Consider the system of quadratic equations \begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*}where $c$ is a real number. (a) For what value(s) of $c$ will the system have exactly one solution $(x, y)?$ (b) For what value(s) of $c$ will the system have more than one real solution? (c) For what value(s) of $c$ will the system have no real solutions? Solutions to the quadratics are $(x, y)$ pairs. Your answers will be in terms of $c,$ but make sure you address both $x$ and $y$ for each part.

Hello, we need to solve this system, c being a real number.

y=y, right? So, it comes.

We can compute the discriminant.

If the discriminant is 0, there is 1 solution.

It means for

And the solution is

If the discriminant is > 0, there are 2 real solutions.

It means 4(4-c) > 0 <=> 4-c > 0 <=>

And the solution are

If the discriminant is < 0, there are no real solutions.

It means 4(4-c) < 0 <=> 4-c < 0 <=>

There are no real solutions and the complex solutions are

Thank you.

28

step-by-step explanation:

8+8+6+6

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this