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2 years ago

Uhhhh last question lol I have to match them

Mathematics

2 answers:

harkovskaia [24]2 years ago

6 0

5-35n
-6x-24
15m-30
24p-28
5b-5
5x+45
Hope this is helpful:D

Anarel [89]2 years ago

4 0

Answer:

7. is 5 - 35n

8. is -6x - 24

9. is 15m - 30

10. is 24p - 28

11. is 5b - 5

12. 5x + 45

RULE:

WHEN MULTIPLYING TWO NEGATIVES YOU WILL GET POSITIVE.

IF ONE IS NEGATIVE AND THE OTHER IS POSITIVE WHEN MULTIPLYING IT WILL BE NEGATIVE.

WHEN MULTIPLYING TWO POSITIVE NUMBERS IT WILL ALWAYS BE POSITIVE

SAME THING IF YOU MULTIPLY A POSITIVE NUMBER WITH A NEGATIVE NUMBER YOU GET A NEGATIVE AS YOUR ANSWER

YOU NEED ONE SIGN OF THE SAME WHEN MULTIPLYING TO BE A POSITIVE AS YOUR ANSWER

YOU NEED ONE SIGN TO BE DIFFERENT FROM THE OTHER WHEN MULTIPLYING TO GET A NEGATIVE AS YOUR ANSWER

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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:

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

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