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3 years ago

3x−4y=21 what does the x and y mean?

Mathematics

1 answer:

neonofarm [45]3 years ago

6 0

Answer:

They are the two variables in the equation. They could will have different or the same values, but are seperate mathematical and logical entities.

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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

Find x so the distance between ( x , 4 ) and ( 3 x + 1 , − 4 ) is 10

Sonja [21]

Answer:

3456

Step-by-step explanation:

3 0

3 years ago

What is the volume of this cube? Enter your answer as a decimal in the box. m³ Cube with a side length of 0.5 meters.

ch4aika [34]

volume = S^3

volume = 0.5^3 = 0.125 m^3

6 0

4 years ago

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I need help plz I don’t know how to do this

Anika [276]

Answer:

x = 4

Step-by-step explanation:

x = 4 is where the parabola can be cut in half and reflected

5 0

3 years ago

Pi/24 is the solution for 4cos2 (4x) - 3 = 0 True or false

inessss [21]

Answer:

True.

Step-by-step explanation:

Given,

4cos2 (4x) - 3 = 0

Now, 4π/24 = π/6

Or, cos π/6 = √3/2

Or, cos^2 π/6 = 3/4

Or, 4 cos^2 π/6 = 3

Now, Left Hand Side= 4cos2 (4x) - 3

= 3-3 =0 = Right Hand Side (Proved)

Here, Left Hand Side= Right Hanad Side. So, 4cos2 (4x) - 3=0 is true.

5 0

3 years ago

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