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mart [117]
3 years ago
8

What is the sum of the geometric series t=1

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0
In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. ... To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
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Step-by-step explanation:

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wolverine [178]

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110

Step-by-step explanation:

Using pythagorean theorm

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Iv)<br>6x+3y=6xy<br>2x + 4y= 5xy​
Margaret [11]

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

8 0
2 years ago
1 point
koban [17]

Answer:

She will be charged $180 once lets the account go past 6 months before making a payment.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P

In this question:

If she pays within 6 months, she is not charged any interest.

However, if after 6 months she has not paid the balance, she is charged 20% interest for this period.

Barbara financed a new bedroom set at the furniture store for $1,800.

This means that P = 1800

20 percent interest

This means that I = 0.2

How much interest will she be charged once she lets the account go past 6 months?

6 months is half a year, so this is E when T = 0.5

E = P*I*t

E = 1800*0.2*0.5

E = 180

She will be charged $180 once lets the account go past 6 months before making a payment.

3 0
2 years ago
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