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Question Number 82879 Answers: 0 Comments: 1

prove that ((cos^2 a+sin^2 b)/(sin acos a + sin bcos b)) = cot (a+b)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{cos}\:^{\mathrm{2}} \mathrm{a}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{b}}{\mathrm{sin}\:\mathrm{acos}\:\mathrm{a}\:+\:\mathrm{sin}\:\mathrm{bcos}\:\mathrm{b}}\:=\:\mathrm{cot}\:\left(\mathrm{a}+\mathrm{b}\right) \\ $$

Question Number 82878 Answers: 1 Comments: 3

Question Number 82920 Answers: 1 Comments: 0

calculate lim_(x→0) ((ln(1+ln(1+x)))/x)

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)}{{x}} \\ $$

Question Number 82919 Answers: 1 Comments: 2

bangun datar

$${bangun}\:{datar} \\ $$

Question Number 82872 Answers: 0 Comments: 1

1)find ∫∫_W ((xdx)/(a^2 +x^2 +y^2 )) with W_a →x^2 +y^2 ≤a^2 and x>0 (a>0) 2)calculate ∫∫_W_1 ((xdx)/(x^2 +y^2 +1))

$$\left.\mathrm{1}\right){find}\:\int\int_{{W}} \:\frac{{xdx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:{with} \\ $$$${W}_{{a}} \rightarrow{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} \:{and}\:{x}>\mathrm{0}\:\:\:\:\:\left({a}>\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int\int_{{W}_{\mathrm{1}} } \:\:\:\frac{{xdx}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 82871 Answers: 0 Comments: 1

find ∫∫_([0,1]^2 ) ∣x^2 −y^2 ∣dxdy

$${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\mid{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \mid{dxdy} \\ $$

Question Number 82873 Answers: 1 Comments: 2

Question Number 82867 Answers: 0 Comments: 3

hello prove that ∫_0 ^(+∞) sin(x^4 )dx=sin((π/8))∫_0 ^(+∞) e^(−x^4 ) dx? verry nice day Good Bless You

$${hello}\:{prove}\:{that}\:\int_{\mathrm{0}} ^{+\infty} {sin}\left({x}^{\mathrm{4}} \right){dx}={sin}\left(\frac{\pi}{\mathrm{8}}\right)\int_{\mathrm{0}} ^{+\infty} {e}^{−{x}^{\mathrm{4}} } {dx}? \\ $$$${verry}\:{nice}\:{day}\:{Good}\:{Bless}\:{You} \\ $$

Question Number 82843 Answers: 1 Comments: 0

show that (((1+(√3) i)^4 (1+i)^8 )/((cos100°−i sin100)^3 ))=−256

$${show}\:{that} \\ $$$$\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{i}\right)^{\mathrm{4}} \left(\mathrm{1}+{i}\right)^{\mathrm{8}} }{\left({cos}\mathrm{100}°−{i}\:{sin}\mathrm{100}\right)^{\mathrm{3}} }=−\mathrm{256} \\ $$

Question Number 82839 Answers: 0 Comments: 8

if the first and fifth terms of arithmetic peogression are equal and the seventh and fourtenth terms of another arithmetic are equal then show that the first term from the first arithmetic is equal the tenth from the second one and so sorry because my english is not so good

$${if}\:{the}\:{first}\:{and}\:{fifth}\:{terms}\:{of}\:{arithmetic} \\ $$$${peogression}\:{are}\:{equal}\:{and}\:{the}\:{seventh} \\ $$$${and}\:{fourtenth}\:{terms}\:{of}\:{another}\:{arithmetic}\:{are} \\ $$$${equal}\:{then}\:{show}\:{that}\:{the}\:{first}\:{term}\:{from} \\ $$$${the}\:{first}\:{arithmetic}\:{is}\:{equal}\:{the}\:{tenth} \\ $$$${from}\:{the}\:{second}\:{one} \\ $$$${and}\:{so}\:{sorry}\:{because}\:{my}\:{english}\:{is} \\ $$$${not}\:{so}\:{good} \\ $$

Question Number 82877 Answers: 1 Comments: 1

1)find xy∈R 2)find x,y∈Z (x+2yi)^6 =8i

$$\left.\mathrm{1}\right){find}\:{xy}\in{R} \\ $$$$\left.\mathrm{2}\right){find}\:{x},{y}\in{Z} \\ $$$$\left({x}+\mathrm{2}{yi}\right)^{\mathrm{6}} =\mathrm{8}{i} \\ $$

Question Number 82821 Answers: 0 Comments: 1

Log_y x+Log_x y =64 find x and y

$${Log}_{{y}} \:{x}+{Log}_{{x}} \:{y}\:=\mathrm{64} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$

Question Number 82806 Answers: 1 Comments: 1