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3 years ago

Find the value of b to the shape

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

6 0

Answer:

b=99°

Step-by-step explanation:

108°+72°+81°+b=360°

b=99°

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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

if the probability of picking a green marble from a bag of green and red marbles is 0.3. if i choose a marble 100 times and repl

vfiekz [6]

Answer:

30 marbles would be green

Step-by-step explanation:

green chance is 0.3

red chance 0.7

.3 times 100

30 green marbles is what you would expect

7 0

3 years ago

Express the ratio 7 days to 6 weeks as a decimal fraction

Mashcka [7]

Answer:

0.166

Step-by-step explanation:

We know that,

1 week = 7 days

i.e.

6 week = 7(6) days = 42 days

We need to express ratio 7 days to 6 weeks as a decimal fraction. So,

$R=\dfrac{7\ \text{days}}{42\ \text{days}}=\dfrac{1}{6}\\\\=0.166$

3 0

3 years ago

Which graph represents the following system of inequalities?<br> y<1/4x+4<br> y ≥5x+1

Readme [11.4K]

Answer:

3rd

Step-by-step explanation:

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3 years ago

Show me a order line 3/10,0.5 ,1/5 greater to the least

Svetradugi [14.3K]

1/5 , 3/10 , 0.5
This will help

5 0

3 years ago