Answer:
For x(θ) = 3cosθ + 2
y² = [9x²/(x - 2)²] - x²
For x(θ) = 3cosθ + 2
x² = [4y²/(y - 1)²] - y²
Step-by-step explanation:
Given the following equivalence:
x² + y² = r²
r = √(x² + y²)
x = rcosθ
cosθ = x/r
y = rsinθ
sinθ = y/r
Applying these to the given equations,
x(θ) = 3cosθ + 2
x = 3(x/r) + 2
xr = 3x + 2r
(x - 2)r = 3x
r = 3x/(x - 2)
Square both sides
r² = 9x²/(x - 2)²
(x - 2)²r² = 9x²
(x - 2)²(x² + y²) = 9x²
(x² + y²) = 9x²/(x - 2)²
y² = [9x²/(x - 2)²] - x²
y(θ) = 2sinθ - 1
y = 2y/r - 1
yr = 2y - r
(y - 1)r = 2y
r = 2y/(y - 1)
Square both sides
r² = 4y²/(y - 1)²
x² + y² = 4y²/(y - 1)²
x² = [4y²/(y - 1)²] - y²
Answer:
Step-by-step explanation:
step 1
Find the circumference
The circumference of a circle is equal to
we have
assume
substitute
step 2
Find the measure in radians for the central angle of a circle whose radius is 5 and intercepted arc length is 7.2 units
Remember that
The circumference of 
subtends a central angle of 
so
using proportion
Let
x-----> the central angle in radians
8( 7x - 1) +4(x + 5) = 56x - 8 + 4x +20
56x - 8 + 4x + 20 = 60x + 12
Answer = 60x + 12
Answer:
smaller number = 17, larger number = 34
Step-by-step explanation:
Let x be the smaller number and y be the larger nuber
x + y = 51 --(1)
y - 17 = x --(2)
Sub (2) into (1)
y - 17 + y = 51
y = 34
Put y = 34 into (2)
34 - 17 = x
x = 17
Ans: smaller number = 17, larger number = 34
