Question and Answers Forum

AlgebraQuestion and Answers: Page 356

Question Number 12889 Answers: 2 Comments: 1

f(x−1)=(2/3)+f(x) f(0)=36−f(21) ⇒f(0)=?

$${f}\left({x}−\mathrm{1}\right)=\frac{\mathrm{2}}{\mathrm{3}}+{f}\left({x}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{36}−{f}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{f}\left(\mathrm{0}\right)=? \\ $$

Question Number 12885 Answers: 1 Comments: 0

f(f(x))=f^2 (x) What is a solution?

$${f}\left({f}\left({x}\right)\right)={f}^{\mathrm{2}} \left({x}\right) \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}? \\ $$

Question Number 12883 Answers: 1 Comments: 0

for −128≤x≤127 and −127≤y≤128 where x,y∈Z Point P(x,y) is a point on the cartesian plane. From the origin, angle θ is made counter −clockwise with the positive x−axis. (1) How many unique angles θ exist if x,y∈P? (2) Furthermore, how many unique angles θ exist for the full range of x,y∈Z?

$$\mathrm{for}\:\:\:\:\:−\mathrm{128}\leqslant{x}\leqslant\mathrm{127} \\ $$$$\mathrm{and}\:\:\:−\mathrm{127}\leqslant{y}\leqslant\mathrm{128} \\ $$$$\mathrm{where}\:\:\:{x},{y}\in\mathbb{Z} \\ $$$$\: \\ $$$$\mathrm{Point}\:{P}\left({x},{y}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{cartesian}\:\mathrm{plane}. \\ $$$$\: \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{angle}\:\theta\:\mathrm{is}\:\mathrm{made}\:\mathrm{counter} \\ $$$$−\mathrm{clockwise}\:\mathrm{with}\:\mathrm{the}\:\mathrm{positive}\:{x}−\mathrm{axis}. \\ $$$$\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{unique}\:\mathrm{angles}\:\theta\:\mathrm{exist} \\ $$$$\mathrm{if}\:{x},{y}\in\mathbb{P}? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Furthermore},\:\mathrm{how}\:\mathrm{many}\:\mathrm{unique} \\ $$$$\mathrm{angles}\:\theta\:\mathrm{exist}\:\mathrm{for}\:\mathrm{the}\:\mathrm{full}\:\mathrm{range}\:\mathrm{of}\:{x},{y}\in\mathbb{Z}? \\ $$

Question Number 12797 Answers: 1 Comments: 2

1 + x + x^2 + ... x^(49) = (1/2)(x^(49) − (1/x)) Find the value of x

$$\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:...\:\mathrm{x}^{\mathrm{49}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{x}^{\mathrm{49}} \:−\:\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 12763 Answers: 0 Comments: 0

Solve simultaneously 2x + y − z = 8 ........... equation (i) x^2 − y^2 + 2z^2 = 14 .......... equation (ii) 3x^3 + 4y^3 + z^3 = 195 ........... equation (iii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{2x}\:+\:\mathrm{y}\:−\:\mathrm{z}\:=\:\mathrm{8}\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:..........\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{iii}\right) \\ $$

Question Number 12698 Answers: 0 Comments: 0

Given A^((−1)) = [((0.5 3)),((4 2)) ] find (A^2 )

$$\mathrm{Given}\:\:\:\mathrm{A}^{\left(−\mathrm{1}\right)} =\begin{bmatrix}{\mathrm{0}.\mathrm{5}\:\:\:\:\:\:\mathrm{3}}\\{\mathrm{4}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{bmatrix} \\ $$$$\mathrm{find}\:\left(\mathrm{A}^{\mathrm{2}} \right) \\ $$

Question Number 12682 Answers: 1 Comments: 0