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Question Number 11740 Answers: 0 Comments: 0

Metal pellets of mass 0.1 kg are fired into an iron plate of large mass m and specific heat capacity c at a temperature of 15°C . 25% of the kinetic energy of the pellets is converted thermal energy and the plate temperature rises to 16°C. The average speed of the pellets before hitting the plate was ?

$$\mathrm{Metal}\:\mathrm{pellets}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{1}\:\mathrm{kg}\:\mathrm{are}\:\mathrm{fired}\:\mathrm{into}\:\mathrm{an}\:\mathrm{iron}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{large}\:\mathrm{mass}\:\mathrm{m} \\ $$$$\mathrm{and}\:\mathrm{specific}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{c}\:\mathrm{at}\:\mathrm{a}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{15}°\mathrm{C}\:.\:\mathrm{25\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{is}\:\mathrm{converted}\:\mathrm{thermal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{temperature} \\ $$$$\mathrm{rises}\:\mathrm{to}\:\mathrm{16}°\mathrm{C}.\:\mathrm{The}\:\mathrm{average}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{before}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{was}\:? \\ $$

Question Number 11737 Answers: 1 Comments: 0

∫ (1/(x(x^n +1))) dx =

$$\int\:\frac{\mathrm{1}}{{x}\left({x}^{{n}} +\mathrm{1}\right)}\:{dx}\:= \\ $$

Question Number 11732 Answers: 1 Comments: 0

0.16 ÷ (2/3) of (2/5) ÷ (1/8)

$$\mathrm{0}.\mathrm{16}\:\boldsymbol{\div}\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{of}\:\frac{\mathrm{2}}{\mathrm{5}}\:\boldsymbol{\div}\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 11714 Answers: 0 Comments: 3

Solve the Crazy equation... x(lnx)^2 +xlnx−1=0

$${Solve}\:{the}\:{Crazy}\:{equation}... \\ $$$${x}\left({lnx}\right)^{\mathrm{2}} +{xlnx}−\mathrm{1}=\mathrm{0} \\ $$

Question Number 11707 Answers: 0 Comments: 0

ax^3 +bx^2 +cx+d=0 pls. solve it in a alzebric way , that a O level(ssc) student can understand...

$$ \\ $$$$ \\ $$$${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${pls}.\:{solve}\:{it}\:{in}\:{a}\:{alzebric}\:{way}\:, \\ $$$${that}\:{a}\:{O}\:{level}\left({ssc}\right)\:{student}\:{can} \\ $$$${understand}... \\ $$$$ \\ $$

Question Number 11701 Answers: 2 Comments: 3

If X∝A and X∝B , then why X∝AB ?? Give me the Mathematical Explanation....

$$ \\ $$$$ \\ $$$${If}\:{X}\propto{A}\:\:\:\:{and}\:{X}\propto{B}\:, \\ $$$${then}\:{why}\:{X}\propto{AB}\:?? \\ $$$${Give}\:{me}\:{the}\:{Mathematical} \\ $$$${Explanation}.... \\ $$$$ \\ $$

Question Number 11781 Answers: 3 Comments: 0

sin(2θ) + 7cos(2θ) = 6 find θ

$$\mathrm{sin}\left(\mathrm{2}\theta\right)\:+\:\mathrm{7cos}\left(\mathrm{2}\theta\right)\:=\:\mathrm{6} \\ $$$$\mathrm{find}\:\theta \\ $$

Question Number 11695 Answers: 2 Comments: 4

Question Number 11672 Answers: 2 Comments: 3

8x^3 −6x+1=0 Solves...

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{Solves}}... \\ $$

Question Number 11664 Answers: 2 Comments: 1

550÷11=50 And here 5^2 +5^2 +0^2 =50 find another three digit number which is divisible by 11 and the quotient is the sum of the square of the every digit of the dividend. /

$$\mathrm{550}\boldsymbol{\div}\mathrm{11}=\mathrm{50}\:{And}\:{here}\:\mathrm{5}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{0}^{\mathrm{2}} =\mathrm{50} \\ $$$${find}\:{another}\:{three}\:{digit}\:{number} \\ $$$${which}\:{is}\:{divisible}\:{by}\:\mathrm{11}\:{and}\:{the} \\ $$$${quotient}\:{is}\:{the}\:{sum}\:{of}\:{the}\: \\ $$$$\:{square}\:{of}\:\:{the}\:{every}\:{digit}\:{of}\: \\ $$$${the}\:{dividend}. \\ $$$$ \\ $$$$/ \\ $$

Question Number 11661 Answers: 1 Comments: 0

8x^3 −6x+1=0. Solves... equation x_1 =? x_2 =?

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{Solves}}...\:\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} =?\:\:\:\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$

Question Number 11660 Answers: 0 Comments: 0

Evaluate ∫x^x dx

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:{Evaluate}\:\:\int{x}^{{x}} {dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 11653 Answers: 0 Comments: 0

Can you give me some problem from your calculus text book...

$${Can}\:{you}\:{give}\:{me}\:{some}\:{problem} \\ $$$${from}\:{your}\:{calculus}\:{text}\:{book}... \\ $$$$ \\ $$

Question Number 11648 Answers: 1 Comments: 0

∣x∣<l Σ_(n=1) ^∞ x^n =?

$$\mid\mathrm{x}\mid<\mathrm{l} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{x}^{\mathrm{n}} =? \\ $$

Question Number 11633 Answers: 1 Comments: 0

A geometric sequence with n terms a_1 , a_2 , a_3 , ..., a_n which has a_1 . a_n = 3 If the product of all n terms = a_1 a_2 a_3 ...a_n = 59049 Determine the value of n

$$\mathrm{A}\:\mathrm{geometric}\:\mathrm{sequence}\:\mathrm{with}\:{n}\:\mathrm{terms}\: \\ $$$${a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:...,\:{a}_{{n}} \:\mathrm{which}\:\mathrm{has}\:{a}_{\mathrm{1}} \:.\:{a}_{{n}} \:=\:\mathrm{3} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:{n}\:\mathrm{terms}\:=\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} ...{a}_{{n}} =\:\mathrm{59049} \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n} \\ $$

Question Number 11632 Answers: 1 Comments: 0

Question Number 11628 Answers: 1 Comments: 0

p(x−1)+p(x+1)=4x^2 −2x+10 p(x)=?

$$\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$

Question Number 11621 Answers: 1 Comments: 0

Evaluate ∫((ax+b)/(cx+d))dx

$${Evaluate}\:\:\int\frac{{ax}+{b}}{{cx}+{d}}{dx} \\ $$

Question Number 11619 Answers: 1 Comments: 1

Evaluate ∫(dx/((x+a)(x+b)))

$${Evaluate}\:\int\frac{{dx}}{\left({x}+{a}\right)\left({x}+{b}\right)} \\ $$

Question Number 11616 Answers: 3 Comments: 0

EvAluate ∫(x^2 +9)^9 dx

$${EvAluate}\:\int\left({x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{9}} {dx} \\ $$

Question Number 11613 Answers: 0 Comments: 0

Can you evaluate the equation of a Ellipse?

$${Can}\:{you}\:{evaluate}\:{the}\:{equation}\:{of} \\ $$$${a}\:{Ellipse}? \\ $$

Question Number 11611 Answers: 0 Comments: 0

Can you prove the Taylor′s series without using mean value theorem?

$${Can}\:{you}\:{prove}\:{the}\:{Taylor}'{s}\:{series}\: \\ $$$${without}\:{using}\:{mean}\:{value}\:{theorem}? \\ $$$$ \\ $$

Question Number 11609 Answers: 1 Comments: 3

Evaluate ∫x^x dx

$$ \\ $$$$ \\ $$$${Evaluate}\:\int{x}^{{x}} {dx} \\ $$

Question Number 11608 Answers: 1 Comments: 0

If f(x)=xtan^(−1) ((1/x)) , x≠0 =0 , x=0 show that f is countinous but not differentiable at x=0.

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{xtan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:,\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{f}\:\mathrm{is}\:\mathrm{countinous}\:\mathrm{but}\:\mathrm{not}\:\mathrm{differentiable} \\ $$$$\mathrm{at}\:\mathrm{x}=\mathrm{0}. \\ $$

Question Number 11607 Answers: 1 Comments: 0

A parabola with equation y = (x^2 /k) − 5 intersects a circle with equation x^2 + y^2 = 25 at exactly 3 points A, B, C Determine all such positive integers k for which the area of ΔABC is an integer

$$\mathrm{A}\:\mathrm{parabola}\:\mathrm{with}\:\mathrm{equation}\:{y}\:=\:\frac{{x}^{\mathrm{2}} }{{k}}\:−\:\mathrm{5}\:\mathrm{intersects} \\ $$$$\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{25}\:\mathrm{at}\:\mathrm{exactly}\:\mathrm{3}\:\mathrm{points}\:{A},\:{B},\:{C} \\ $$$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{such}\:\mathrm{positive}\:\mathrm{integers}\:{k}\:\mathrm{for}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer} \\ $$

Question Number 11606 Answers: 1 Comments: 0

What is the smallest positive integer x for which (1/(32)) = (x/(10^y )) for some positive integer y ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:{x}\:\mathrm{for} \\ $$$$\mathrm{which}\:\frac{\mathrm{1}}{\mathrm{32}}\:=\:\frac{{x}}{\mathrm{10}^{{y}} }\:\:\mathrm{for}\:\mathrm{some}\:\mathrm{positive}\:\mathrm{integer}\:{y}\:? \\ $$

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