Can anyone solve the problem on the picture?

a = 70°

b = 55°

c = 40°

Answer:

321

Good Luck!!

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Explanation:

We use De Moivre's Theorem. It says that if you started with

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

then raising both sides to the nth power leads to

[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]

The term out front r is raised to the nth power. We also have copies of n inside the trig functions.

The square root operation undoes the squaring operation, so we'll be dealing with n = 2.

If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.

[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]

Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.

The complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number in the trigonometric form:

Z = √(3[cosπ/2 + i sinπ/2])

It is required to find the square root of the complex number.

To find the square root of the complex number we can use the De Moivre's theorem:

If

Z = r[cosθ + i sinθ]

Zⁿ = rⁿ[cosnθ + i sinnθ]

Using the above theorem:

Z =  √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]

Z =  √3[cosπ/4 + i sinπ/4]

Thus, the complex number Z =  √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.

Learn more about the complex number here:

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Answer:

24

Step-by-step explanation:

Answer:

the equation is y=x^2+8

Answer:

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]   or  10.42 = h

Step-by-step explanation:

The area of a trapezoid is [tex]A = \frac{1}{2}h(b_{1} + b_{2} )[/tex].

[tex]200 = \frac{1}{2}h(10\sqrt{2} + 14\sqrt{3})[/tex]

[tex]400 = { h(10\sqrt{2} + 14\sqrt{3} )[/tex]             Multiply both sides by 2

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]

 [tex]\frac{400}{38.39} = h[/tex]

10.42 = h  

Answer:

non so cosa intendi per intero

Step-by-step explanation:

Può essere più preciso?

Answer:

the line is perpendicular to what line you didn't mention that

Step-by-step explanation:

Answer:  52 boys

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Explanation:

g = number of girls

g+26 = number of boys because there are 26 more compared to girls

The ratio of boys to girls is 2:1, meaning g+26 is twice as large compared to g

number of boys = 2*(number of girls)

g+26 = 2g

26 = 2g-g

26 = g

g = 26

There are 26 girls and g+26 = 26+26 = 52 boys. Note how 52 is double that of 26.

Answer:

35

Step-by-step explanation:

210 - 175 = 35

175 - 140 = 35

140 - 105 = 35

105 - 70 = 35

I hope this helps!

Hello There!

The formula for finding the area of a Trapezium is as follows.

A = a + b over 2, h

The first base being = a

The second base being = b

and the height being = h

So to solve plug in the values as described below.

a + b = ab

ab divided by 2

ab- times h

ab-h = Area

I hope I helped!

Brainliest is always appreciated.

Answer:

x = 5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

[tex] \frac{32}{40} \times 100[/tex]

[tex] \frac{32}{4} \times 10[/tex]

[tex]8 \times 10[/tex]

[tex]80[/tex]

80 is the answer

Answer:

(32/40×100%)= x

(32/ 40 ) × 100 = x

0.8 × 100 = x

x = 80

(32/40×100%)= 80

[tex]A = \frac{B r_{1}r_{2}}{ C {x}^{2} } \\ = > A C {x}^{2} = B r_{1}r_{2} \\ = > r_{1} r_{2} = \frac{A C {x} ^{2} }{B} \\ = > r_{1} = \frac{A C {x} ^{2} }{B r_{2}} [/tex]

[tex]r_{1} = \frac{A C {x} ^{2} }{B r_{2}} [/tex]

Hope it helps.

Do comment if you have any query.

Answer:

489,162

Step-by-step explanation:

Hope it can help you lovelots

Answer:

The length, breadth and height of cuboid are 60 cm, 40 cm and 20 cm.

Step-by-step explanation:

Let,

Now, substuting all the given values in the formula to find the value of x.

[tex]\longrightarrow{\sf{V_{(Cuboid)} = l \times b \times h}}[/tex]

[tex]\begin{gathered} \qquad\longrightarrow{\sf{V_{(Cuboid)} = l \times b \times h}}\\\\\qquad\longrightarrow{\sf{48000 = 3x \times 2x \times x}}\\\\\qquad\longrightarrow{\sf{48000 = 3x \times 2{x}^{2}}}\\\\\qquad\longrightarrow{\sf{48000 = 6{x}^{3}}}\\\\\qquad\longrightarrow{\sf{{x}^{3} = \dfrac{48000}{6}}}\\\\\qquad\longrightarrow{\sf{{x}^{3} = 8000}}\\\\\qquad\longrightarrow{\sf{x = \sqrt[3]{8000}}}\\\\\qquad\longrightarrow{\sf{x = 20}}\\\\ \qquad{\star{\underline{\boxed{\sf{\purple{x = 20}}}}}} \end{gathered}[/tex]

Hence, the value of x is 20.

