Let p_2 be the vector space of polynomials of degree at most 2, with coefficients in the real numbers. the following operation defines an inner product on this space (p, q) = p(-) + p(0)(0) + p(1)q(1) use this inner product to find (p, q). ||q||, and the angle between p(x) and q2), for p(q) = -2° + 3x – 3 and qq) = 2x + 3. (p, q) = ||p|= ||q|| = a= (in radians).

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Evaluate 5 + 6 · 2 – 8 ÷ 4 + 7 using the correct order of operations. a. 22 b. 11 c. 27 d. 5

Which expression is equivalent to 64 - 9x^2?