Graph the circle x2 + y2 + 10x + 6y + 18 = 0.
2 answers:
Answer:
see below for a graph
Step-by-step explanation:
Completing the square for x and y terms can help you put this in the standard form.
(x^2 +10x) +(y^2 +6y) = -18
(x^2 +10x +25) +(y^2 +6x +9) = -18 +25 +9 . . . . add square of half linear coefficient
(x +5)^2 +(y +3)^2 = 16 . . . . . . . circle centered at (-5, -3) with radius 4
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9514 1404 393
Answer:
671 feet
Step-by-step explanation:
There are a couple of ways to figure this. One is to use a sort of shortcut equation to find the distance traveled (d) by an object when subject to some initial velocity (v) and acceleration (a). Here the acceleration due to gravity is -32 ft/s².
v² = 2ad
d = v²/(2a) = (192 ft/s)^2/(2·32 ft/s²) = 576 ft
This height is in addition to the starting height of 95 ft, so the arrow's maximum height is ...
max height = 95 ft + 576 ft = 671 ft
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Another way to work this problem is to start with the equation for ballistic motion. Filling in the given initial velocity and height, we have ...
h(t) = -16t^2 +192t +95
The time the arrow reaches the maximum height is the time representing the axis of symmetry of the parabola:
t = -(192)/(2(-16)) = 6
Then the maximum height is ...
h(6) = -16·6^2 +192·6 +95 = 671
The maximum height is 671 feet.
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<em>Additional comment</em>
For the standard-form quadratic ...
y = ax^2 +bx +c
The axis of symmetry is ...
x = -b/(2a)
