Answer Key: Math Exercise 5

1. Find the center and radius of the circle ( x² + y² + 8x - 8y + 23 = 0) on the coordinate plane.
answer: C(-4, 4) r = 3

2. What is the equation of the circle on the coordinate plane with a radius of 4 and its center at (4, -5)?
answer: x² + y² - 8x + 10y + 25 = 0

3. Evaluate: i⁴³⁷⁹
answer: -i

4. Evaluate: (12 + 3i) / (4 – 3i) ; answers: in polar and rectangular forms
answer: 1.56 + 1.92i ; 2.474<50 .91°

5. Two lines: y = 5x - 10 ; y = 2x - 1 intersect each other on a coordinate plane. Find their point of intersection.
answer: (3, 5)

6. Convert to Roman Numerals:
a. 3 456 = MMMCDLVI
b. 543 342 = DXLIII bar CCCXLII
c. 2 043 598 = II (inside doorframe) XLIII bar DXCVIII

7. Convert to Arabic Numerals:
a. XLVI = 46
b. MDCCXLIX = 1749
c. DXXIV = 524

8. Find the area of the circle inscribed in a square if the area of the latter is 49.
answer: 38.48

9. A Sphere with a volume of 36π is inscribed in a Cylinder.
a. Find the Surface Area of the Sphere = 113.1
b. Find the Surface Area of the Cylinder = 169.65
c. Find the Volume of the Cylinder = 169.65
d. Find the height of the Cylinder = 6
e. Find the area of the top of the Cylinder = 28.27


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