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Question Number 209706 Answers: 2 Comments: 0

find the sum of sin^2 1°+sin^2 2°+...+sin^2 60°=?

$${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+...+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$

Question Number 209695 Answers: 1 Comments: 0

If: (a + b)∙(√2) = 7∙(a−b−4) Find: (2a + b) = ?

$$\mathrm{If}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\right)\centerdot\sqrt{\mathrm{2}}\:=\:\mathrm{7}\centerdot\left(\mathrm{a}−\mathrm{b}−\mathrm{4}\right) \\ $$$$\mathrm{Find}: \\ $$$$\left(\mathrm{2a}\:+\:\mathrm{b}\right)\:=\:? \\ $$

Question Number 209694 Answers: 1 Comments: 0

x^2 +xy+y^2 =α^2 y^2 +yz+z^2 =β^2 z^2 +zx+x^2 =α^2 +β^2 Find x+y+z for x, y, z ∈R^+

$${x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\alpha^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{yz}+{z}^{\mathrm{2}} =\beta^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} \\ $$$$\mathrm{Find}\:{x}+{y}+{z}\:\mathrm{for}\:{x},\:{y},\:{z}\:\in\mathbb{R}^{+} \\ $$

Question Number 209691 Answers: 0 Comments: 0

∫(2x^(3x^2 +4x−7) )(log _2 (x^2 +3x−7))e^(x^2 +3x−5) dx=?

$$\:\:\:\int\left(\mathrm{2x}^{\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{7}} \right)\left(\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{7}\right)\right)\mathrm{e}^{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{5}} \:\mathrm{dx}=? \\ $$

Question Number 209687 Answers: 3 Comments: 0

Question Number 209685 Answers: 1 Comments: 0

Question Number 209672 Answers: 2 Comments: 0

Question Number 209671 Answers: 2 Comments: 0

5x+3x=10

$$\mathrm{5}{x}+\mathrm{3}{x}=\mathrm{10} \\ $$

Question Number 209670 Answers: 2 Comments: 0

find the sum of sin^2 (1)+...+sin^2 (90)

$${find}\:{the}\:{sum}\:{of}\:{sin}^{\mathrm{2}} \left(\mathrm{1}\right)+...+{sin}^{\mathrm{2}} \left(\mathrm{90}\right) \\ $$

Question Number 209662 Answers: 1 Comments: 0

∫(1/(sin^2 x(1+cos^2 x)))dx

$$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$

Question Number 209659 Answers: 3 Comments: 0

Question Number 209656 Answers: 2 Comments: 0

2cos^2 x−3cosx+sinx+1=0 help

$$ \\ $$$$\:\:\:\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{3}{cosx}+{sinx}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:{help} \\ $$$$ \\ $$

Question Number 209650 Answers: 0 Comments: 1

if the acceleration is constant, what will be the average and instantaneous accelerations?

$${if}\:{the}\:{acceleration}\:{is}\:{constant},\:{what}\: \\ $$$${will}\:{be}\:{the}\:{average}\:{and}\:{instantaneous} \\ $$$${accelerations}? \\ $$

Question Number 209639 Answers: 1 Comments: 1

Question Number 209637 Answers: 1 Comments: 8

Question Number 209633 Answers: 2 Comments: 0

Question Number 209630 Answers: 1 Comments: 0

If A varies as r^2 and V varies as r^3 find percentage increase in A and V if r is increased by 20%

$$\:\:{If}\:{A}\:\:{varies}\:{as}\:{r}^{\mathrm{2}} \:{and}\:{V}\:\:{varies}\:{as}\:{r}^{\mathrm{3}} \\ $$$$\:{find}\:{percentage}\:{increase}\:{in}\:{A}\:{and}\:{V} \\ $$$$\:{if}\:\:{r}\:{is}\:{increased}\:{by}\:\mathrm{20\%} \\ $$

Question Number 209631 Answers: 0 Comments: 0

Let u_n be a set satisfying u_1 =1 & u_(n+1) =u_n +((ln n)/u_n ) , ∀ n ≥1 1. Prove that u_(2023) >(√(2023.ln 2023)). 2. Find: lim_(n→∞) ((u_n .ln n)/n).

$$\mathrm{Let}\:{u}_{{n}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{set}\:\mathrm{satisfying}\:{u}_{\mathrm{1}} =\mathrm{1}\:\&\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} +\frac{\mathrm{ln}\:{n}}{{u}_{{n}} }\:\:,\:\forall\:{n}\:\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:{u}_{\mathrm{2023}} >\sqrt{\mathrm{2023}.\mathrm{ln}\:\mathrm{2023}}. \\ $$$$\mathrm{2}.\:\mathrm{Find}:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{u}_{{n}} .\mathrm{ln}\:{n}}{{n}}. \\ $$

Question Number 209624 Answers: 1 Comments: 0

I=∫_0 ^( ∞) ∫_0 ^( ∞) (( 1)/(1+ x^2 +y^2 +x^2 y^2 )) dxdy=? using polar system...

$$ \\ $$$$ \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \:\frac{\:\mathrm{1}}{\mathrm{1}+\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{x}^{\mathrm{2}} {y}^{\mathrm{2}} }\:{dxdy}=? \\ $$$$\:{using}\:\:\:\:{polar}\:\:{system}... \\ $$

Question Number 209604 Answers: 0 Comments: 0

Question Number 209602 Answers: 2 Comments: 0

Question Number 209599 Answers: 4 Comments: 0

Question Number 209598 Answers: 3 Comments: 0

Question Number 209597 Answers: 2 Comments: 1

Question Number 209593 Answers: 0 Comments: 1

Question Number 209594 Answers: 0 Comments: 1

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