Question and Answers Forum

AllQuestion and Answers: Page 1881

Question Number 13658 Answers: 1 Comments: 0

Prove that cos^2 x + cos^2 3x + cos^2 5x + ... to n terms = (1/2)[n + ((sin4nx)/(2sin2x))]

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} \mathrm{3}{x}\:+\:\mathrm{cos}^{\mathrm{2}} \mathrm{5}{x}\:+\:...\:\mathrm{to}\:{n}\:\mathrm{terms} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left[{n}\:+\:\frac{\mathrm{sin4}{nx}}{\mathrm{2sin2}{x}}\right] \\ $$

Question Number 13654 Answers: 1 Comments: 0

The sum of the series sinθ + sin(((n − 4)/(n − 2)))θ + sin(((n − 6)/(n − 2)))θ + ... n terms is equal to (1) sin(((nθ)/(2 − n))) (2) cos(((2nθ)/(2 − n))) (3) tannθ (4) cotnθ

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{sin}\theta\:+\:\mathrm{sin}\left(\frac{{n}\:−\:\mathrm{4}}{{n}\:−\:\mathrm{2}}\right)\theta\:+\:\mathrm{sin}\left(\frac{{n}\:−\:\mathrm{6}}{{n}\:−\:\mathrm{2}}\right)\theta\:+\:...\:{n}\:\mathrm{terms} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}\left(\frac{{n}\theta}{\mathrm{2}\:−\:{n}}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{cos}\left(\frac{\mathrm{2}{n}\theta}{\mathrm{2}\:−\:{n}}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{tan}{n}\theta \\ $$$$\left(\mathrm{4}\right)\:\mathrm{cot}{n}\theta \\ $$

Question Number 13649 Answers: 1 Comments: 0

2xyy′+(x−1)y^2 =x^2 e^x

$$\mathrm{2}{xyy}'+\left({x}−\mathrm{1}\right){y}^{\mathrm{2}} ={x}^{\mathrm{2}} {e}^{{x}} \\ $$

Question Number 13647 Answers: 0 Comments: 6

x^2 +y^2 =5.....(1) 3x^2 +xy+y^2 =1.....(2) please help find x and y

$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{5}.....\left(\mathrm{1}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} =\mathrm{1}.....\left(\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

Question Number 13645 Answers: 0 Comments: 0

please is factor theorem and error and trial the same? please help cause i think theres a difference but i cant explain it. Thankz.

$$\mathrm{please}\:\mathrm{is}\:\mathrm{factor}\:\mathrm{theorem}\:\mathrm{and}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{trial}\:\mathrm{the}\:\mathrm{same}?\:\mathrm{please}\:\mathrm{help}\: \\ $$$$\mathrm{cause}\:\mathrm{i}\:\mathrm{think}\:\mathrm{theres}\:\mathrm{a}\:\mathrm{difference} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{cant}\:\mathrm{explain}\:\mathrm{it}. \\ $$$$ \\ $$$$\mathrm{Thankz}. \\ $$

Question Number 13636 Answers: 1 Comments: 0

A steam envine of efficiency 70% burns 20g of coal to produce 10kJ of energy.If it burns 200g of coal per second,calculate its output power.

$$\mathrm{A}\:\mathrm{steam}\:\mathrm{envine}\:\mathrm{of}\:\mathrm{efficiency}\:\mathrm{70\%} \\ $$$$\mathrm{burns}\:\mathrm{20g}\:\mathrm{of}\:\mathrm{coal}\:\mathrm{to}\:\mathrm{produce}\:\mathrm{10kJ} \\ $$$$\mathrm{of}\:\mathrm{energy}.\mathrm{If}\:\mathrm{it}\:\mathrm{burns}\:\mathrm{200g}\:\mathrm{of}\:\mathrm{coal}\: \\ $$$$\mathrm{per}\:\mathrm{second},\mathrm{calculate}\:\mathrm{its}\:\mathrm{output} \\ $$$$\mathrm{power}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 13627 Answers: 1 Comments: 0

Question Number 13626 Answers: 1 Comments: 0

Prove that cosech^(−1) (x) = sinh^(−1) ((1/x))

