Given end points of diameter,
(x1,y1)=(-3,-4)
(x2,y2)=(0,0)
Now,
the equation of circle is,
(x-x1)(x-x2)+(y-y1)(y-y2)=0
or, (x+3)(x-0)+(y+4)(y-0)=0
or, x^2 +3x +y^2 +4y =0
or, x^2 +y^2 +3x + 4y=0
which is in the form of x^2 +y^2 +2gx +2fy + c=0
where,
g=3/2
h=2
c=0
Now,
Refer to the diagram shown below.
When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)
Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)
From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.
From (1) and (2), obtain
225a + k = 15
2025a + k = 6
Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft
Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125
A graph of the solution verifies that the solution is correct.
<em>《</em><em>°</em><em>♡</em><em> </em><em>i think that the answer to this question is -5 1/3</em><em> </em><em>(</em><em>-16</em><em>/</em><em>3</em><em>)</em><em> </em><em>hope this helps!</em><em> </em><em>♡</em><em>°</em><em>》</em>
Answer:
Step-by-step explanation:
We need only identify the x- and y-coordinates of the point of intersection of these two graphs. That point is (-4, 2).
Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.
They can form a triangle.
Now if c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if
, the triangle is right
- if
, the triangle is acute
- if
, the triangle is obtuse
The triangle is obtuse.
The answer is D.
