Answer:
Step-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
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<h3>a)</h3>
Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
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<h3>c)</h3>
For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
Simply multiply 3162 times 10 to find that 31620 is the answer.
An equilateral triangles has 3 equal sides and 3 equal angles.
All the angles of an equilateral triangle have a measure of 60 degrees.
Using the Pythagorean theorem, the length of the hypotenuse squared is the length of one leg squared plus the length of another leg squared.
Here's the equation for the Pythagorean theorem.
Let c be the length of the hypotenuse.
Let a and b be the length of the two legs.
a^2 + b^2 = c^2
Have an awesome day! :)
Necesit. la versión en español plz 9
Answer:
x = 9
Step-by-step explanation:
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
5(x - 6 + 5) = 4(x - 3 + 4)
5(x - 1) = 4(x + 1) ← distribute parenthesis on both sides
5x - 5 = 4x + 4 ( subtract 4x from both sides )
x - 5 = 4 ( add 5 to both sides )
x = 9
