Question and Answers Forum

AllQuestion and Answers: Page 12

Question Number 221288 Answers: 1 Comments: 0

Question Number 221271 Answers: 1 Comments: 0

Find the remainder when x^(100) is divided by (x^2 +x+1)

$$\:\:{Find}\:{the}\:{remainder}\:{when}\:{x}^{\mathrm{100}} \: \\ $$$$\:\:{is}\:{divided}\:{by}\:\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right) \\ $$

Question Number 221270 Answers: 1 Comments: 0

p,q∈P Use prime number p,q to find all prime number represented by p^q +q^p

$${p},{q}\in\mathbb{P}\: \\ $$$$\: \\ $$$$\mathrm{Use}\:\mathrm{prime}\:\mathrm{number}\:{p},{q}\:\mathrm{to}\:\mathrm{find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{number}\: \\ $$$$\mathrm{represented}\:\mathrm{by}\:{p}^{{q}} +{q}^{{p}} \\ $$

Question Number 221268 Answers: 1 Comments: 1

Question Number 221264 Answers: 0 Comments: 9

A wooden block and a solid lead ball are placed in a container fully filled with water Now if the lead ball is placed on top of the floating wooden block,what is the change in water level in the container??

$${A}\:{wooden}\:{block}\:{and}\:{a}\:{solid}\:{lead}\:{ball}\:{are}\: \\ $$$${placed}\:{in}\:{a}\:{container}\:{fully}\:{filled}\:{with}\:{water} \\ $$$${Now}\:{if}\:{the}\:{lead}\:{ball}\:{is}\:{placed}\:{on}\:{top}\:{of}\:{the} \\ $$$${floating}\:{wooden}\:{block},{what}\:{is}\:{the}\:{change} \\ $$$${in}\:{water}\:{level}\:{in}\:{the}\:{container}?? \\ $$

Question Number 221262 Answers: 2 Comments: 1

if a, b, c, > 0 , show that; (a^5 /b^2 ) + (b/c) + (c^3 /a^2 ) > 2a

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:{a},\:{b},\:{c},\:>\:\mathrm{0}\:\:,\:\mathrm{show}\:\mathrm{that}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{5}} }{{b}^{\mathrm{2}} }\:+\:\frac{{b}}{{c}}\:+\:\frac{{c}^{\mathrm{3}} }{{a}^{\mathrm{2}} }\:>\:\mathrm{2}{a} \\ $$$$ \\ $$

Question Number 221260 Answers: 1 Comments: 0

Question Number 221256 Answers: 0 Comments: 0

∫∫∫_( [0,1]) ((ln[(1+x)(1+y)(1+z])/(1 + xyz)) dxdydz

$$ \\ $$$$\:\:\int\int\int_{\:\left[\mathrm{0},\mathrm{1}\right]} \:\frac{\mathrm{ln}\left[\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{y}\right)\left(\mathrm{1}+{z}\right]\right.}{\mathrm{1}\:+\:{xyz}}\:{dxdydz}\:\:\:\: \\ $$$$ \\ $$

Question Number 221255 Answers: 1 Comments: 3

Let X be a point inside a square ABCD, such that XA = 10 cm, XB = 6 cm and XC = 14 cm. Find the area of the square.

$$\mathrm{Let}\:\mathrm{X}\:\mathrm{be}\:\mathrm{a}\:\mathrm{point}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{square}\:\mathrm{ABCD},\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{XA}\:=\:\mathrm{10}\:\mathrm{cm},\:\mathrm{XB}\:=\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and} \\ $$$$\mathrm{XC}\:=\:\mathrm{14}\:\mathrm{cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$

Question Number 221254 Answers: 0 Comments: 0

∫∫∫_([0,1]^3 ) (1/((1−xyz)(1−xy)(1−yz)(1−zx))) dxdydz

$$\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \:\frac{\mathrm{1}}{\left(\mathrm{1}−{xyz}\right)\left(\mathrm{1}−{xy}\right)\left(\mathrm{1}−{yz}\right)\left(\mathrm{1}−{zx}\right)}\:{dxdydz}\:\:\:\: \\ $$$$ \\ $$

