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Sergio [31]
3 years ago
10

Find the cartesian equation of r = 8 sin thet + 8 cos theta

Mathematics
1 answer:
Semenov [28]3 years ago
4 0
Use following substitutions: 

<span>r cosθ = x </span>
<span>r sinθ = u </span>
<span>r² = x² + y² </span>

<span>r = 8 cosθ + 4 sinθ </span>

<span>Multiply both sides by r </span>

<span>r² = 8 r cosθ + 4 r sinθ </span>
<span>x² + y² = 8x + 4y </span>

<span>This is equation of circle. We can put in standard form: </span>

<span>x² − 8x + y² − 4y = 0 </span>
<span>x² − 8x + 16 + y² − 4y + 4 = 16 + 4 </span>
<span>(x − 4)² + (y − 2)² = 20 </span>

<span>Circle centered at point (4, 2) with radius = √20</span><span />
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What type of triangle has no sides that are the same ?
Goryan [66]

Answer:

Scalene Triangle

Step-by-step explanation:

A triangle with all different sides is a scalene triangle.

Hope this helps!

Please mark brainliest!

8 0
3 years ago
Read 2 more answers
1. A package contains 7 red candies, 4 blue candies, and 3 green candies. Three candies are drawn
erastovalidia [21]

Answer:

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6 0
3 years ago
Paralell to y=4x-6 through (12,10)
stiks02 [169]

<u>ANSWER</u>

The line that is parallel to y=4x-6 through (12,10) is  y=2x-14.



<u>EXPLANATION</u>


The equation that is parallel to the line y=4x-6 has a slope that is equal to the slope of this line.

By comparing this equation to the general slope intercept form,

y=mx+c,this line has slope m=2.


Hence the line parallel to this line also has slope m=2.

Let y=mx+b be the equation of the line parallel to the line

y=4x-6

We can substitute m=2 to obtain;

y=2x+b


If the line passes through the point (12,10),then this point must satisfy its equation.


We substitute x=12 and y=10 to obtain;


10=2(12)+b


We this equation for b.


\Rightarrow 10=24+b


\Rightarrow 10-24=b


\Rightarrow -14=b


We substitute this value of  b=-14 in to y=2x+b to get;


y=2x+-14.


Hence the equation of the line that is parallel to y=4x-6 through (12,10) is  y=2x-14.




3 0
2 years ago
you have a big bag of 17 marbles for our blue sticks are green 2 are red and the others are yellow what is the probability of dr
Alex Ar [27]

Answer:

  • 3/68

Step-by-step explanation:

<u>Given</u>

  • Total 17 marbles
  • 4 - blue marbles
  • 6 - green marbles
  • 2 - red marbles
  • The rest - yellow marbles

<u>Probability of drawing red first:</u>

  • P(red) = number of red / total number = 2/17

<u>Probability of drawing green second, without replacement:</u>

  • P(green) = number of green / number left in the bag = 6/16 = 3/8

<u>Probability of red and green in order:</u>

  • P = P(red)*P(green) = 2/17*3/8 = 3/68

5 0
3 years ago
What is the answer for 6 1/2 +3 1/4
andriy [413]
First you have to find a common denominator which is 4.
6 2/4 + 3 1/4 = 9 3/4
So your final answer is 9 3/4
Hope this helps!!!!
3 0
3 years ago
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