What is the center and radius of the circle? * x^2+ y^2+ 4y + 4 = 36
1 answer:
Answer:
(0, - 2 ), r = 6
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Rearrange the given equation collecting the terms in y together, that is
x² + y² + 4y + 4 = 36 ( subtract 4 from both sides )
x² + y² + 4y = 32
Use the method of completing the square on the y- terms
add ( half the coefficient of the y- term)² to both sides
x² + y² + 2(2)y + 4 = 32 + 4
x² + (y + 2)² = 36 ← in standard form
with (h, k ) = (0, - 2 ) and r² = 36, thus
centre = (0, - 2 ) and r = = 6
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Answer:
Q-12 The vertical length of the top part of elevator to ground is 0.8484 meters .
Q -14 The glide runway path is 24,752.47 feet .
Step-by-step explanation:
Q - 12
Given as :
The diagonal length of the elevator = e = 1.2 meters
The vertical length of the top part of elevator to ground = x meters
The angle made by elevator with ground = Ф = 45°
<u>Now, According to figure</u>
Sin angle =
Or, Sin Ф =
Or, Sin 45° =
Or, 0.707 × 1.2 meters = x
∴ x = 0.8484 meters
So, The vertical length of the top part of elevator to ground = x = 0.8484 meters
Hence,The vertical length of the top part of elevator to ground is 0.8484 meters . Answer
Q-14
Given as:
The altitude of decent of plane = H = 10,000 feet
The angle of descend = Ф = 22°
Let the glide runway path = y feet
<u>Now, According to question</u>
Tan angle =
Or, Tan Ф =
Or, Tan 22° =
Or, 0.4040 =
Or, y =
∴ y = 24,752.47
So,The glide runway path = y = 24,752.47 feet
Hence, The glide runway path is 24,752.47 feet . Answer