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cosech}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{sinh}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$

Question Number 13609 Answers: 1 Comments: 0

Question Number 13608 Answers: 0 Comments: 2

if distance is given by x(t)=2t+5 then ,the acceleration at 4s is............

$$\mathrm{if}\:\mathrm{distance}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{x}\left(\mathrm{t}\right)=\mathrm{2t}+\mathrm{5}\:\mathrm{then}\:,\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{at}\:\mathrm{4s}\:\mathrm{is}............ \\ $$

Question Number 13606 Answers: 1 Comments: 0

Show that 19^(93) − 13^(99) is a positive integer divisible by 162.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{19}^{\mathrm{93}} \:−\:\mathrm{13}^{\mathrm{99}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{162}. \\ $$

Question Number 13732 Answers: 1 Comments: 3

Sum the following: tan x+2tan 2x+2^2 tan 2^2 x+...+2^n tan 2^n x

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{following}: \\ $$$$\mathrm{tan}\:{x}+\mathrm{2tan}\:\mathrm{2}{x}+\mathrm{2}^{\mathrm{2}} \mathrm{tan}\:\mathrm{2}^{\mathrm{2}} {x}+...+\mathrm{2}^{{n}} \mathrm{tan}\:\mathrm{2}^{{n}} {x} \\ $$

Question Number 13601 Answers: 1 Comments: 0

Let f : R − {(3/5)} → R be defined by f(x) = ((3x + 2)/(5x − 3)) . Then, (a) f^(−1) (x) = x (b) f^(−1) (x) = −f(x) (c) fof(x) = −x (d) f^(−1) (x) = (1/(19))f(x)

$$\mathrm{Let}\:{f}\::\:\mathbb{R}\:−\:\left\{\frac{\mathrm{3}}{\mathrm{5}}\right\}\:\rightarrow\:\mathbb{R}\:\mathrm{be}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{3}{x}\:+\:\mathrm{2}}{\mathrm{5}{x}\:−\:\mathrm{3}}\:.\:\mathrm{Then}, \\ $$$$\left(\mathrm{a}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:{x} \\ $$$$\left(\mathrm{b}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:−{f}\left({x}\right) \\ $$$$\left(\mathrm{c}\right)\:{fof}\left({x}\right)\:=\:−{x} \\ $$$$\left(\mathrm{d}\right)\:{f}^{−\mathrm{1}} \left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{19}}{f}\left({x}\right) \\ $$

Question Number 13622 Answers: 1 Comments: 0

Evaluate: ∫_0 ^(2π) e^(x/2) sin ((x/2) + (π/4))dx

$$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{\frac{{x}}{\mathrm{2}}} \mathrm{sin}\:\left(\frac{{x}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right){dx} \\ $$

Question Number 13623 Answers: 1 Comments: 0

Evaluate: ∫_0 ^(2π) e^x cos ((π/4) + (x/2))dx

$$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{{x}} \:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}\:+\:\frac{{x}}{\mathrm{2}}\right){dx} \\ $$

Question Number 13598 Answers: 0 Comments: 1

If g(x) = x^2 + x − 2 and (1/2) gof(x) = 2x^2 − 5x + 2, then prove that f(x) = 2x − 3.

$$\mathrm{If}\:{g}\left({x}\right)\:=\:{x}^{\mathrm{2}} \:+\:{x}\:−\:\mathrm{2}\:\mathrm{and} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:{gof}\left({x}\right)\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{2},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{3}. \\ $$

Question Number 13595 Answers: 1 Comments: 0

If f : R → (−1, 1) is defined by f(x) = ((−x∣x∣)/(1 + x^2 )) , then prove that f^(−1) (x) = −sgn(x)(√((∣x∣)/(1 − ∣x∣)))

$$\mathrm{If}\:{f}\::\:\mathbb{R}\:\rightarrow\:\left(−\mathrm{1},\:\mathrm{1}\right)\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\:\frac{−{x}\mid{x}\mid}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:,\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)\:=\:−\mathrm{sgn}\left({x}\right)\sqrt{\frac{\mid{x}\mid}{\mathrm{1}\:−\:\mid{x}\mid}} \\ $$

