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3 years ago

6

What is 20-23 (work does not need to be shown)

1 answer:

lukranit [14]3 years ago

7 0

The answer is -3
Hope this helps :)

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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

100 members of a Gym are surveyed. The results are shown below. Given the gym member chosen at random is a female, what is the p

Lina20 [59]

Answer:

$\frac{17}{28}$

Step-by-step explanation:

There are 56 females

There is 56 females

34 are 20+

34/56 simplfies to 17/28

8 0

3 years ago

3x^2+20x+12<br> pls show work ;-;

RoseWind [281]

Answer:

$3 {x}^{2} + 20x + 12 \\ 3 {x}^{2} + 18x + 2x + 12 \\ 3x(x + 6) + 2(x + 6) \\( 3x + 2)(x + 6)$

5 0

2 years ago

Four people enter their names into a drawing. The winner receives one of two different prizes that are randomly selected. The tr

galina1969 [7]

A) (-4,2π/3)
b) (4,4π/3)
c) (-2,π/3)
d) (2,5π/3)

7 0

3 years ago

Can anyone help me solve this.I need proper equation..Thanks

artcher [175]

Answer:

y = 9 $\sqrt{2}$

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = $\frac{1}{\sqrt{2} }$

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{9}{y}$

Multiply both sides by y

y × sin45° = 9, that is

y × $\frac{1}{\sqrt{2} }$ = 9

Multiply both sides by $\sqrt{2}$

y = 9 $\sqrt{2}$

3 0

4 years ago

Read 2 more answers