Question and Answers Forum

AllQuestion and Answers: Page 1906

Question Number 15555 Answers: 1 Comments: 0

Prove that ((cos 8x − cos 7x)/(1 + 2 cos 5x)) = cos 3x − cos 2x

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{cos}\:\mathrm{8}{x}\:−\:\mathrm{cos}\:\mathrm{7}{x}}{\mathrm{1}\:+\:\mathrm{2}\:\mathrm{cos}\:\mathrm{5}{x}}\:=\:\mathrm{cos}\:\mathrm{3}{x}\:−\:\mathrm{cos}\:\mathrm{2}{x} \\ $$

Question Number 15543 Answers: 2 Comments: 0

Q#13724 Reposted. E_ ^ xpansion of 1000! has 24 0′s at the end. Find the first non- zero digit from right. 1000!=....d0000...0 What is the the value of d?

$$\mathrm{Q}#\mathrm{13724}\:\mathcal{R}{eposted}. \\ $$$$\mathcal{E}_{\:} ^{\:} \mathrm{xpansion}\:\mathrm{of}\:\mathrm{1000}! \\ $$$$\mathrm{has}\:\mathrm{24}\:\:\mathrm{0}'\mathrm{s}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{non}-\:\mathrm{zero}\:\mathrm{digit}\: \\ $$$$\mathrm{from}\:\mathrm{right}. \\ $$$$\mathrm{1000}!=....\mathrm{d0000}...\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{d}? \\ $$$$ \\ $$

Question Number 15541 Answers: 0 Comments: 1

If θ lies in the first quadrant which of the following is not true?

$$\mathrm{If}\:\theta\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{not}\:\mathrm{true}? \\ $$

Question Number 15539 Answers: 0 Comments: 0

Question Number 15538 Answers: 0 Comments: 0

Question Number 15534 Answers: 1 Comments: 1

Question Number 15504 Answers: 1 Comments: 3

Solve ⌈x^2 ⌉=(⌊x⌋)^2 +2x

$$\mathrm{Solve}\:\lceil{x}^{\mathrm{2}} \rceil=\left(\lfloor{x}\rfloor\right)^{\mathrm{2}} +\mathrm{2}{x} \\ $$

Question Number 15501 Answers: 1 Comments: 0

Solve x^3 −⌊x⌋=3

$$\mathrm{Solve} \\ $$$${x}^{\mathrm{3}} −\lfloor{x}\rfloor=\mathrm{3} \\ $$

Question Number 15497 Answers: 1 Comments: 5

P=Σ_(n∈P) ^∞ n Q=Σ_(n∉P) ^∞ n P=2+3+5+7+... Q=1+4+6+8+... Is P>Q? Is Q>P?

$${P}=\underset{{n}\in\mathbb{P}} {\overset{\infty} {\sum}}{n}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Q}=\underset{{n}\notin\mathbb{P}} {\overset{\infty} {\sum}}{n} \\ $$$${P}=\mathrm{2}+\mathrm{3}+\mathrm{5}+\mathrm{7}+... \\ $$$${Q}=\mathrm{1}+\mathrm{4}+\mathrm{6}+\mathrm{8}+... \\ $$$$\: \\ $$$$\mathrm{Is}\:{P}>{Q}?\:\:\:\mathrm{Is}\:{Q}>{P}? \\ $$

Question Number 15495 Answers: 0 Comments: 2

Question Number 15485 Answers: 1 Comments: 0

Question Number 15480 Answers: 1 Comments: 1

Question Number 15471 Answers: 1 Comments: 0

Question Number 15470 Answers: 0 Comments: 0

Question Number 15474 Answers: 0 Comments: 0

Question Number 15473 Answers: 0 Comments: 0

Question Number 16613 Answers: 1 Comments: 2

Question Number 15463 Answers: 1 Comments: 0

Find the domain and range of a function for which f(x)=((1+2x)/x).

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{a}\:{function}\:{for}\:{which}\:{f}\left({x}\right)=\frac{\mathrm{1}+\mathrm{2}{x}}{{x}}. \\ $$

Question Number 15452 Answers: 1 Comments: 0

Question Number 15448 Answers: 0 Comments: 2

A vector A^→ of magnitude A is turned through an angle θ. Calculate the change in the magnitude of vector.

$$\mathrm{A}\:\mathrm{vector}\:\overset{\rightarrow} {{A}}\:\mathrm{of}\:\mathrm{magnitude}\:{A}\:\mathrm{is}\:\mathrm{turned} \\ $$$$\mathrm{through}\:\mathrm{an}\:\mathrm{angle}\:\theta.\:\mathrm{Calculate}\:\mathrm{the} \\ $$$$\mathrm{change}\:\mathrm{in}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{vector}. \\ $$

Question Number 15440 Answers: 3 Comments: 9

Question Number 15434 Answers: 1 Comments: 8

Question Number 15407 Answers: 1 Comments: 0

A ball is thrown vertically upward with velocity 20 m/s from a rail road car moving with a velocity 5 m/s horizontally. A person standing on the ground observes its motion as projectile. Find maximum height attained by the ball if point of projection is at a height 3 m from the ground.

