Question and Answers Forum

The perimeter of a square and a rectangle is the same. The width of the rectangle is 6 cm and its area is 16 cm^2 less than the area of the square. Find the area of the square.

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{and}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{same}.\:\mathrm{The}\:\mathrm{width}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{6}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{its}\:\mathrm{area} \\ $$$$\mathrm{is}\:\mathrm{16}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}. \\ $$

Question Number 33783 Answers: 1 Comments: 0

Two commodities X and Y cost $70.00 and $80.00 per kg respectively. If 34.5 kg of X is mixed with 26kg of Y and the mixture is sold at $85.00 per kg, calculate the percentage profit.

$$\mathrm{Two}\:\mathrm{commodities}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{cost}\:\$\mathrm{70}.\mathrm{00}\:\mathrm{and}\:\$\mathrm{80}.\mathrm{00} \\ $$$$\mathrm{per}\:\mathrm{kg}\:\mathrm{respectively}.\:\mathrm{If}\:\mathrm{34}.\mathrm{5}\:\mathrm{kg}\:\mathrm{of}\:\mathrm{X}\:\mathrm{is}\:\mathrm{mixed}\:\mathrm{with}\: \\ $$$$\mathrm{26kg}\:\mathrm{of}\:\mathrm{Y}\:\mathrm{and}\:\mathrm{the}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{sold}\:\mathrm{at}\:\$\mathrm{85}.\mathrm{00}\:\mathrm{per}\:\mathrm{kg}, \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{profit}. \\ $$

Question Number 33743 Answers: 0 Comments: 1

let p(x)=(1+x^2 )(1+x^4 )....(1+x^2^n ) with n integr 1) find the roots of p(x) 2) factorize p(x) inside C[x]

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)....\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right)\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$

Question Number 33702 Answers: 0 Comments: 1

let p(x) =a_0 +a_1 x +a_2 x^2 +...a_n x^n prove that a_k = ((p^((k)) (0))/(k!)) ∀ k ∈[[0,n]] .

$${let}\:{p}\left({x}\right)\:={a}_{\mathrm{0}} \:+{a}_{\mathrm{1}} {x}\:+{a}_{\mathrm{2}} {x}^{\mathrm{2}} \:+...{a}_{{n}} {x}^{{n}} \\ $$$${prove}\:{that}\:\:{a}_{{k}} =\:\frac{{p}^{\left({k}\right)} \left(\mathrm{0}\right)}{{k}!}\:\:\forall\:{k}\:\in\left[\left[\mathrm{0},{n}\right]\right]\:. \\ $$

Question Number 33569 Answers: 1 Comments: 0

Given f(x) = x^3 + ax^2 + bx + c with a, b, c ∈ R, the roots are x_1 , x_2 , x_3 ∈ R Let λ is an positive integer that satisfied x_2 − x_1 = λ x_3 > (1/2)(x_1 + x_2 ) What is the max value of ((2a^3 + 27c − 9ab)/λ^3 ) ?

$$\mathrm{Given}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c} \\ $$$$\mathrm{with}\:{a},\:{b},\:{c}\:\in\:\mathbb{R},\:\mathrm{the}\:\mathrm{roots}\:\mathrm{are}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} \:\in\:\mathbb{R} \\ $$$$\mathrm{Let}\:\lambda\:\mathrm{is}\:\mathrm{an}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{that}\:\mathrm{satisfied} \\ $$$${x}_{\mathrm{2}} \:−\:{x}_{\mathrm{1}} \:=\:\lambda \\ $$$${x}_{\mathrm{3}} \:>\:\frac{\mathrm{1}}{\mathrm{2}}\left({x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \right) \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{2}{a}^{\mathrm{3}} \:+\:\mathrm{27}{c}\:−\:\mathrm{9}{ab}}{\lambda^{\mathrm{3}} }\:? \\ $$

Question Number 33518 Answers: 0 Comments: 0

α^4 +β^(4 ) solve please

$$\alpha^{\mathrm{4}} +\beta^{\mathrm{4}\:} {solve}\:{please} \\ $$

Question Number 33515 Answers: 0 Comments: 1

expand α^4 +β^(β ) please

$${expand}\:\alpha^{\mathrm{4}} +\beta^{\beta\:\:} {please} \\ $$

Question Number 33496 Answers: 1 Comments: 0

prove that e^(iπ) +1=0

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{e}^{\mathrm{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$

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