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2 years ago

What is the image on segment Oj rotated 270 counterclockwise around point 0?

Mathematics

1 answer:

inysia [295]2 years ago

6 0

Answer:

OL and M

Step-by-step explanation:

(1)

270° ÷ 30° = 9

Count 9 dashed lines from OJ counterclockwise, then

OJ → OL

(2)

120° ÷ 30° = 4

Count 4 dashed lines from R counterclockwise, then

R → M

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The polar coordinates of a point are 3π 4 and 7.00 m. What are its Cartesian coordinates (in m)? (x, y) = 6.06,−3.5 m

Keith_Richards [23]

Answer:

a) $\left(x,y\right)=\left(4.95,-4.95\right)$

b) $r\angle\theta = 7\angle0.5236\,\text{radians}$

Step-by-step explanation:

Polar coordinates are represented as: $r\angle\theta$ , where 'r' is the length (or magnitude) of the line, and ' $\theta$ ' is the angle measured from the positive x-axis.

in our case:

$7\angle\dfrac{3\pi}{4}$

to covert the polar to cartesian:

$x = r\cos{\theta}$

$y = r\sin{\theta}$

we can plug in our values:

$x = 7\cos{\dfrac{3\pi}{4}} = -7\dfrac{\sqrt{2}}{2}$

$y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}$

the Cartesian coordinates are:

$\left(x,y\right)=\left(-7\dfrac{\sqrt{2}}{2},7\dfrac{\sqrt{2}}{2}\right)$

$\left(x,y\right)=\left(4.95,-4.95\right)$

(b) to convert (x,y) = (6.06,-3.5)

we'll use the pythagoras theorem to find 'r'

$r^2 = x^2+y^2$

$r^2 = (6.06)^2+(-3.5)^2$

$r = \sqrt{48.97} \approx 7$

the angle can be found by:

$\tan{\theta} = \dfrac{y}{x}$

$\tan{\theta} = \dfrac{3.5}{6.06}$

$\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}$

$\theta = 0.5236 \text{radians}$

to convert radians to degrees:

$\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ$

writing in polar coordinates:

$r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}$

5 0

3 years ago

Explain the systematic trial method for solving equations

adoni [48]

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.

8 0

3 years ago

If the 6th term of an A.p is 11and its first term is 1 find the common diferent

hram777 [196]

Answer:

$thank \: you$

4 0

2 years ago

Read 2 more answers

I need help asap please

Step2247 [10]

Answer:

Angle A: 30°

Angle B: 60°

Angle C: 90°

Step-by-step explanation:

Hopefully this helps! :)

8 0

2 years ago

01. Se tienen los angulos consecutivos AOB, BOC y COD. se cumple m& AOC=125° m

Citrus2011 [14]

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°.

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.

<h3>Cómo analizar tres ángulos consecutivos</h3>

Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.

De acuerdo con el enunciado, tenemos las siguientes condiciones:

∠AOB + ∠BOC = 125° (1)

∠BOC + ∠COD = 100° (2)

Por (1) y (2) tenemos las siguiente identidad:

∠AOB - 25° = ∠COD

∠AOB - ∠COD = 25°

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°. $\blacksquare$

En el segundo caso, tenemos el siguiente sistema:

∠AOB = ∠BOC + ∠COD (3)

∠AOB + ∠BOC - ∠COD = 40° (4)

Por (3) y (4) tenemos la siguiente identidad:

2 · ∠BOC = 40°

∠BOC = 20°

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°. $\blacksquare$

Para aprender más sobre ángulos, invitamos cordialmente a ver esta pregunta verificada: brainly.com/question/21209282

8 0

1 year ago