Advanced Math
posted by Brittney Hoang .
A circle of center (3 , 2) passes through the points (0 , 6) and (a , 0). Find a.
The triangle bounded by the lines y = 0, y = 2x and y = 0.5x + k, with k positive, is equal to 80 square units. Find k.
When the polynomial P(x) = x3 + 3x2 2Ax + 3, where A is a constant, is divided by x2 + 1 we get a remainder equal to 5x. Find A.
And would like to see work that can justify the answer. Thank you!

Hints:
(a)
find the radius r which corresponds to the distance between (3,2) and (0,6). Then
(3a)^2+(20)^2 = r^2
(b)
y=0 is horizontal (1)
y=2x (2) is a line through the origin sloping upwards
y=0.5x+k (3) is a line sloping downwards with xintercept: 0.5x+k=0, or x=2k.
You'll need to find the intercept between lines (2) and (3) and determine the height of the triangle.
(3)
This means that (x^2+1) divides P(x)5x, or
P(x)5x = (x^2+1)(x+3)=
=x^3+3*x^2+x+3
Therefore
P(x)=x^3+3*x^2+x+3 + 5x
=x^3+3*x^2+6x+3
=> A=3
Respond to this Question
Similar Questions

Advanced Math
Write the standard form of the equation of a circle that passes through the points at (0,8) (8,0) and (16,8). Then identify the center and radius of the circle. (x8)^2 + (y8)^2 = 64 (x^2 / 64) + (y^2 / 64) = 64 center=(8,8) radius=8 … 
Math
Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle. 
math_precalc
Find the equation of a circle that passes through the points (6,3) ans (4,3) and whose center lies on the line y=2x7 
Math 101
Find the equation for each of the following items below: a. A line that passes through (6,26) and has a slope of 3. b. A line that passes though the points (5,5) and (10,20) c. A line that passes through (9,25) and has a slope of 3. … 
Advanced Math
write the equation of the circle that satisfies each set of conditions. the center of the circle is on the xaxis, its radius is 1, and it passes through the point (square root of 2 over 2, square root of two over 2) 
MATH!!!!
A triangle with side lengths 26, 28, and 30 is constructed so that the longest and shortest sides are tangent to a circle. the third side passes through the center of the circle. compute the radius of the circle. I DON'T KNOW HOW TO … 
Algebra II
Find the radius and center of the circle which passes through the points (2,3), (0,3), (4,3). 
math
can u help this the qustion is : A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y3=0.Find (i) the equation of the circle and it parametric equations . (ii) the centre,diameter and area of the circle … 
Equations of a Circle
Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle. I have r=8, center=(8,8). What now? 
Math (urgent)
the equation x^2+y^=25 describes a circle with center at the origin and radius 5. The line y=x1 passes through the circle. Using the substitution method, find the points at which the circle and line intersect. a) (4,3) and (4,3) …