Question Number 13591 Answers: 1 Comments: 1

for: x^2 +(y−1)^2 =1 show that it can be written as: r=2sin(θ)

$$\mathrm{for}: \\ $$$${x}^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{it}\:\mathrm{can}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}: \\ $$$${r}=\mathrm{2sin}\left(\theta\right) \\ $$

Question Number 13584 Answers: 2 Comments: 10

Calculate 19^(93) (mod 81).

$$\mathrm{Calculate}\:\mathrm{19}^{\mathrm{93}} \:\left(\mathrm{mod}\:\mathrm{81}\right). \\ $$

Question Number 13570 Answers: 1 Comments: 0

A motor boat going downstream overcomes a float at a point A. 60 minutes later it turns and after some time passes the float at a distance of 12 km from the point A. Find the velocity of the stream (assuming constant velocity for the boat in still water)

$$\mathrm{A}\:\mathrm{motor}\:\mathrm{boat}\:\mathrm{going}\:\mathrm{downstream} \\ $$$$\mathrm{overcomes}\:\mathrm{a}\:\mathrm{float}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:{A}.\:\mathrm{60}\:\mathrm{minutes} \\ $$$$\mathrm{later}\:\mathrm{it}\:\mathrm{turns}\:\mathrm{and}\:\mathrm{after}\:\mathrm{some}\:\mathrm{time}\:\mathrm{passes} \\ $$$$\mathrm{the}\:\mathrm{float}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{12}\:\mathrm{km}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{point}\:{A}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{stream} \\ $$$$\left(\mathrm{assuming}\:\mathrm{constant}\:\mathrm{velocity}\:\mathrm{for}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{boat}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}\right) \\ $$

Question Number 13563 Answers: 1 Comments: 3

Question Number 13544 Answers: 0 Comments: 6

Question Number 13529 Answers: 0 Comments: 7

Let p be a prime number > 3. What is the remainder when p^2 is divided by 12?

$$\mathrm{Let}\:{p}\:\mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:>\:\mathrm{3}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:{p}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\mathrm{12}? \\ $$

Question Number 13578 Answers: 4 Comments: 0

Question Number 13514 Answers: 1 Comments: 21

From Developer We are planning an update to this app in next 4−6 weeks. Please provide your input on problems/suggestion for improvement on this app. You can give feedback as a comment to this post or email us at infoattinkutara.com.

$$\mathrm{From}\:\mathrm{Developer} \\ $$$$\mathrm{We}\:\mathrm{are}\:\mathrm{planning}\:\mathrm{an}\:\mathrm{update}\:\mathrm{to} \\ $$$$\mathrm{this}\:\mathrm{app}\:\mathrm{in}\:\mathrm{next}\:\mathrm{4}−\mathrm{6}\:\mathrm{weeks}. \\ $$$$\mathrm{Please}\:\mathrm{provide}\:\mathrm{your}\:\mathrm{input}\:\mathrm{on} \\ $$$$\mathrm{problems}/\mathrm{suggestion}\:\mathrm{for}\: \\ $$$$\mathrm{improvement}\:\mathrm{on}\:\mathrm{this}\:\mathrm{app}. \\ $$$$\mathrm{You}\:\mathrm{can}\:\mathrm{give}\:\mathrm{feedback}\:\mathrm{as}\:\mathrm{a}\:\mathrm{comment} \\ $$$$\mathrm{to}\:\mathrm{this}\:\mathrm{post}\:\mathrm{or}\:\mathrm{email}\:\mathrm{us}\:\mathrm{at} \\ $$$$\mathrm{infoattinkutara}.\mathrm{com}. \\ $$

Question Number 13508 Answers: 1 Comments: 0

5!! = ? please workings, how is the answer 15

$$\mathrm{5}!!\:=\:? \\ $$$$\mathrm{please}\:\mathrm{workings},\:\mathrm{how}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{15} \\ $$

Pg 1876 Pg 1877 Pg 1878 Pg 1879 Pg 1880 Pg 1881 Pg 1882 Pg 1883 Pg 1884 Pg 1885

Contact: info@tinkutara.com