Answer:
B.) 45
Step-by-step explanation:
Answer: the first term of the series is 128
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
r = 1/4 = 0.25
n = 4
S4 = 170
Therefore, the expression for the sum of the 4 terms, S4 is
170 = a(1 - 0.25^4)/(1 - 0.25)
170 = a(1 - 0.00390625)/(1 - 0.25)
170 = a(0.99609375)/(0.75)
170 = 1.328125a
a = 170/1.328125
a = 128
Answer:
Step-by-step explanation:
We want to write the trignometric expression:
As an algebraic equation.
First, we can focus on the inner expression. Let θ equal the expression:
Take the secant of both sides:
Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:
By substitutition:
Using an double-angle identity:
We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:
Simplify. Therefore:
Answer:
0.5
Step-by-step explanation:
→ Find the difference in y
7 - 3 = 4
→ Find the difference in x
9 - 1 = 8
→ Divide the results
4 ÷ 8 = 0.5