Question Number 221247 Answers: 1 Comments: 1

Question Number 221245 Answers: 1 Comments: 0

Which is greater ((√7)+1) or ((√3)+(√5))?????

$${Which}\:{is}\:{greater}\:\:\:\:\:\:\:\left(\sqrt{\mathrm{7}}+\mathrm{1}\right)\:\:{or}\:\:\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)????? \\ $$

Question Number 221239 Answers: 1 Comments: 0

2^x =4^y =8^z and ((1/(2x))+1(1/(4y))+(1/(6z)))=((24)/7) z=??

$$\mathrm{2}^{{x}} =\mathrm{4}^{{y}} =\mathrm{8}^{{z}} \:\:{and}\:\left(\frac{\mathrm{1}}{\mathrm{2}{x}}+\mathrm{1}\frac{\mathrm{1}}{\mathrm{4}{y}}+\frac{\mathrm{1}}{\mathrm{6}{z}}\right)=\frac{\mathrm{24}}{\mathrm{7}}\:\:\: \\ $$$${z}=?? \\ $$

Question Number 221238 Answers: 3 Comments: 0

a=5+2(√6) then {(√a)−(1/( (√a)))}=??

$${a}=\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\:{then}\:\left\{\sqrt{{a}}−\frac{\mathrm{1}}{\:\sqrt{{a}}}\right\}=?? \\ $$

Question Number 221234 Answers: 2 Comments: 1

let 0 ≤ a,b,c, ≤ 2 , and a + b + c = 3 Prove that; (3/2) ≤ (1/(a + 1)) + (1/(b + 1)) + (1/(c +1 )) ≤ ((11)/6)

$$ \\ $$$$\:\:\mathrm{let}\:\mathrm{0}\:\leqslant\:{a},{b},{c},\:\leqslant\:\mathrm{2}\:,\:\mathrm{and}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}; \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{2}}\:\leqslant\:\frac{\mathrm{1}}{{a}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{b}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{{c}\:+\mathrm{1}\:}\:\leqslant\:\frac{\mathrm{11}}{\mathrm{6}} \\ $$$$ \\ $$

Question Number 221233 Answers: 1 Comments: 2

if a,b,c,d,e,f > 0 and abcdef = 1 , then (1/( (√(1 + ad)))) + (1/( (√(1 + be)))) + (1/( (√(1 + cf)))) ≤ (3/( (√2))) Profosed by Craciun Georghe

$$ \\ $$$$\:\mathrm{if}\:{a},{b},{c},{d},{e},{f}\:>\:\mathrm{0}\:\mathrm{and}\:{abcdef}\:=\:\mathrm{1}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then} \\ $$$$\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{ad}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{be}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:+\:{cf}}}\:\leqslant\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{2}}}\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Profosed}\:\mathrm{by}\:\mathrm{Craciun}\:\mathrm{Georghe} \\ $$

Question Number 221228 Answers: 1 Comments: 0

Σ_(n = 1) ^∞ Σ_(m = 1) ^∞ (1/((m^2 + n^2 )^2 ))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{{m}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({m}^{\mathrm{2}} \:+\:{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 221218 Answers: 0 Comments: 1

Question Number 221203 Answers: 1 Comments: 0

∫ tan(((1/x)/(sec(x)))) + ((1 − sec(x))/(sec(x))) dx

$$ \\ $$$$\:\:\:\:\:\int\:\mathrm{tan}\left(\frac{\frac{\mathrm{1}}{{x}}}{\mathrm{sec}\left({x}\right)}\right)\:+\:\frac{\mathrm{1}\:−\:\mathrm{sec}\left({x}\right)}{\mathrm{sec}\left({x}\right)}\:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 221196 Answers: 1 Comments: 0

Question Number 221195 Answers: 1 Comments: 1

Question Number 221188 Answers: 1 Comments: 2

Question Number 221185 Answers: 5 Comments: 0

Question Number 221184 Answers: 3 Comments: 2

Question Number 221179 Answers: 0 Comments: 0

Question Number 221170 Answers: 3 Comments: 1

Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14 Pg 15 Pg 16

Contact: info@tinkutara.com