Answer:
centre = (- 12, 9), radius = 5
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
Given
x² + y² + 24x - 18y + 200 = 0
Collect the terms in x/ y together and subtract 200 from both sides
x² + 24x + y² - 18y = - 200
Using the method of completing the square
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(12)x + 144 + y² + 2(- 9)y + 81 = - 200 + 144 + 81
(x + 12)² + (y - 9)² = 25 ← in standard form
with centre (- 12, 9) and r = = 5
Answer:
11984.18 dollars
Step-by-step explanation:
Given that an amount of 5700 dollars is invested at 11.2% p.a. for seven years compounded.
We have compound interest formula for Principal P for n years at r% compounded annually is
Final amount =
Final amount for 5700 dollars at 11.2% p.a. for 7 years would be
11984.18 dollars.
Answer is 11984.18 dollars
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Explanation:
The remainder theorem says that if we divide some polynomial p(x) over (x-k), then p(k) is the remainder.
The expression x+1 is the same as x-(-1). Comparing this to x-k shows k = -1.
So we'll need to evaluate p(-1)
To do so visually, draw a vertical line through -1 on the x axis. Make sure this vertical line crosses the blue curve at some point, which I'll call point A.
From point A, draw a horizontal line to the y axis. You should reach y = 3.
This is all shown in the diagram below.
In other words, the point (-1,3) is on the blue curve, and p(-1) = 3.
So the remainder is 3.
