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Question Number 86541 Answers: 0 Comments: 1

Question Number 86540 Answers: 0 Comments: 3

prove that cos ((A/2))+cos ((B/2))+cos ((C/2)) = 4 cos (((π+A)/4))cos (((π+B)/4))cos (((π−C)/4)) where A+B+C = π

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{cos}\:\left(\frac{\mathrm{A}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{B}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{C}}{\mathrm{2}}\right)\:=\: \\ $$$$\mathrm{4}\:\mathrm{cos}\:\left(\frac{\pi+\mathrm{A}}{\mathrm{4}}\right)\mathrm{cos}\:\left(\frac{\pi+\mathrm{B}}{\mathrm{4}}\right)\mathrm{cos}\:\left(\frac{\pi−\mathrm{C}}{\mathrm{4}}\right) \\ $$$$\mathrm{where}\:\mathrm{A}+\mathrm{B}+\mathrm{C}\:=\:\pi \\ $$

Question Number 86537 Answers: 0 Comments: 0

help given total cost=4x+y p_1 =25−3x−2y p_2 =12−x−y total revenue=p_1 x+p_2 y calculate: a). quantity sold for each item to get maximum profit b). respective price for each item c). the maximum profit>

$$\mathrm{help}\: \\ $$$$\mathrm{given}\:\mathrm{total}\:\mathrm{cost}=\mathrm{4x}+\mathrm{y} \\ $$$$\mathrm{p}_{\mathrm{1}} =\mathrm{25}−\mathrm{3x}−\mathrm{2y} \\ $$$$\mathrm{p}_{\mathrm{2}} =\mathrm{12}−\mathrm{x}−\mathrm{y} \\ $$$$\mathrm{total}\:\mathrm{revenue}=\mathrm{p}_{\mathrm{1}} \mathrm{x}+\mathrm{p}_{\mathrm{2}} \mathrm{y} \\ $$$$\mathrm{calculate}: \\ $$$$\left.\mathrm{a}\right).\:\mathrm{quantity}\:\mathrm{sold}\:\mathrm{for}\:\mathrm{each}\:\mathrm{item} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{to}\:\mathrm{get}\:\mathrm{maximum}\:\mathrm{profit} \\ $$$$\left.\mathrm{b}\right).\:\:\mathrm{respective}\:\mathrm{price}\:\mathrm{for}\:\mathrm{each}\:\mathrm{item} \\ $$$$\left.\mathrm{c}\right).\:\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{profit}> \\ $$

Question Number 86534 Answers: 0 Comments: 2

Mr.Tanmay can you please help me in question no.86454

$${Mr}.{Tanmay}\:{can}\:{you} \\ $$$${please}\:{help}\:{me}\:{in} \\ $$$${question}\:{no}.\mathrm{86454} \\ $$

Question Number 86532 Answers: 0 Comments: 2

∫((x^7 .dx)/((1+x^3 )^((1/2)) ))

$$\int\frac{{x}^{\mathrm{7}} .{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} } \\ $$

Question Number 86528 Answers: 0 Comments: 5

Question Number 86518 Answers: 0 Comments: 1

∫ (dx/(e^(2x) −5e^x ))

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{5e}^{\mathrm{x}} } \\ $$

Question Number 86515 Answers: 0 Comments: 2

log_2 (x) + log_3 (x) = 1 x =

$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{x}\right)\:+\:\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{x}\right)\:=\:\mathrm{1}\: \\ $$$$\mathrm{x}\:=\: \\ $$

Question Number 86507 Answers: 0 Comments: 1

If e^(cos x) −e^(−cos x) = 4, then the value of cos x is

$$\mathrm{If}\:{e}^{\mathrm{cos}\:{x}} −{e}^{−\mathrm{cos}\:{x}} =\:\mathrm{4},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{cos}\:{x}\:\mathrm{is} \\ $$

Question Number 86499 Answers: 1 Comments: 1

The digit at unit′s place in the number 17^(1995) + 11^(1995) −7^(1995) is

$$\mathrm{The}\:\mathrm{digit}\:\mathrm{at}\:\mathrm{unit}'\mathrm{s}\:\mathrm{place}\:\mathrm{in}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{17}^{\mathrm{1995}} +\:\mathrm{11}^{\mathrm{1995}} −\mathrm{7}^{\mathrm{1995}} \:\:\mathrm{is} \\ $$

Question Number 86498 Answers: 0 Comments: 0

If (1/(√(4x+1))){(((1+(√(4x+1)))/2))^n − (((1−(√(4x+1)))/2))^n } = a_0 +a_1 x+...+a_5 x^5 , then n=

$$\mathrm{If}\:\frac{\mathrm{1}}{\sqrt{\mathrm{4}{x}+\mathrm{1}}}\left\{\left(\frac{\mathrm{1}+\sqrt{\mathrm{4}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} −\:\left(\frac{\mathrm{1}−\sqrt{\mathrm{4}{x}+\mathrm{1}}}{\mathrm{2}}\right)^{{n}} \right\} \\ $$$$\:\:\:\:=\:{a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+...+{a}_{\mathrm{5}} {x}^{\mathrm{5}} ,\:\mathrm{then}\:{n}= \\ $$

Question Number 86491 Answers: 2 Comments: 1

∫ ((x^2 +1)/(x^4 +1)) dx ?

$$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:?\: \\ $$

Question Number 86490 Answers: 1 Comments: 1

If sin θ + cos θ=(√2) cos θ then cos θ−sin θ is equal to

$$\mathrm{If}\:\:\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta=\sqrt{\mathrm{2}}\:\mathrm{cos}\:\theta\:\mathrm{then} \\ $$$$\mathrm{cos}\:\theta−\mathrm{sin}\:\theta\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 86486 Answers: 0 Comments: 5

If sin x + cos x = (2/3) find (1/(sin x)) + (1/(cos x)) = ?

$$\mathrm{If}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}}\:=\:? \\ $$

Question Number 86484 Answers: 2 Comments: 9

∫(x^6 /(1+x^(12) ))dx

$$\int\frac{{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{12}} }{dx} \\ $$

Question Number 86480 Answers: 0 Comments: 1

∫_0 ^∞ (x e^(1−x) −⌊x⌋e^(1−⌊x⌋) )dx

$$\int_{\mathrm{0}} ^{\infty} \left({x}\:{e}^{\mathrm{1}−{x}} \:−\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$

Question Number 86479 Answers: 1 Comments: 0

a ball is droped from a height 20 m. Given that it rebounce with a velocity of (3/4) that which it hit the ground find the time interval between the first and second rebounce.

$$\mathrm{a}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{droped}\:\mathrm{from}\:\mathrm{a}\:\mathrm{height}\:\mathrm{20}\:\mathrm{m}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{it} \\ $$$$\mathrm{rebounce}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{that}\:\mathrm{which}\:\mathrm{it}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{time}\:\mathrm{interval}\:\mathrm{between}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{rebounce}. \\ $$

Question Number 86476 Answers: 0 Comments: 1

show that sin^(−1) α=−i ln (α±(√(α^2 −1)))−(π/2)

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \alpha=−{i}\:\mathrm{ln}\:\left(\alpha\pm\sqrt{\alpha^{\mathrm{2}} −\mathrm{1}}\right)−\frac{\pi}{\mathrm{2}} \\ $$

Question Number 86472 Answers: 1 Comments: 0