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Question Number 171362 Answers: 1 Comments: 0

A rectangle is divided into 40 equal parts. How many of these parts should be shadded in other to cover three-five of the rectangle

$$ \\ $$$$\mathrm{A}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{40}\:\mathrm{equal}\: \\ $$$$\:\mathrm{parts}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{parts}\: \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{shadded}\:\mathrm{in}\:\mathrm{other}\:\mathrm{to}\:\mathrm{cover}\: \\ $$$$\:\mathrm{three}-\mathrm{five}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\: \\ $$

Question Number 171379 Answers: 0 Comments: 1

f(x)= { ((2x+3 ;x>0)),((3x−5 ;x≤0)) :} ((df(x))/dx)=?

$${f}\left({x}\right)=\begin{cases}{\mathrm{2}{x}+\mathrm{3}\:\:\:;{x}>\mathrm{0}}\\{\mathrm{3}{x}−\mathrm{5}\:\:;{x}\leqslant\mathrm{0}}\end{cases} \\ $$$$\frac{{df}\left({x}\right)}{{dx}}=? \\ $$

Question Number 171360 Answers: 1 Comments: 0

Solve for real numbers: log_9 x ∙ log_2 (7 − x) = 1

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{log}_{\mathrm{9}} \:\mathrm{x}\:\:\centerdot\:\:\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{7}\:−\:\mathrm{x}\right)\:=\:\mathrm{1} \\ $$

Question Number 171359 Answers: 1 Comments: 0

A heavenly body has mass one third of the earth and its radius is half as that of the earth. if a stone weights 200N on the earth′s surface, find its weight on that heavenly body.

$$\mathrm{A}\:\mathrm{heavenly}\:\mathrm{body}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{one}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{and}\:\mathrm{its} \\ $$$$\:\mathrm{radius}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{if}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{weights}\:\mathrm{200N}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface},\:\mathrm{find}\:\mathrm{its}\:\mathrm{weight}\:\mathrm{on}\:\mathrm{that}\:\mathrm{heavenly}\:\mathrm{body}. \\ $$

Question Number 171356 Answers: 0 Comments: 0

Solve 1) (2x−y)dx+(4x−2y+4)dy=0 2) (2x−y+4)dy+(x−2y+5)dx=0

$${Solve} \\ $$$$\left.\mathrm{1}\right)\:\left(\mathrm{2}{x}−{y}\right){dx}+\left(\mathrm{4}{x}−\mathrm{2}{y}+\mathrm{4}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\left(\mathrm{2}{x}−{y}+\mathrm{4}\right){dy}+\left({x}−\mathrm{2}{y}+\mathrm{5}\right){dx}=\mathrm{0} \\ $$

Question Number 171346 Answers: 0 Comments: 2

solve: ((m+(mn^2 )^(1/3) +(m^2 n)^(1/3) )/(m−n)) × (((m^(1/3) −n^(1/3) ))/m^(1/3) )

$$\:\:\mathrm{solve}: \\ $$$$\:\:\:\frac{\mathrm{m}+\left(\mathrm{mn}^{\mathrm{2}} \right)^{\mathrm{1}/\mathrm{3}} +\left(\mathrm{m}^{\mathrm{2}} \mathrm{n}\right)^{\mathrm{1}/\mathrm{3}} }{\mathrm{m}−\mathrm{n}}\:×\:\frac{\left(\mathrm{m}^{\mathrm{1}/\mathrm{3}} −\mathrm{n}^{\mathrm{1}/\mathrm{3}} \right)}{\mathrm{m}^{\mathrm{1}/\mathrm{3}} } \\ $$

Question Number 171343 Answers: 0 Comments: 0

Given M=(m_(ij) +t) a real square matrix, with t∈R. Show that the determinant of M is linear function (affine) of t.

$${Given}\:{M}=\left({m}_{{ij}} +{t}\right)\:{a}\:{real}\:{square} \\ $$$${matrix},\:{with}\:{t}\in\mathbb{R}. \\ $$$${Show}\:{that}\:{the}\:{determinant}\:{of}\:{M} \\ $$$${is}\:{linear}\:{function}\:\left({affine}\right)\:{of}\:{t}. \\ $$

Question Number 171342 Answers: 1 Comments: 1

Question Number 171341 Answers: 2 Comments: 1

lim_(x→0) ((x^2 +sin3x)/(2x−sinx))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +{sin}\mathrm{3}{x}}{\mathrm{2}{x}−{sinx}}=? \\ $$

Question Number 171339 Answers: 1 Comments: 0

an integer n 1≤n≤144 is picked at random what is the probability that n is the square of an inteer?

$${an}\:{integer}\:{n}\:\mathrm{1}\leq{n}\leq\mathrm{144}\:{is}\:{picked} \\ $$$${at}\:{random}\: \\ $$$${what}\:{is}\:{the}\:{probability}\:{that} \\ $$$$\:{n}\:{is}\:{the}\:{square}\:{of}\:{an} \\ $$$${inteer}? \\ $$

Question Number 171336 Answers: 1 Comments: 0

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