Now, we know the value of x. So, calculating the dimensions of cuboid :

Length = 3x

Breadth = 2x

Height = x

[tex]\rule{300}{2.5}[/tex]

Answer:

$1.129

Step-by-step explanation:

If the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

Recall:

Given the algebraic expressions for the dimension of the rectangular court as:

length = (7x + 8) ft

width = (3x + 6) ft

Area = [tex](7x + 8) \times (3x + 6)[/tex]

[tex]Area =7x(3x + 6) +8(3x + 6)\\\\Area = 21x^2 + 42x + 24x + 48\\\\[/tex]

[tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

Therefore, if the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

Learn more here:

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Answer:

20

Step-by-step explanation:

Given,

The mean of 16, X, 3, 14, 57 is 22.

Therefore,

(16+X+3+14+57)/5 = 22

(16+X+3+14+57) = 110

(90+X) = 110

X = 110-90

X = 20

The value of x will be 20.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mean of set 16, X, 3, 14, 57 is 22.

Now,

Since, The mean of 16, X, 3, 14, 57 is 22.

Hence, By definition of mean we get;

⇒ 16 + X + 3 + 14 + 57 / 5 = 22

Solve for x as;

⇒ 90 + X / 5 = 22

⇒ 90 + X = 22 × 5

⇒ 90 + X = 110

⇒ X = 110 - 90

⇒ X = 20

Thus, The value of x will be 20.

Learn more about the mathematical expression visit:

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Answer:

  (b)  congruent segments

Step-by-step explanation:

One copies the length of a segment to make congruent segments. This is done by setting the compass radius to the length of the segment to be copied, then marking the segment length on another line using a given point as a center.

_____

Additional comment

The appearance here is that the segments are not actually congruent, so apparently a mistake has been made in the construction. No angles are shown, and there aren't enough points or arcs shown to support a conclusion that some other construction is being attempted.

Answer:

B' (3, 1 )

Step-by-step explanation:

Given

A (- 1, 3 ) → A' (- 3, 7 )

x- coordinate goes from - 1 → - 3 , that is - 2

y- coordinate goes from 3 → 7 , that is + 4

Translation rule is (x, y ) → (x - 2, y + 4 ) , then

B (5, - 3 ) → B' (5 - 2, - 3 + 4 ) → B' (3, - 1 )

Answer:

x = 2.7

Step-by-step explanation:

5.4 = 2x

2x = 5.4

Divide both sides by 2.

x = 2.7

Answer: x= 2.7

1. Divide 2 on both sides

2. cancel terms who have the same numerator and denominator

Answer:

First is 1, then 2, then 10

Step-by-step explanation:

I think this is right, could be completely wrong but I did blank times 50 equals 50, that is 1. Repeated with all the problems.

Yes it is possible.

- BRAINLIEST answerer

Step-by-step explanation:

how many cups of water do you need to fill in one jar maths

Answer:

In an hour, Alex can wash 14 windows.

Step-by-step explanation:

10 1/2 windows per 3/4 hour

per usually means a / sign because you are finding the unit rate

10.5/0.75 (I just converted everything into a fraction to make it easier)

solve:

10.5/0.75 = 14

Another way to solve:

10 1/2 / 3/4

= 21/2 * 4/3

= 21*4/2*3

= 84/6

= 14

Check:

If Alex washes 14 windows per hour, you can check by multiplying 14 by 3/4 of an hour

14*3/4

=42/4

=10.5

10.5 is the same as 10 1/2

the awnser 2=2=2=2=22=2=2=2=2=2+0+7867+

Answer:

45

Step-by-step explanation:

-5(-12)+(-15)

--> Multiply -5 and -12 to get 60

60-15

--> Subtract 15 from 60 to get 45

Hope this helps you!

Answer:

i would say either F or G

i guess choose F

Answer:

8

Step-by-step explanation: