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Question Number 66846 Answers: 0 Comments: 2

Question Number 66842 Answers: 0 Comments: 2

Question Number 66845 Answers: 0 Comments: 1

A cylindrical tank of radius 2m and height 1.5m initially contains water to a depth of 50cm. Water is added to the tank at the rate of 62.84l per minute for 15 minutes. Find the new height of water in the tank.

$${A}\:{cylindrical}\:{tank}\:{of}\:{radius}\:\mathrm{2}{m}\: \\ $$$${and}\:{height}\:\mathrm{1}.\mathrm{5}{m}\:{initially}\:{contains} \\ $$$${water}\:{to}\:{a}\:{depth}\:{of}\:\mathrm{50}{cm}.\:{Water} \\ $$$${is}\:{added}\:{to}\:{the}\:{tank}\:{at}\:{the}\:{rate}\:{of}\: \\ $$$$\mathrm{62}.\mathrm{84}{l}\:{per}\:{minute}\:{for}\:\mathrm{15}\:{minutes}. \\ $$$${Find}\:{the}\:{new}\:{height}\:{of}\:{water}\:{in} \\ $$$${the}\:{tank}. \\ $$

Question Number 66832 Answers: 2 Comments: 0

solve the system of congruence {: ((x≡ 1 (mod 5))),((x ≡ 2 (mod 7))),((x≡ 3(mod 9))),((x ≡ 4( mod 11))) }

$${solve}\:{the}\:{system}\:{of}\:{congruence} \\ $$$$\:\:\:\left.\begin{matrix}{{x}\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{5}\right)}\\{{x}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right)}\\{{x}\equiv\:\:\mathrm{3}\left({mod}\:\mathrm{9}\right)}\\{{x}\:\equiv\:\mathrm{4}\left(\:{mod}\:\mathrm{11}\right)}\end{matrix}\right\} \\ $$

Question Number 66830 Answers: 0 Comments: 4

evaluate. ∫_1 ^( ∞) (1/x^(2 ) ) dx. can i assume lim_(t→0) ∫_1 ^( t) (1/x^(2 ) ) dx ????

$${evaluate}. \\ $$$$\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{2}\:} }\:{dx}. \\ $$$$ \\ $$$${can}\:{i}\:{assume}\:\underset{{t}\rightarrow\mathrm{0}} {\:\mathrm{lim}}\:\int_{\mathrm{1}} ^{\:\:{t}} \frac{\mathrm{1}}{{x}^{\mathrm{2}\:} }\:{dx}\:???? \\ $$

Question Number 66803 Answers: 1 Comments: 3

prove that Σ_(r=k) ^n r = (1/2)n(n+1) show with a diagram that the volume of a parallepipe is a.(b×c)

$$\:{prove}\:{that} \\ $$$$\underset{{r}={k}} {\overset{{n}} {\sum}}\:{r}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right) \\ $$$$ \\ $$$${show}\:{with}\:{a}\:{diagram}\:{that}\:{the}\:{volume}\:{of}\:{a}\:{parallepipe}\:{is}\:\:\:{a}.\left({b}×{c}\right) \\ $$

Question Number 66802 Answers: 0 Comments: 6

given that f(x) = 3x^3 − 2x^2 + 5x + 7 find a) α + β + γ b) αβγ c) α^2 + β^2 + γ^2 d) α^3 + β^3 + γ^3 any solutions directly?

$${given}\:{that}\: \\ $$$${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{7}\:\:{find} \\ $$$$\left.{a}\right)\:\:\alpha\:+\:\beta\:+\:\gamma \\ $$$$\left.{b}\right)\:\alpha\beta\gamma\:\: \\ $$$$\left.{c}\right)\:\alpha^{\mathrm{2}} \:+\:\beta^{\mathrm{2}} \:+\:\gamma^{\mathrm{2}} \\ $$$$\left.{d}\right)\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \:+\:\gamma^{\mathrm{3}} \\ $$$${any}\:\:{solutions}\:\:{directly}? \\ $$

Question Number 66767 Answers: 0 Comments: 2

In a school there are 30 more boys than girls. One-quarter of the boys and two-thirds of the girls are boarders. If there are 255 boarders, find the number of students in the school.

$${In}\:{a}\:{school}\:{there}\:{are}\:\mathrm{30}\:{more}\:{boys} \\ $$$${than}\:{girls}.\:{One}-{quarter}\:{of}\:{the}\:{boys} \\ $$$${and}\:{two}-{thirds}\:{of}\:{the}\:{girls}\:{are}\:{boarders}. \\ $$$${If}\:{there}\:{are}\:\mathrm{255}\:{boarders},\:{find}\:{the} \\ $$$${number}\:{of}\:{students}\:{in}\:{the}\:{school}. \\ $$

Question Number 66765 Answers: 0 Comments: 2

Simba had 57 denomination notes which he deposited in his account. He had six times as many two-hundred shilling notes as one-thousand shilling notes and twice as many one-hundred shilling notes as two- hundred shilling notes. The rest were fifty shilling notes. If he deposited a total of sh 7750, find the number of fifty shilling notes he had.

$${Simba}\:{had}\:\mathrm{57}\:{denomination}\:{notes} \\ $$$${which}\:{he}\:{deposited}\:{in}\:{his}\:{account}. \\ $$$${He}\:{had}\:{six}\:{times}\:{as}\:{many}\:{two}-{hundred} \\ $$$${shilling}\:{notes}\:{as}\:{one}-{thousand}\: \\ $$$${shilling}\:{notes}\:{and}\:{twice}\:{as}\:{many}\: \\ $$$${one}-{hundred}\:{shilling}\:{notes}\:{as}\:{two}- \\ $$$${hundred}\:{shilling}\:{notes}.\:{The}\:{rest}\:{were} \\ $$$${fifty}\:{shilling}\:{notes}.\:{If}\:{he}\:{deposited} \\ $$$${a}\:{total}\:{of}\:{sh}\:\mathrm{7750},\:{find}\:{the}\:{number} \\ $$$${of}\:{fifty}\:{shilling}\:{notes}\:{he}\:{had}. \\ $$

Question Number 66756 Answers: 2 Comments: 0

solve the equations, x+y=17 xy−5x=32

$${solve}\:{the}\:{equations}, \\ $$$${x}+{y}=\mathrm{17} \\ $$$${xy}−\mathrm{5}{x}=\mathrm{32} \\ $$

Question Number 66746 Answers: 2 Comments: 0

A point T divides a line AB internally in the ratio 5:2. Given that A is (-4,10) and B is (10,3), find the coordinates of T.

$${A}\:{point}\:{T}\:\:{divides}\:{a}\:{line}\:{AB}\:{internally}\:{in}\:{the}\:{ratio}\:\mathrm{5}:\mathrm{2}.\:{Given}\:{that}\:{A}\:{is}\:\left(-\mathrm{4},\mathrm{10}\right)\:{and}\:{B}\:{is}\:\left(\mathrm{10},\mathrm{3}\right),\:{find}\:{the}\:{coordinates}\:{of}\:{T}. \\ $$

Question Number 66562 Answers: 1 Comments: 1

given that ∣z − i∣ = ∣z − 4 +3 i∣ sketch the locus of z find the catersian equation of this locus.

$${given}\:{that}\:\:\mid{z}\:−\:\mathrm{i}\mid\:=\:\mid{z}\:−\:\mathrm{4}\:+\mathrm{3}\:\mathrm{i}\mid \\ $$$${sketch}\:{the}\:{locus}\:{of}\:\:{z} \\ $$$${find}\:{the}\:{catersian}\:{equation}\:{of}\:{this}\:{locus}. \\ $$

Question Number 66548 Answers: 0 Comments: 1

Evaluate:∫(√(x(√(x+1)) ))dx

$$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}\:}{dx} \\ $$

Question Number 66513 Answers: 1 Comments: 4

when finding ∫_0 ^2 (2x +4)^5 dx must we change limits?

$${when}\:{finding}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{2}{x}\:+\mathrm{4}\right)^{\mathrm{5}} {dx}\: \\ $$$${must}\:{we}\:{change}\:{limits}? \\ $$

Question Number 66497 Answers: 1 Comments: 0

Question Number 66489 Answers: 3 Comments: 0

Question Number 66467 Answers: 0 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((n+x^n )^2 )) with n>1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({n}+{x}^{{n}} \right)^{\mathrm{2}} }\:\:\:{with}\:{n}>\mathrm{1} \\ $$

Question Number 66461 Answers: 0 Comments: 0

x(n)=3n^2 −2n+7 find even and odd component

$${x}\left({n}\right)=\mathrm{3}{n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{7} \\ $$$${find}\:{even}\:{and}\:{odd}\:{component} \\ $$

Question Number 66439 Answers: 0 Comments: 4

for a geometric series. can the sun to infinty use the two formulas S_∞ = (a/(1−r)) ∣r∣ <1 and S_∞ = (a/(r−1)) ∣r∣ > 1 ?? please i am getting confused on this.

$${for}\:{a}\:{geometric}\:{series}. \\ $$$${can}\:{the}\:{sun}\:{to}\:{infinty}\:{use}\:{the}\:{two}\:{formulas} \\ $$$${S}_{\infty} =\:\frac{{a}}{\mathrm{1}−{r}}\:\:\mid{r}\mid\:\:<\mathrm{1}\:\:{and}\:{S}_{\infty} \:=\:\frac{{a}}{{r}−\mathrm{1}}\:\mid{r}\mid\:>\:\mathrm{1}\:??\:{please}\:{i}\:{am}\:{getting}\:{confused}\:{on}\:{this}. \\ $$

Question Number 66421 Answers: 1 Comments: 0

show that for a given complex number z z^n = r^n (cosnθ + isinnθ)

$${show}\:{that}\:{for}\:{a}\:{given}\:{complex}\:{number}\:{z} \\ $$$$\:{z}^{{n}} \:=\:{r}^{{n}} \:\left({cosn}\theta\:+\:{isinn}\theta\right)\: \\ $$

Question Number 66420 Answers: 0 Comments: 3

solve the differential equation 2(d^2 y/dx^2 ) + (dy/dx) − e^(−x) = 4

$${solve}\:{the}\:{differential}\:{equation} \\ $$$$\:\mathrm{2}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:−\:{e}^{−{x}} \:=\:\mathrm{4} \\ $$

Question Number 66399 Answers: 0 Comments: 1

Show that for all real values of x; x^(2/3) + 6x^(1/3) + 10 >0

$${Show}\:{that}\:{for}\:{all}\:{real} \\ $$$${values}\:{of}\:{x};\: \\ $$$$\:\:{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:+\:\mathrm{6}{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:\mathrm{10}\:>\mathrm{0} \\ $$

Question Number 66356 Answers: 1 Comments: 0