Zadanie 1a
Find its 23rd term.
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Znaleziono 1343 zadania
Find its 23rd term.
The sum of its first n terms is zero, where n is a positive integer. Find n.
Find (i) θ; (ii) r.
Find the total shaded area.
(i) Show that the normal to H at x=t has slope −t2/9. (ii) Hence show that its equation is y = −(t2/9)x + t3/9 − 9/t.
(i) Eliminate t to show that every such normal has m<0 and (−m)c2 = 9(m2 − 1)2. (ii) State the set of possible intercepts c.
For which intercepts c is there (i) exactly one distinct normal to H through (0,c); (ii) exactly two distinct normals through (0,c)?
On one pair of axes sketch (i) H; (ii) its two distinct normals passing through (0,1). Mark each point of normal contact. Exact contact coordinates and line equations are not required.
The normal to F at A is y = −t2x + kt3 − k/t. (i) Show that its intersections with F satisfy x2 − k(t − t−3)x − k2/t2 = 0. (ii) Hence, using a sum/product of roots or another valid method, find B.
Prove that angle BCA is a right angle.