Answer: (y-3)^2= 52(x+7)
The focus is (-10, -7) and the directrix is x=16. The y-coordinate of the vertex should be same as the focus(k=-7). Then the x-coordinate of the vertex would be:
p + (-10)= 16 - p
2p= 16 + 10
p=26/2= 13
The x-coordinate of the vertex would be:
h= p+ (-10)
h= 13 - 10= 3
The vertex coordinate would be: (h, k)= (3, -7)
For a vertex (h, k), the formula for equation would be
(y-k)^2=4 p(x-h)
(y-3)^2= 4*13(x--7)
(y-3)^2= 52(x+7)
(x-h)^2 + (y-k)^2 = r^2
r=3
(x-h)^2 + (y-k)^2 = 3^2
the center lies on the y-axis --> h=0
x^2 + (y-k)^2 = 3^2 = 9
expand
x^2 + y^2 -2ky + k^2 = 9
x^2 + y^2 -2ky + (k^2 - 9) = 0
compare to general form
A=1 , B=1 and C =0
D= -2k and E=k^2 - 9
Answer:
25.9 years
Step-by-step explanation:
The half life of an isotope is related to the actual amounts by the equation:
N = Ni*(1/2)^(t/HL)
where N and Ni are the final and initial (Ni) amounts, t is the time (in years for this problem) and HL is the half-life, in years.
In this problem, we can write:
100 = 360*(1/2)^(x/14)
I'll reduce this to:
1 = 3.6*(1/2)^(x/14)
This can be solved by taking the log of both sides.
x = 25.87 or 25.9 years
Answer:
64 + 64sqrt(3)
174.9 cm²
Step-by-step explanation:
AD/2 = 8cos(60) = 4
AD = 8 cm
Height of each triangle = 8sin(60)
= 4sqrt(3)
sqrt: square root
Area = 8² + 4(½ × 8 × 4sqrt(3))
= 64 + 64sqrt(3) cm²
= 174.8512517 cm²
Answer:
x=39
Step-by-step explanation:
I can explain later but I know you have a time limit right now.
