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Question Number 171332 Answers: 0 Comments: 2

A bicycle has a constant velocity of 10 m/s. A person starts from rest and runs to catch up to the bicycle in 30 s. What is the acceleration of the person?

Question Number 171331 Answers: 0 Comments: 0

Question Number 176850 Answers: 1 Comments: 0

f(x)=2(x−1) (fofo...of)_(50 times) (x)=?

$${f}\left({x}\right)=\mathrm{2}\left({x}−\mathrm{1}\right) \\ $$$$\underset{\mathrm{50}\:\mathrm{times}} {\underbrace{\left({fofo}...{of}\right)}}\left({x}\right)=? \\ $$

Question Number 176849 Answers: 0 Comments: 0

The constant term in the polynomial P(x)=(x^2 +x−7)Q(x+1)+2x+1 is −20. What is the sum of coefficients of the polynomial Q(x) ?

$$\mathrm{The}\:\mathrm{constant}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left({x}\right)=\left({x}^{\mathrm{2}} +{x}−\mathrm{7}\right){Q}\left({x}+\mathrm{1}\right)+\mathrm{2}{x}+\mathrm{1} \\ $$$$\mathrm{is}\:−\mathrm{20}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{coefficients}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{polynomial}\:\mathrm{Q}\left({x}\right)\:? \\ $$

Question Number 176848 Answers: 1 Comments: 0

Question Number 171315 Answers: 1 Comments: 0

The tangent to the curve y=ax^2 +bx+2 at (1,(1/2)) is parallel to the normal to the curve y=x^2 +6x+10 at (−2,2). Find the values of a and b.

$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{2} \\ $$$$\mathrm{at}\:\left(\mathrm{1},\frac{\mathrm{1}}{\mathrm{2}}\right)\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{10}\:\mathrm{at}\:\left(−\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$

Question Number 171314 Answers: 1 Comments: 0

If C_r , C_s are cyclic groups such that g.c.d(r,s)=1, then show that C_r ×C_s is a cyclic group. Mastermind

$${If}\:{C}_{{r}} ,\:{C}_{{s}} \:{are}\:{cyclic}\:{groups}\:{such}\:{that} \\ $$$${g}.{c}.{d}\left({r},{s}\right)=\mathrm{1},\:{then}\:{show}\:{that}\:{C}_{{r}} ×{C}_{{s}} \:{is} \\ $$$${a}\:{cyclic}\:{group}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171312 Answers: 0 Comments: 4

Question Number 171311 Answers: 0 Comments: 0

2^x^(−i^2 ) +2^x^2 =2^(x^3 −i^2 ) x=?

$$\mathrm{2}^{{x}^{−{i}^{\mathrm{2}} } } +\mathrm{2}^{{x}^{\mathrm{2}} } =\mathrm{2}^{{x}^{\mathrm{3}} −{i}^{\mathrm{2}} } \\ $$$${x}=? \\ $$

Question Number 171318 Answers: 1 Comments: 1

if f(x)=x^((13)/5) and g(x)=(x^(13) )^(1/5) Which one is correct? 1) f(x)=g(x) 2)f(x)≠g(x)

$${if}\:{f}\left({x}\right)={x}^{\frac{\mathrm{13}}{\mathrm{5}}} \:{and}\:{g}\left({x}\right)=\sqrt[{\mathrm{5}}]{{x}^{\mathrm{13}} }\: \\ $$$${Which}\:{one}\:{is}\:{correct}? \\ $$$$\left.\mathrm{1}\left.\right)\:{f}\left({x}\right)={g}\left({x}\right)\:\:\:\:\mathrm{2}\right){f}\left({x}\right)\neq{g}\left({x}\right) \\ $$

Question Number 171307 Answers: 1 Comments: 1

Simplify Σ_(k=0) ^(n−1) 3^k 2^(n−k)

$$\mathrm{Simplify} \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\mathrm{3}^{{k}} \mathrm{2}^{{n}−{k}} \\ $$

Question Number 171301 Answers: 0 Comments: 1

∫_1 ^2 6x^2 −2x+3

$$\int_{\mathrm{1}} ^{\mathrm{2}} \mathrm{6}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$

Question Number 171296 Answers: 0 Comments: 1

Question Number 176853 Answers: 2 Comments: 0

Question Number 171289 Answers: 1 Comments: 0

(x,y)∈R x^2 −xy−12y^2 =0 ((2x^2 +4y^2 )/(xy))=?

$$\left({x},{y}\right)\in{R}\:\:\:{x}^{\mathrm{2}} −{xy}−\mathrm{12}{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}{y}^{\mathrm{2}} }{{xy}}=? \\ $$

Question Number 171284 Answers: 2 Comments: 0

g(x)=−x^2 +1−ln∣x∣ Study the variations of the function g and draw up its table of variations

$${g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$Study the variations of the function g and draw up its table of variations

Question Number 171281 Answers: 0 Comments: 0

Question Number 171283 Answers: 0 Comments: 2

Question Number 171267 Answers: 0 Comments: 2

Find the coordinates of the point on the curve y=(x/(1+x)) at which the tangents to the curve are parallel to the line x−y+8=0. Find the equations of the tangents at these points.

Question Number 171265 Answers: 0 Comments: 0

find the drivative of f(x,y,z)=cos(xy)+e^(zy) +ln(zy) at point (1,0,(1/2)) in the direction v=i+2j+2k

$${find}\:{the}\:{drivative}\:{of}\: \\ $$$${f}\left({x},{y},{z}\right)={cos}\left({xy}\right)+{e}^{{zy}} +{ln}\left({zy}\right) \\ $$$${at}\:{point}\:\left(\mathrm{1},\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)\:{in}\:{the}\:{direction} \\ $$$${v}={i}+\mathrm{2}{j}+\mathrm{2}{k} \\ $$

Question Number 171260 Answers: 1 Comments: 0

Change to polar coordinates: ∫^( 4a) _0 ∫_(y^2 /4a) ^a (((x^2 −y^2 )/(x^2 +y^2 ))) dx dy

$$\underline{{Change}\:{to}\:{polar}\:{coordinates}:} \\ $$$$\underset{\mathrm{0}} {\int}^{\:\:\mathrm{4}{a}} \underset{{y}^{\mathrm{2}} /\mathrm{4}{a}} {\int}\overset{{a}} {\:}\:\:\left(\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)\:{dx}\:{dy} \\ $$

Question Number 171255 Answers: 1 Comments: 2