Question and Answers Forum

AllQuestion and Answers: Page 1507

Question Number 60155 Answers: 1 Comments: 0

Show that: (1/2) + cos(x) + cos(2x) + ... + cos(nx) = ((sin(n + (1/2))x)/(2 sin((1/2))x)) By principle of mathematical induction

$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{2x}\right)\:+\:...\:+\:\mathrm{cos}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{sin}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}} \\ $$$$\mathrm{By}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$

Question Number 60143 Answers: 1 Comments: 0

Two passenger trains, A and B, 450km apart, start to move towards each other at the same time and meet after 2 hours. If train B, travels (8/7) as fast as train A, find the speed of each train.

$$\mathrm{Two}\:\mathrm{passenger}\:\mathrm{trains},\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\:\mathrm{450km}\:\mathrm{apart}, \\ $$$$\mathrm{start}\:\mathrm{to}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{and}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{train}\:\mathrm{B}, \\ $$$$\mathrm{travels}\:\frac{\mathrm{8}}{\mathrm{7}}\:\mathrm{as}\:\mathrm{fast}\:\mathrm{as}\:\mathrm{train}\:\mathrm{A},\:\mathrm{find}\:\mathrm{the}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{train}. \\ $$

Question Number 60135 Answers: 1 Comments: 0

Question Number 60133 Answers: 2 Comments: 1

Question Number 60132 Answers: 0 Comments: 1

Question Number 60121 Answers: 2 Comments: 3

Question Number 60115 Answers: 0 Comments: 2

Question Number 60095 Answers: 1 Comments: 1

Question Number 60088 Answers: 1 Comments: 1

Question Number 60085 Answers: 1 Comments: 4

Question Number 60058 Answers: 1 Comments: 1

Question Number 60056 Answers: 1 Comments: 1

Question Number 60054 Answers: 1 Comments: 1

Question Number 60053 Answers: 0 Comments: 0

Question Number 60052 Answers: 0 Comments: 0

Question Number 60050 Answers: 1 Comments: 1

calculate ∫_0 ^1 (x^3 −2)(√(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$

Question Number 60045 Answers: 1 Comments: 2

Question Number 60043 Answers: 2 Comments: 0

Show that in a 30°−60°−90° triangle the altitude on the hypotaneuse divides the hypotaneuse into segments whose length has the ratio 1/3. without using trigonometry.

$${Show}\:{that}\:{in}\:{a}\:\mathrm{30}°−\mathrm{60}°−\mathrm{90}°\:{triangle}\:{the}\: \\ $$$${altitude}\:{on}\:{the}\:{hypotaneuse}\:{divides}\:{the}\: \\ $$$${hypotaneuse}\:{into}\:{segments}\:{whose}\:{length} \\ $$$${has}\:{the}\:{ratio}\:\mathrm{1}/\mathrm{3}. \\ $$$${without}\:{using}\:{trigonometry}. \\ $$

Question Number 60039 Answers: 2 Comments: 3

find all solutions for z∈C z^i =(1/2)−(1/2)i z^(1−i) =1+i

$$\mathrm{find}\:\mathrm{all}\:\mathrm{solutions}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$${z}^{\mathrm{i}} =\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{i} \\ $$$${z}^{\mathrm{1}−\mathrm{i}} =\mathrm{1}+\mathrm{i} \\ $$

Question Number 60036 Answers: 1 Comments: 0

Question Number 60027 Answers: 1 Comments: 0

∫x^i dx=?

$$\int{x}^{{i}} {dx}=? \\ $$

Question Number 60025 Answers: 0 Comments: 0

Question Number 60022 Answers: 0 Comments: 0

construct M^′ z^′ =(1/2)(((z+∣z∣)/3))

$${construct}\:{M}^{'} \:{z}^{'} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{z}+\mid{z}\mid}{\mathrm{3}}\right) \\ $$

Question Number 60021 Answers: 1 Comments: 0

Question Number 60016 Answers: 1 Comments: 0

A car dealar made a profit of 22.5% by selling a car for 58000 cedis. Find correct to two decimal places the percentage profit if the car had been sold for 61,200 cedis.

$$\mathrm{A}\:\mathrm{car}\:\mathrm{dealar}\:\mathrm{made}\:\mathrm{a}\:\mathrm{profit}\:\mathrm{of}\:\mathrm{22}.\mathrm{5\%} \\ $$$$\mathrm{by}\:\mathrm{selling}\:\mathrm{a}\:\mathrm{car}\:\mathrm{for}\:\mathrm{58000}\:\mathrm{cedis}.\:\mathrm{Find}\: \\ $$$$\mathrm{correct}\:\mathrm{to}\:\mathrm{two}\:\mathrm{decimal}\:\mathrm{places}\:\mathrm{the}\: \\ $$$$\mathrm{percentage}\:\mathrm{profit}\:\mathrm{if}\:\mathrm{the}\:\mathrm{car}\:\mathrm{had}\:\mathrm{been}\: \\ $$$$\mathrm{sold}\:\mathrm{for}\:\mathrm{61},\mathrm{200}\:\mathrm{cedis}.\: \\ $$

Question Number 60015 Answers: 0 Comments: 0

Pg 1502 Pg 1503 Pg 1504 Pg 1505 Pg 1506 Pg 1507 Pg 1508 Pg 1509 Pg 1510 Pg 1511

Contact: info@tinkutara.com