Answer:
Step-by-step explanation:
If the diagonals of the rectangle are congruent,
AC = BD
By using formula to calculate the distance between two points,
Distance between two points =
Distance between A(0, -3) and C(2, 8),
AC =
=
=
Similarly, distance between two points B(-4, 0) and D(6, 5),
BD =
=
=
Therefore, both the diagonals are congruent.
Hence, given quadrilateral ABCD is a rectangle.
The standard equation of a circle is:
(x-h)^2+(y-k)^2=r^2, where (h,k) is the center of the circle and r is the radius.
We are given two endpoints of the diameter, so the midpoint of these points is the center of the circle. (2,8) and (2, -4) so the midpoint of the circle is:
((2+2)/2, (8-4)/2)
(2,2)
The radius is just half the length of the diameter. The length of the diameter is 8--4=12 so the radius is 6 units, so our circle equation is:
(x-2)^2+(y-2)^2=36
Answer:
To calculate , calculate the quotient of two consecutive terms.
For all , , so the series converges, as the series grows (even more than) exponentially.
Formula for exponential growth is:
A = P(1+r)^t
Where A is the resulting amount, P is the initial value, r is the rate, and t is the time passed.
Filling this out for this situation gets you:
13400 = 10000(1+r)^6
Solving for r:
Divide 13400 by 10000
1.34 = (1+r)^6
Take the 6th root of both sides...
1 + r = 1.05
No more work is needed, since you aren’t solving for r.
Full equation:
V = 10000(1.05)^t
Answer C is correct
Answer:
6,5×10¹¹/1,3×10⁸= 65/13 ×10³= 5×10³=5000