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upward} \\ $$$$\mathrm{with}\:\mathrm{velocity}\:\mathrm{20}\:\mathrm{m}/\mathrm{s}\:\mathrm{from}\:\mathrm{a}\:\mathrm{rail}\:\mathrm{road} \\ $$$$\mathrm{car}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{5}\:\mathrm{m}/\mathrm{s} \\ $$$$\mathrm{horizontally}.\:\mathrm{A}\:\mathrm{person}\:\mathrm{standing}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{observes}\:\mathrm{its}\:\mathrm{motion}\:\mathrm{as}\:\mathrm{projectile}. \\ $$$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{height}\:\mathrm{attained}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{ball}\:\mathrm{if}\:\mathrm{point}\:\mathrm{of}\:\mathrm{projection}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height} \\ $$$$\mathrm{3}\:\mathrm{m}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 15405 Answers: 1 Comments: 0

A body is projected at time t = 0 from a certain point on a planet surface with a certain velocity at a certain angle with the planet′s surface (assumed horizontal). The horizontal and vertical displacement x and y in metre are related to time as x = 10(√3)t and y = 10t − 4t^2 . Find vertical component of velocity of the particle when it is at a height half of the maximum height attained.

$$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{at}\:\mathrm{time}\:{t}\:=\:\mathrm{0}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{certain}\:\mathrm{point}\:\mathrm{on}\:\mathrm{a}\:\mathrm{planet}\:\mathrm{surface}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{certain}\:\mathrm{velocity}\:\mathrm{at}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{angle} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{planet}'\mathrm{s}\:\mathrm{surface}\:\left(\mathrm{assumed}\right. \\ $$$$\left.\mathrm{horizontal}\right).\:\mathrm{The}\:\mathrm{horizontal}\:\mathrm{and}\:\mathrm{vertical} \\ $$$$\mathrm{displacement}\:{x}\:\mathrm{and}\:{y}\:\mathrm{in}\:\mathrm{metre}\:\mathrm{are} \\ $$$$\mathrm{related}\:\mathrm{to}\:\mathrm{time}\:\mathrm{as}\:{x}\:=\:\mathrm{10}\sqrt{\mathrm{3}}{t}\:\mathrm{and} \\ $$$${y}\:=\:\mathrm{10}{t}\:−\:\mathrm{4}{t}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{vertical}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{height}\:\mathrm{half}\:\mathrm{of}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{height} \\ $$$$\mathrm{attained}. \\ $$

Question Number 15393 Answers: 1 Comments: 0

A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30°, and when he moves up further a distance c metres, the angle of depression of that point is 45°. The angle of inclination of the slope with the horizontal is?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{observes}\:\mathrm{that}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres}\:\mathrm{on}\:\mathrm{a}\:\mathrm{slope},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{from}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{slope}\:\mathrm{is}\:\mathrm{30}°,\:\mathrm{and}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{further}\:\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres},\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{that}\:\mathrm{point}\:\mathrm{is}\:\mathrm{45}°.\:\mathrm{The} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{inclination}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{is}? \\ $$

Question Number 15392 Answers: 1 Comments: 0

Each side of an equilateral triangle subtends angle of 60° at the top of a tower of height h standing at the centre of the triangle. If 2a be the length of the side of the triangle, then (a^2 /h^2 ) = ?

$$\mathrm{Each}\:\mathrm{side}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{subtends}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{tower}\:\mathrm{of}\:\mathrm{height}\:{h}\:\mathrm{standing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{centre} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}.\:\mathrm{If}\:\mathrm{2}{a}\:\mathrm{be}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{then}\:\frac{{a}^{\mathrm{2}} }{{h}^{\mathrm{2}} }\:=\:? \\ $$

Pg 1901 Pg 1902 Pg 1903 Pg 1904 Pg 1905 Pg 1906 Pg 1907 Pg 1908 Pg 1909 Pg 1910

Contact: info@tinkutara.com