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4 years ago

Look at the figure below:

Mathematics

2 answers:

xeze [42]4 years ago

8 0

Answer:

You get 80 degrees

Step-by-step explanation:

50 plus 50 gets you 100. 180-100 80

nikdorinn [45]4 years ago

6 0

Answer:

1) angle MPN = angle MNT | Given

2) angle PMN = angle PMN | Common angles

Step-by-step explanation:

Therefore, by the AA theorem of similarity angle PMN = angle NMT

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Use the following image to answer the question:

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Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20%5Csf%20%20%5Clarge%20%5C%3A%20find%20%5C%3A%20%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%20%5C%3A

solong [7]

Given :

$\: \: \:$

$\rm \large \: x = a ( \Theta + Sin \Theta )$

$\: \: \:$

$\rm \large y = a ( 1 - cos \: \Theta )$

$\: \:$

Now , x = a ( θ + sin θ )

 $\: \:$ 

$\: \: \:$

$\rm \large\frac{dx}{dθ } = a \: \frac{d}{dθ} (θ + \sin\theta )$

$\: \:$

$\boxed{ \rm \large\underline{ \frac{dx}{d \theta} = a(1 + \cos \theta ) }}$

$\: \:$

Now y = a ( 1-cosθ)

$\: \:$

Diff w.r.t " θ " we get .

$\: \:$

$\rm \large \frac{dy}{d \theta} = a \frac{d}{d \theta} (1 - cos \theta)$

$\: \: \:$

$\boxed{ \rm \large \underline{ \frac{dy}{d \theta} = a \sin \theta}}$

$\: \: \:$

From eqn ( 1 ) & ( 2 )

$\: \:$

$\rm \large \frac{dy}{dx} = \frac{ \frac{dy}{d \theta} }{\frac{dx}{d \theta}}$

$\: \: \:$

$\: \: \: \rm \large = \frac{ \cancel{a} \: sin \theta}{ \cancel a \: (1 + cos \theta)}$

$\: \:$

$\rm \large \: = \frac{sin \theta}{1 + \cos \theta }$

$\: \: \:$

$\rm \large \: \frac{2 \sin( \frac{\theta }{2} ) cos\frac{\theta }{2} }{2 \: cos ^{2} \frac{\theta }{2}} \: \: ......(sin \: a \: = 2 \: sin \frac{a}{2} \: cos \frac{a}{2} 1 + \: cos \: a \: = 2cos ^{2} \frac{a}{2} )$

$\: \:$

$\rm \large \: \frac{dy}{dx} = \frac{sin \frac{ \theta}{2} }{cos \frac{ \theta}{2} }$

$\: \:$

$\rm \large \: \frac{dy}{dx} = tan \frac{ \theta}{2}$

$\: \:$

$\rm \large \: ( \frac{dy}{dx} ) = tan \frac{ \frac{ \theta}{2} }{2}$

$\: \:$

$\rm \large \: = tan( \frac{ \theta}{4} )$

$\: \:$

$\boxed{ \rm \large \underline{ ( \frac{dy}{dx} ) = \frac{\pi}{2} = 1}}$

$\: \:$

Hope Helps!:)

4 0

2 years ago

According to the graph, what is the value of the constant in the equation

kobusy [5.1K]

Answer:

100

Step-by-step explanation:

x-value is width and y-value is height. Therefore if you multiply the height x width you get the constant.

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3 years ago