Answer:
y = (x/(1-x))√(1-x²)
Step-by-step explanation:
The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
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r = sec(θ) -2cos(θ)
r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)
r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²
(x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations
x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor
y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)
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The attached graph shows the equivalence of the polar and rectangular forms.
Answer:
1. y = 9(x+1/2)^2 -13/4
Step-by-step explanation:
y = 9x^2 + 9x – 1
first isolate the x terms
y = 9(x^2 +x) -1
then add 1/4 inside the brackets to make it a perfect square trinomial (half of the coefficient of the x term squared is how we get 1/4)
since we just added 1/4 we need to subtract what we just added to balance the equation. so 1/4 times 9 is 9/4 ( the number we just added to the equation). then you subtract 9/4 outside of the brackets.
y = 9(x^2 +x +1/4) -1 -9/4
then simplify
y = 9(x+1/2)^2 -13/4
Answer:
statement
the sum of two adjacent angle of a triangle is 180° . prove that sides are parallel.
Answer:
5s⁷/6
s⁵
3r⁴s⁵
-r⁴s⁶
-6rs⁵
4r/5⁶ can't be the first term.
We start with the highest degree term
Answer:
x = 3
Step-by-step explanation:
The smaller triangle and larger one are similar, so corresponding sides are proportional.
8/4 = (8 +(x -1))/5
10 = x +7 . . . . . . . . . multiply by 5 and simplify
3 = x . . . . . . . . . subtract 7
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<em>Alternate solution</em>
The short segments are also proportional:
(x -1)/(5 -4) = 8/4
x -1 = 2 . . . . simplify
x = 3 . . . . . . add 1
