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AllQuestion and Answers: Page 1895

Question Number 12074 Answers: 1 Comments: 0

Question Number 12071 Answers: 0 Comments: 0

Question Number 12064 Answers: 0 Comments: 0

A heat pump gas C.P = 3, while the indoor temperature is 27°C and the outdoor temperature is 8°C. How much work per hour is required to pump 3.07 J of heat per hour into the individual unit of 10^5 J.

$$\mathrm{A}\:\mathrm{heat}\:\mathrm{pump}\:\mathrm{gas}\:\mathrm{C}.\mathrm{P}\:=\:\mathrm{3},\:\mathrm{while}\:\mathrm{the}\:\mathrm{indoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{27}°\mathrm{C}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{outdoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{8}°\mathrm{C}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{work}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{pump} \\ $$$$\mathrm{3}.\mathrm{07}\:\mathrm{J}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{into}\:\mathrm{the}\:\mathrm{individual}\:\mathrm{unit}\:\mathrm{of}\:\mathrm{10}^{\mathrm{5}} \:\mathrm{J}.\: \\ $$

Question Number 12063 Answers: 1 Comments: 0

Question Number 12062 Answers: 2 Comments: 0

lim_(x→y) ((x^n − y^n )/(x − y))

$$\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{n}} \:−\:\mathrm{y}^{\mathrm{n}} }{\mathrm{x}\:−\:\mathrm{y}} \\ $$

Question Number 12047 Answers: 1 Comments: 1

∫4x^3 (3x^2 + 2)^5 dx

$$\int\mathrm{4}{x}^{\mathrm{3}} \left(\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{2}\right)^{\mathrm{5}} \:{dx} \\ $$

Question Number 12046 Answers: 1 Comments: 0

how much matrices of integers number A= [(a,b),(c,d) ]if A^2 +A=2I, c=0, det(A)=4

$${how}\:{much}\:{matrices}\:{of}\:{integers}\:{number} \\ $$$${A}=\begin{bmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{bmatrix}{if}\:{A}^{\mathrm{2}} +{A}=\mathrm{2}{I},\:{c}=\mathrm{0},\:{det}\left({A}\right)=\mathrm{4} \\ $$

Question Number 12045 Answers: 1 Comments: 0

how much matrices of integers number A= [(a,b),(c,d) ]if A^2 =I and b=c

$${how}\:{much}\:{matrices}\:{of}\:{integers}\:{number} \\ $$$${A}=\begin{bmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{bmatrix}{if}\:{A}^{\mathrm{2}} ={I}\:{and}\:{b}={c} \\ $$

Question Number 12044 Answers: 1 Comments: 0

A∈M_(n×n) A^2 =A (I+A)^(−1) =....???

$${A}\in{M}_{{n}×{n}} \\ $$$${A}^{\mathrm{2}} ={A} \\ $$$$\left({I}+{A}\right)^{−\mathrm{1}} =....??? \\ $$

Question Number 12326 Answers: 1 Comments: 0

Π_(n=1) ^x a_n =9^(x!) a_4 =?

$$\underset{{n}=\mathrm{1}} {\overset{{x}} {\prod}}{a}_{{n}} =\mathrm{9}^{{x}!} \\ $$$${a}_{\mathrm{4}} =? \\ $$

Question Number 12040 Answers: 2 Comments: 0

Prove that ∀x,y∈R ⇒ 1+ ((x^2 +y^2 +xy)/3) ≥ x+y

$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\:\forall\boldsymbol{{x}},\boldsymbol{{y}}\in\boldsymbol{{R}} \\ $$$$\Rightarrow\:\mathrm{1}+\:\frac{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{xy}}}{\mathrm{3}}\:\geqslant\:\boldsymbol{{x}}+\boldsymbol{{y}} \\ $$

Question Number 12030 Answers: 1 Comments: 0

Question Number 12028 Answers: 1 Comments: 0

Express : sin(33) in surd form.

$$\mathrm{Express}\::\:\mathrm{sin}\left(\mathrm{33}\right)\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form}. \\ $$

Question Number 12023 Answers: 3 Comments: 0

Solve simultaneously x + y − (√(xy)) = 3 .......... (i) (√(x + 1)) + (√(y + 1)) = 4 .......... (ii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:−\:\sqrt{\mathrm{xy}}\:=\:\mathrm{3}\:\:\:\:\:..........\:\left(\mathrm{i}\right) \\ $$$$\sqrt{\mathrm{x}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{4}\:\:\:\:\:..........\:\left(\mathrm{ii}\right) \\ $$

Question Number 12019 Answers: 1 Comments: 0

Question Number 12018 Answers: 0 Comments: 0

Question Number 12017 Answers: 0 Comments: 0

How Can we expand (a+b)^(1/2) and (a+b)^(−n) ?

$${How}\:{Can}\:{we}\:{expand}\:\left({a}+{b}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{and} \\ $$$$\left({a}+{b}\right)^{−{n}} \:? \\ $$

Question Number 12015 Answers: 1 Comments: 0

prove that for all x ∈R, e^x ≥x^e

$${prove}\:{that}\:{for}\:{all}\:{x}\:\in{R}, \\ $$$${e}^{{x}} \geqslant{x}^{{e}} \\ $$

Question Number 12013 Answers: 1 Comments: 0

The slope of a curve is, 7x + 3 and it passes through the point (2, 4), Find the equation of the point

$$\mathrm{The}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{is},\:\mathrm{7x}\:+\:\mathrm{3}\:\:\mathrm{and}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\:\mathrm{4}\right), \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point} \\ $$

Question Number 12008 Answers: 1 Comments: 1

Question Number 11998 Answers: 0 Comments: 4

Question Number 11994 Answers: 0 Comments: 1

4x=60

$$\mathrm{4}{x}=\mathrm{60} \\ $$

Question Number 11991 Answers: 0 Comments: 0

show that: ((2n)/(2n+1))=1−(1/(2n+1)) via power series, and other methods

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}{n}}{\mathrm{2}{n}+\mathrm{1}}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$$\mathrm{via}\:\mathrm{power}\:\mathrm{series},\:\mathrm{and}\:\mathrm{other}\:\mathrm{methods} \\ $$

Question Number 11988 Answers: 2 Comments: 3

Question Number 11987 Answers: 1 Comments: 0

The radius of the moon is (1/4), and its mass is (1/(81)) that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8m/s^2 . What is its value on the moon′s surface.

$$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{moon}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{4}},\:\mathrm{and}\:\mathrm{its}\:\mathrm{mass}\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{81}}\:\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{is}\:\mathrm{9}.\mathrm{8m}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{its}\:\mathrm{value}\:\mathrm{on}\:\mathrm{the}\:\mathrm{moon}'\mathrm{s}\:\mathrm{surface}. \\ $$

Question Number 11982 Answers: 1 Comments: 0

∫x^5 ((√(x^3 + 1))) dx

$$\int\mathrm{x}^{\mathrm{5}} \left(\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\right)\:\mathrm{dx} \\ $$

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