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lilavasa [31]
2 years ago
9

[100 points]

Mathematics
1 answer:
Veronika [31]2 years ago
8 0

Answer:

Multiply the moduli and add the arguments.Step-by-step explanation:First write out the two terms being multiplied: z1z2= [r1(cos(theta 1) + isin(theta 1))][r2(cos(theta 2)+ isin(theta 2))] z1z2= r1r2 (cos(theta 1) + isin(theta 1))(cos(theta 2)+ isin(theta 2)) z1z2= r1r2(cos(theta 1)cos(theta 2))+(icos(theta 1)sin(theta 2))+(icos(theta 2)sin(theta 1))+(i^2 sin(theta 1)sin(theta 2)) Next group and rewrite the like term with the sums and differences. Your answer is the multiplication of the moduli and the addition of the arguments: z1z2= r1r2[cos(theta 1 + theta 2) + i sin (theta 1 and theta 2)].

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Does (-2)^n/( 3^n+1) converge or diverge?
hodyreva [135]
\left|\dfrac{(-2)^n}{3^n+1}\right|=\dfrac{2^n}{3^n+1}

As n\to\infty, the sequence a_n=\left(\dfrac23\right)^n converges to zero.

If you're talking about the infinite series

\displaystyle\sum_{n\ge0}\dfrac{(-2)^n}{3^n+1}

well we've shown by comparison that this series must also converge because we know any geometric series \sum\limits_n r^n will converge as long as |r|.
3 0
2 years ago
Ramu and ravi borrowed rs 8000​
Phoenix [80]

Answer: Rs. 11,520

Step-by-step explanation:

As the method of compounding is not stated, the default of simple interest will be used.

Simple interest is a fixed amount that is paid over the course of the loan and is based on the original amount borrowed.

Formula is:

Amount owed = Amount borrowed * ( 1 + rate * time)

= 8,000 * ( 1 + 8% * 5.5 years)

= 8,000 * 1.44

= rs 11,520

4 0
2 years ago
Type the correct answer in each box, Write the coordinates in the form (x, y). If necessary, use / for the fraction bar(s).
Blizzard [7]

Answer:

point a are (-10,-4) and point I are (-3.875,-10.125)

Step-by-step explanation:

8 0
3 years ago
Write a formula that will yield the nth term of the sequence: 3,-2,-7,-12
RUDIKE [14]

Answer:

-5n + 8

Step-by-step explanation:

<u>1. What is the difference?</u>

  The sequence goes down by 5. This means that the formula will have -5n in it.

<u>2. Work out the term before the first term.</u>

    The first term is 3, and we know that the sequence goes up by 5. So, to get the term before 3 we would add 5.

3 + 5 = 8   Remember, this is positive 8. (+8)

<u>3. Put that term at the end of the equation. </u>

   We have -5n already and we just worked out the term before the first one which is positive 8 - so put that at the end of the equation.

-5n + 8  This is our answer!

Just to prove it works:

<em>Substitute:   n = term</em>

Lets see if we can get the 3rd term which is -7. (n = 3)

-5(3) + 8

-15 + 8 = -7

See, it works!

8 0
3 years ago
Two stores offer differently priced sales for the same paper towels, according to the table below. Which store offers the better
Verizon [17]
Store 1 : 12 paper towels for 3.60
3.60 / 12 = 0.30......30 cents per roll

store 2 : 10 paper towels for 3.50
3.50/10 = 0.35....35 cents per roll

the better deal is store 1 with paper towels costing 30 cents per roll
5 0
2 years ago
Read 2 more answers
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