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AVprozaik [17]
3 years ago
9

Write -3r+3u in polar form PLEASE HELP

Mathematics
1 answer:
tamaranim1 [39]3 years ago
6 0
We have that
<span> -3r+3u
</span>
Step 1
<span>Use the distance formula to find the radius
</span><span>r = √(x^2 + y^2)
 (x,y)----------> (</span>-3,3)
r= √(-3^2 + 3^2)=√18=3√2

Step 2
Use the tangent to find the angle  
θ = arctan(y/x)  
θ = arcTan(3/-3)= -45°-------> II Quadrant
then 
θ=180-45=135°

Step 3 
write in polar form
(x,y)------------> (r, θ)
so
(-3,3)----------> (3√2, 135°)

the answer is (3√2, 135°)
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<em><u>Solution:</u></em>

<em><u>Given the system of equations are:</u></em>

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We have to find the solution to above system of equations

<em><u>We can solve the system by substitution method</u></em>

From eqn 1,

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A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle and; the other will be bent to
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Let us assume the circumference of the circle  = k cm

So, the circumference of the square  = ( 40 - k) cm

Now,as circumference of circle = 2πR

⇒2πR = k cm    or, R  = (\frac{k}{2\pi})

Area  of the  circle = πR²  

or, A  = \pi (\frac{k}{2\pi} )^2  

 = \pi \times (\frac{k^2}{(2\pi)^2} )  = \frac{k^2}{4 \pi} \\\implies A =  \frac{k^2}{4 \pi}   ....... (1)

Similarly , perimeter of square  = 4 x Side

⇒ 4 x Side  =  ( 40 - k) cm    ⇒ S = (\frac{40 - k}{4} )

Area  of the  square = (Side)²    = (\frac{40 - k}{4} ) ^2

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So, combining (1) and (2), total area A is

A = (\frac{k^2}{4 \pi} ) + \frac{k^2 + 1600 - 80 k }{16}

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⇒ k = 17.6 inches

So, the perimeter of circle  = 17.6 cm

Perimeter of square  = (40 - 17.6 )  = 22.4 cm

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3 years ago
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