Zadanie 1c
Find the common difference.
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Znaleziono 1343 zadania
Find the common difference.
Find the chord length AB.
Find the area of the major sector between OA and OB.
On the same axes, sketch (i) C₁ and (ii) C₂ in the window −2≤x≤5,−5≤y≤5. Mark their intersections with the coordinate axes.
(i) State the coordinates of C₂’s two inflection points. (ii) Identify two features that distinguish C₁ from C₂.
Vary the positive integer b in y2 = (x − 1)3 + b. Suggest two features shared by every curve in this family.
Now restrict y2 = (x − 1)3 − 4(x − 1) to its right component x≥3. (i) Show that for x>3, . (ii) Hence explain why neither open branch x>3 has a local maximum or minimum.
Now restrict y2 = (x − 1)3 − 4(x − 1) to its right component x≥3. The two inflection points on this right component share an x-coordinate. Find that coordinate in exact radical form.
A rational point has two rational coordinates. On C : y2 = x3 − 3x + 4, let P=(0,2). The tangent at P meets C again at Q; let S=(0,−2). (i) Find the tangent equation at P. (ii) Hence find Q, expressing its coordinates as fractions.
A rational point has two rational coordinates. On C : y2 = x3 − 3x + 4, let P=(0,2). The tangent at P meets C again at Q; let S=(0,−2). Use the tangent construction to determine Q, then find the third intersection of the full straight line through Q and S with C.