p. If q is prime and 3Q ^ 2 + 5p = 517, then p + q =?

p. If q is prime and 3Q ^ 2 + 5p = 517, then p + q =?

fifteen
p=13
q=2

As shown in the figure, it is known that ∠ a = 60 ° and P and Q are the moving points on both sides of ∠ A. (1) when AP = 1 and AQ = 3, calculate the length of PQ; (2) the sum of the lengths of AP and AQ is the fixed value 4, and calculate the minimum PQ of the line segment

(1) ∵) ∠ a = 60 °, AP = 1, AQ = 3, ｜ from cosine theorem: pq2 = pa2 + aq2-2ap · aqcos 60 ° = 1 + 9-2 × 1 × 3 × 12 = 7, ｜ PQ = 7; (2) let AP = x, then AQ = 4-x, (0 ＜ x ＜ 4), from cosine theorem: pq2 = pa2 + aq2-2ap · aqcos 60 ° = x2 + (4-x) 2-2x (4-x)

Given p (x1, Y1), q (X2, Y2), find the coordinates of vector PQ and QP

PQ (x2-x1, y2-y1), QP (x1-x2, y1-y2); it is the definition of coordinate vector, subtract the starting point coordinate from the end point coordinate

If there are two moving points PQ, e (3,0) on the ellipse x2 / 36 + Y2 / 9 = 1 and EP is perpendicular to EQ, what is the minimum value of QP multiplied by EP?
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EP * QP = EP * (QE + EP) = EP & # 178;, then the minimum length of EP is obtained. Let P (6cos θ, 3sin θ) (parametric equation) then EP & # 178; = (6cos θ - 3) & # 178; + (3sin θ - 0) & # 178; = 27cos & # 178; θ - 36cos θ + 18 be regarded as a quadratic function, then the minimum length is obtained when cos θ = 36 / (2 * 27) = 2 / 3