1
Step-by-step explanation:
In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.
Mathematically, the sum of terms in a geometric series can be calculated as;
S = a(r^n-1)/( r-1)
where a is the first term that we are looking for
r is the common ratio which is 3 according to the question
n is the number of terms which is 8
S is the sum of the number of terms which is 3280 according to the question
Plugging these values, we have
3280 = a(3^8 -1)/(3-1)
3280 = a( 6561-1)/2
3280 = a(6560)/2
3280 = 3280a
a = 3280/3280
a = 1
T because all variables are letters
Answer:
2
Step-by-step explanation:
Answer:
a). 59.049°C
b). 2.1179 seconds
Step-by-step explanation:
Expression representing the final temperature after decrease in temperature of the metal from 100°C to T°C is,
T = ![100(0.9)^{x}](https://tex.z-dn.net/?f=100%280.9%29%5E%7Bx%7D)
where x = duration of cooling
a). Temperature when x = 5 seconds
T = 100(0.9)⁵
= 59.049
≈ 59.049°C
b). If the temperature of the metal decreases from 100°C to 80°C
Which means for T = 80°C we have to calculate the duration of cooling 'x' seconds
80 = ![100(0.9)^{x}](https://tex.z-dn.net/?f=100%280.9%29%5E%7Bx%7D)
0.8 = ![(0.9)^{x}](https://tex.z-dn.net/?f=%280.9%29%5E%7Bx%7D)
By taking log on both the sides
log(0.8) =log[
]
-0.09691 = x[log(0.9)]
-0.09691 = -0.045757x
x = ![\frac{0.09691}{0.045757}](https://tex.z-dn.net/?f=%5Cfrac%7B0.09691%7D%7B0.045757%7D)
x = 2.1179
x ≈ 2.1179 seconds
Answer:
1) 2 & 6, 4 & 8, 1 & 5, 3 & 7
2) 3 & 6, 4 & 5
3) 1 & 8, 2 & 7