Paladin

Hi, i can't seem to solve this problem no matter what i do!

The vector (imagine this is in component form),

(a - b, b) is parallel to the x axis and the vector ( a + b, 2a - b) is parallel to (2, 1). Find the values of "a" and "b".

Thanks in advance :)

I'm really not sure on how to solve this one?

Find all the values of x in the interval [0, pi] which satisfy the equation cos(2x) = sin^2(x)

So far i've tried doing this:

cos(2x) = sin^2(x)

cos(2x) = 1 - cos^2(x)

cos^2(x) + cos(2x) - 1 = 0

Now that we have a quadratic equation we apply the discriminant formula

D = b^2 - 4ac

D = 1 - 4(1)(-1)

D = 1+ 4

D = 5

so

x1 = (1 + sqrt(5)) / (2)

x2 = (1 - sqrt(5)) / (2)

Is the process correct so far? And what do i do next?

The polynomial x^2 - 4x + 3 is a factor of x^3+(a-4)x^2 + (3-4a)x + 3. Calculate what a is.

I just can't seem to solve it, i want to see the whole process of solving it.

Thank you in advance. :)

I just can't seem to solve this problem, so far i've done this:

Find the equation of a circle with the centre on the x-axis. The circles passes through points (2,2) & (-4,-4)

Since it's centre is on the x axis, the y coordinate of the center is 0.

Let's name the points A and B:

A(2, 2)

B(-4, -4)

So for A:

q=0 therefore,

(2-p)^2+(2-0)^2 = r^2

4 - 4p +p^2 + 4 = r^2

p^2 - 4p + 8 = r^2

And for B:

(-4-p)^2+(-4-0)^2 = r^2

16 + 8p + p^2 +16 = r^2

p^2 + 8p + 32 = r^2

Now since both of these points can be found on the circle, we know that the radii are the same, so we can equal them.

p^2 - 4p + 8 = p^2 + 8p + 32

p^2 + 8p + 32 - p^2 + 4p - 8 = 0

12p = -24

p = -2

So

p = -2

q = 0

Therefore the equation of the circle is

(x + 2)^2 + y^2 = r^2

Now the thing i don't get is: how do you get the radius?

Consider the equation (1+2k)x^2 - 10x + k - 2 = 0

k € R

Find the set of values of k for which the equation has real roots.

For what values of k is the straight line y = kx + 1 a tangent to the circle with the origin at (5, 1) and a radius of 3 (r = 3)?

I'm just not sure how to approach this problem.

I'm not really sure how to answer

|x+1| + |x-1| = 3

thing is, it's easy when you have one absolute value, but i get confused when I see two. I'd just like the answer and a brief process.

thanks!

A surveying team are trying to find the height of a hill. They take a sight on top of the hill and find that the angle of elevation is 23º27'. They move a distance of 250m on level ground directly away from the base of the hill and take a second sight. From this point, the angle of elevation is 19º46'. Draw a diagram to represent the situation and find the height of the hill to the nearest metre.

Spare the diagram, but how would I solve this?