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2 years ago

What is the circumference of this circle

Mathematics

1 answer:

Levart [38]2 years ago

8 0

Answer:

31.4 cm

Step-by-step explanation:

Let C be the circumference and r be the radius of the circle.

$\therefore \: C = 2\pi \: r \\ \hspace{19 pt}= 2 \times 3.14 \times 5 \\ \hspace{19 pt} = 3.14 \times 10 \\ \hspace{19 pt} = 31.4 \: cm \\$

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I NEED HELP AS SOON AS POSSIBLE

Xelga [282]

The answer is D. 200m = 2cm. That's because to get from meters to centimeters, you need to multiply by 100. 200 * 100 is not 2, therefore D is the answer.

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3 years ago

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Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

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2 years ago

Which point could be removed in order to make the relation a function? (–9, –8), (–{(8, 4), (0, –2), (4, 8), (0, 8), (1, 2)}

stepan [7]

We are given order pairs (–9, –8), (–{(8, 4), (0, –2), (4, 8), (0, 8), (1, 2)}.

We need to remove in order to make the relation a function.

Note: A relation is a function only if there is no any duplicate value of x coordinate for different values of y's of the given relation.

In the given order pairs, we can see that (0, –2) and (0, 8) order pairs has same x-coordinate 0.

<h3>So, we need to remove any one (0, –2) or (0, 8) to make the relation a function.</h3>

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2 years ago

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What is the value of x?

Molodets [167]

Answer:

x = 4√5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Trigonometry

Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use Pythagorean Theorem.

a = 19

b = x

c = 21

Step 2: Find x

Substitute: 19² + x² = 21²
Isolate x term: x² = 21² - 19²
Evaluate: x² = 441 - 361
Subtract: x² = 80
Isolate x: x = √80
Simplify: x = 4√5

And we have our final answer!

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3 years ago

Solve the equation: .2x(.7x-5)+0.2=1.4(x-1.6)

Ilia_Sergeevich [38]

9514 1404 393

Answer:

x = 8/7

Step-by-step explanation:

.2(.7x-5)+0.2=1.4(x-1.6) . . . . given

Eliminating parentheses, we have ...

0.14x -1 +0.2 = 1.4x -2.24

1.44 = 1.26x . . . . . . . add 2.24-0.14x to both sides

x = 1.44/1.26 . . . . . . divide by the coefficient of x

x = 8/7 . . . . . . . . . . .simplify the fraction

As a repeating decimal, the value of x is ...

$x=1.\overline{142857}$

However, the notation 1.(142857) is usually reserved for the case where the contents of parentheses are being multiplied by the factor in front. You would need to consult your instructions to see how the decimal version of the answer should be entered. (Quite often, rounding is suggested.)

_____

Additional comment

The equation in the text of your question is different from the one in the picture. We have answered for the one in the picture. The text asks for the solution of a quadratic. Those two solutions are approximately 1.085 and 16.057.

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2 years ago

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What is the circumference of this circle ​

What is the circumference of this circle