1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leona [35]
2 years ago
5

Determine in which quadrant the product of 5(cos3pi/8 + isin 3pi/8) and sqrt 2(cos pi/12 + sin pi/12) lies.

Mathematics
1 answer:
ohaa [14]2 years ago
6 0
When you multiply two complex numbers given in polar form, the argument of the product is the sum of the arguments of the factors. Meanwhile, the modulus of the product is the product of the moduli of the factors.


In this case, you'd have

\dfrac{3\pi}8+\dfrac\pi{12}=\dfrac{11\pi}{24}

and the modulus would simply be 5\sqrt2. Since

\dfrac{11\pi}{24}

we would expect the final product to fall in the first quadrant.
You might be interested in
When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100
ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the <em>future value FV.</em>  

In order to see the rule of formation, let's see the value (in $) for the first few years

<u>End of year 0</u>

1,000

<u>End of year 1(capital + interest + new deposit)</u>

1,000*(1.09)+10  

<u>End of year 2 (capital + interest + new deposit)</u>

(1,000*(1.09)+10)*1.09 +10 =

\bf 1,000*(1.09)^2+10(1+1.09)

<u>End of year 3 (capital + interest + new deposit)</u>

\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)

and we can see that at the end of year 50, the future value is

\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}

The sum  

\bf 1+1.09+(1.09)^2+...+(1.09)^{49}

is the <em>sum of a geometric sequence </em>with common ratio 1.09 and is equal to

\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356

and the future value is then

\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564

The <em>present value PV</em> is

\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62

rounded to the nearest hundredth.

5 0
3 years ago
A line passes through the point (2, 10) and has a y-intercept of 4. What is the equation of the line? Help me please
joja [24]

Step-by-step explanation:

If it's a straight line the use formula

y = mx + c

m= gradient of line

c = y-intercept

we know that y-intercept is 4 so coordinate is

(0,4)

Equation also passes (2,10)

Use both coordinate to find gradient

m= vertical distance / horizontal distance

= (10-4) / (2-0)

= 3

y = 3x + 4

6 0
2 years ago
dennis ran a mile in 593.7 seconds.martina ran a mile in 573.36 seconds. what was the difference in their running times? A-5.14
Svetlanka [38]

subtract them

593.7-573.36 = 20.34seconds

 so c is the answer


8 0
3 years ago
Read 2 more answers
How to write x^2 + y^2 - 2x + 2y = 7 in standard form​
kodGreya [7K]

Answer:

7 is its standared form

Step-by-step explanation:

3 0
3 years ago
I need help on 13. Please someone help me. Don’t put a link. Please help me.
Viktor [21]

Answer and Step-by-step explanation:

How to know if the side lengths can form a triangle:

Add together two of the lowest numbers. If it is greater than the largest number, it can form a triangle.

13. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9.

-- 9 is greater than 7, the largest length.

14. No, these side lengths can't form a triangle.

-- 2 + 3 = 6

-- 6 is equal to 6, not greater than.

15. Yes, these side lengths can form a triangle.

-- 2 + 4 = 6

-- 6 is greater than 5, the largest number.

16. Yes, these side lengths can form a triangle.

-- Don't get confused when you see that there are two side lengths that are the same (it means that this is an isosceles triangle); the rules still apply.

-- 2 + 8 = 10

-- 10 is greater than 8, the largest number.

17. Yes, these side lengths can form a triangle.

-- 5 + 6 = 11

-- 11 is greater than 9, the largest number.

18. Yes, these side lengths can form a triangle.

-- 4 + 5 = 9

-- 9 is greater than 8, the largest number.

<em><u>I hope this helps!!</u></em>

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

5 0
2 years ago
Other questions:
  • baker has 3 1/2 bags of flour. each bag holds 5 1/3 pounds of flour . how many pounds of flour does the baker have in all.
    9·2 answers
  • How do you write the following linear equations in standard form ?
    7·1 answer
  • I need help on how to do combinations
    10·1 answer
  • How do I solve this, I can't figure it out and it's my Home work
    14·1 answer
  • 7. The value of a computer has a decay factor of 0.85 per year. After 2 years, the computer is worth $1445. What was the origina
    14·2 answers
  • The graph shows the amount of money Tanya earns from tutoring compared with the number of hours she works. Select the correct st
    15·2 answers
  • Please HELP me!! Will choose brainliest (:
    13·1 answer
  • If Nike is having a 30% off sale, and you want a pair of Jordan's that originally cost $100, what is the sale price?​
    12·2 answers
  • What is the solution to the inequality 7x + 2 &lt; 3x + 1?
    14·1 answer
  • Plz help me
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!