MATHEMATICS HIGH SCHOOL

Which of the following is a solution of z^5 = 1 + √3 i? 5√2 (cos150° + isin150°)
5√2 (cos156° + isin156°)
5√2 (cos174° + isin174°)
5√2 (cos204° + isin204°)

Please show me how to work it out.

Answers

Answer 1
Answer:

Answer:

Option 2 is right

Step-by-step explanation:

Given that

z^5=1+√(3) i

We can write this in polar form with modulus and radius

|z^5|= √(1+3) =2\ntan of Angle t =√(3) \n

Hence angle = 60 degrees and

|z^5|= 2(cos60+isin60)

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360

Using Demoivre theorem we get 5th root would be

5th root of 2 multiplied by 1/5 th of 60, 420, 780,....

z= \sqrt[5]{2} (cos12+isin12)\nz=\sqrt[5]{2} (cos84+isin84)\n\nz=\sqrt[5]{2} (cos156+isin156)\n\nz=\sqrt[5]{2} (cos228+isin228)\n\nz=\sqrt[5]{2} (cos300+isin300)\n

Out of these only 2nd option suits our answer

Hence answer is Option 2.

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BD bisects ABC. m ABD=2y m DBC=5y-12. What is ABC?

Answers

Answer:

  16

Step-by-step explanation:

The two angle created by the bisector have equal measures, so ...

  m∠ABD = m∠DBC

  2y = 5y -12

  0 = 3y -12

  0 = y -4

  4 = y

  2y = 2·4 = 8

m∠ABC = 2×m∠ABD = 2×8

m∠ABC = 16

_____

We presume the angle measures are in degrees, though that is not specified by the problem given here. These numbers could all be radians, but 16 radians is more than a couple of times around the circle.

Simplify the product using the distributive property. (-4h +2)(3h +7)

Answers

Answer: -12h^2-22h+14

Step-by-step explanation:

According to distributive property under multiplication over addition

We can write a.(b+c)=a.b+a.c

Since, The given expression, (-4h+2)(3h+7)

By applying distribution in first bracket.

we can write, (-4h+2)(3h+7)= -4h(3h+7)+2(3h+7)

Again on applying distribution property,

we get, (-4h+2)(3h+7)= -4h×3h+(-4h)×7+2×3h+2×7

⇒ (-4h+2)(3h+7)= -12h^2-28h+6h+14 = -12h^2-22h+14
-2(2h - 1)(3h + 7)
(-2(2h) - 2(-1))(3h + 7)
(-4h + 2)(3h + 7)
-4h(3h + 7) + 2(3h + 7)
-4h(3h) - 4h(7) + 2(3h) + 2(7)
-12h² - 28h + 6h + 14
-12h² - 22h + 14

PLEASE HELP. A playground is shaped like a rectangle with a width 5 times its length (l). What is a simplified expression for the distance between opposite corners of the playground?

Answers

Look at the picture.

Use the Pythagorean Teorem:
l^2+(5l)^2=d^2\nl^2+5^2l^2=d^2\nd^2=l^2+25l^2\nd^2=26l^2\nd=√(26)^2\nd=√(26)\cdot√(l^2)\n\boxed{d=l√(26)}

A garden has 2500 trees. Out of which, 15 percent are Orange trees, 30 percent are mango trees, and the rest are lemon trees. Find the number of each variety of tree. a) Orange trees: 375, Mango trees: 750, Lemon trees: 1375 b) Orange trees: 400, Mango trees: 800, Lemon trees: 1300 c) Orange trees: 450, Mango trees: 900, Lemon trees: 1150 d) Orange trees: 500, Mango trees: 1000, Lemon trees: 1000

Answers

the answer is A. :)))

What is a polynomial with 4 terms called?

Answers

it is called Polynomial ;)
hope this helps ;)
It's called a "polynomial of the 3rd order". This because the  order of the power in this function:
f(x) = 3x³  + 2x² - 6x + 7

is three (notice the ³ there).

How many solutions does the equation 3x + 6 = − 1 − 3 + 4x have?Two
Zero
One
Infinitely many

Answers

Answer:

The number of solutions of the equation is:

                                    One.

Step-by-step explanation:

We are asked to find the number of solutions of the equation:

3x+6= -1-3+4x

(

We know that a expression has a unique or one solution if it gives a single value of x after solving the expression.

and we obtain a no solution when the equation gives a false result i.e. the left and right hand side of equality are different.

and infinite many solution if the left and right hand side of equality is same but we can't get a fix value of x )

Now on solving the expression we have:

                     3x+6= -4+4x

i.e.                 4x-3x=6+4

i.e.                      x=10  

Hence, we get a unique value of x.

Hence, the equation has one solution.
it has One solution and to get it solve the equation for x :
6+1+3=4x-3x
x=10
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