2.the radius of the circle=a*tan30=a/3
Then the diameter of the square=2a/3
area=(2a/3 sin45)^2=a^2/9
For #4 I think you mean
#4: x=pi/8 or 3pi/8
]]>Solve for x and y in terms of m to understand how x and y behave when m varies:
After a lot of algebraic thrashing and some trial and error:
These values of m satisfy the constraints x>0 and y>0
]]>10. Let -1 ≤ p ≤ 1. Show that the equation 4x[sup]3[/sup] - 3x - p = 0 has a unique root in the interval [½, 1] and identify it.
]]>6. If a, b, c are the three sides of a triangle and C = 60°, prove that
7. If a>0, b>0, and c>0, prove that
8.Find the equations of straight lines passing through (-2, -7) and having an interept of length 3 between the striaght lines
4x+3y = 12 and 4x+3y = 3.
2. A circle is inscribed in an equilateral triangle of side a. Find the area of the square inscribed in this circle.
3. Find the general value of θ satisfying the equation
tan[sup]2[/sup]θ + sec2θ = 1.
4. Solve the equation
sin x - 3sin 2x + sin 3x = cos x - 3cos 2x + cos 3x.