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WINSTONCH [101]
3 years ago
13

There is a circular park of radius 15 meters. Three friends Lillian, William, and Jacob are sitting at equal distance on its bou

ndary each having a toy telephone (connected using strings) in their hands to talk to each other. Find the length of the string between the pair of the telephones.

Mathematics
1 answer:
marissa [1.9K]3 years ago
7 0

Answer:

15√3 meters ≈ 26 meters

Step-by-step explanation:

The three boys are sitting at equal distances on the circle, so they form an equilateral triangle.

Draw one line cutting the triangle in half, and another line from one corner to the center of the circle.  These two lines form a large 30-60-90 triangle on one side, and a smaller 30-60-90 triangle on the other side.

The hypotenuse of the smaller triangle is the radius of the circle, so the short leg is equal to 7.5 meters.  That means the height of the equilateral triangle is 15 meters + 7.5 meters = 22.5 meters.

To find the side length of the equilateral triangle, we can either find the hypotenuse of the larger 30-60-90 triangle, or double the long leg of the smaller 30-60-90 triangle.  Either way, it's 15√3 meters.

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Vera_Pavlovna [14]
6 be cause 8 times 6 equals 48
7 0
3 years ago
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A 12- pack of 8- ounce juice boxes costs $5.90. How much would an 18- pack of the same 8- ounce juice boxes cost?
stira [4]

Answer:

$8.85

Step-by-step explanation:

This a question of direct variation, so we can make out a relationship between the two factors. 12 is 2/3 of 18, so the cost of 12 would also be 2/3 of the cost of 18. We can now make an equation to solve.

\frac{2}{3} x=5.9\\2x=17.7\\x=8.85

6 0
3 years ago
Use the inequality 18 &lt; -3(4x - 2)<br> Solve the inequality for x. <br> Show your work.
IrinaVladis [17]

Answer:

x > -1

Step-by-step explanation:

Simplify the inequality using the distributive property (multiply the term outside the bracket with each number inside the bracket). Then, isolate 'x' by performing the reverse operations for every number that's on the same side as 'x'. (Reverse operations 'cancel out' a number.)

18 < -3(4x - 2)           Expand this to simplify

18 < (-3)(4x) - (-3)(2)             Multiply -3 with 4x and -2

18 < -12x + 6               Start isolating 'x'

18 - 6 < -12x + 6 - 6                 Subtract 6 from both sides

18 - 6 < -12x                  '+ 6' is cancelled out on the right side

12 < -12x                    Subtracted 6 from 18 on the left side

12/-12 < -12x/-12                    Divide both sides by -12

12/-12 < x                    'x' is isolated. Simplify left side

-1 < x                    Answer

x > -1             Standard formatting puts variable on the left side

6 0
3 years ago
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.

3 0
3 years ago
I need to know the answer
Anni [7]
The answer is (x+3)(x+5).
7 0
2 years ago
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