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Question Number 177957 Answers: 2 Comments: 0

let a > 0 find the sum of the infinite series 1 + (((loga)^2 )/(2!)) + (((loga)^4 )/(4!)) + (((loga)^6 )/(6!))...

$$\mathrm{let}\:\:\mathrm{a}\:>\:\mathrm{0}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\: \\ $$$$\mathrm{series} \\ $$$$\:\mathrm{1}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{2}} \:}{\mathrm{2}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{4}} \:}{\mathrm{4}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{6}} \:}{\mathrm{6}!}... \\ $$

Question Number 177922 Answers: 1 Comments: 0

Question Number 177870 Answers: 0 Comments: 0

Question Number 177859 Answers: 1 Comments: 0

Question Number 177835 Answers: 1 Comments: 0

Question Number 177400 Answers: 3 Comments: 2

∫((√(9a^2 −1))/a)da Evaluate

$$\int\frac{\sqrt{\mathrm{9a}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{a}}\mathrm{da} \\ $$$$ \\ $$$$\mathrm{Evaluate} \\ $$

Question Number 177336 Answers: 0 Comments: 3

A tank GM by 4m by 3m. calculate one−third of its volume. please help!

$$\mathrm{A}\:\mathrm{tank}\:\mathrm{GM}\:\mathrm{by}\:\mathrm{4m}\:\mathrm{by}\:\mathrm{3m}.\:\mathrm{calculate} \\ $$$$\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{its}\:\mathrm{volume}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}! \\ $$

Question Number 177179 Answers: 1 Comments: 1

If a number is 20% more the other, how much percent is the second number less than the first. please help!

$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20\%}\:\mathrm{more}\:\mathrm{the}\:\mathrm{other},\:\mathrm{how} \\ $$$$\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{number} \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{first}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}! \\ $$

Question Number 177068 Answers: 1 Comments: 0

Let a,b,c be real numbers such that: a+b+c=0. Prove that: ((a^2 b^2 c^2 )/4)+(((ab+bc+ca)^3 )/(27))≤0

$${Let}\:{a},{b},{c}\:{be}\:{real}\:{numbers}\:{such}\:{that}: \\ $$$${a}+{b}+{c}=\mathrm{0}.\:{Prove}\:{that}: \\ $$$$\frac{{a}^{\mathrm{2}} {b}^{\mathrm{2}} {c}^{\mathrm{2}} }{\mathrm{4}}+\frac{\left({ab}+{bc}+{ca}\right)^{\mathrm{3}} }{\mathrm{27}}\leqslant\mathrm{0} \\ $$

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Question Number 176607 Answers: 1 Comments: 0

Question Number 176440 Answers: 0 Comments: 0

Question Number 176424 Answers: 0 Comments: 0

Using perseval′s Identity Evaluate : ∫_0 ^∞ (((1−cosx)/x))^2 dx Mastermind

$$\mathrm{Using}\:\mathrm{perseval}'\mathrm{s}\:\mathrm{Identity} \\ $$$$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}}\right)^{\mathrm{2}} \mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 176360 Answers: 0 Comments: 0

Question Number 176132 Answers: 0 Comments: 0

Question Number 176098 Answers: 1 Comments: 0

The deviations of a set of numbers from 12 are 3, −2, 1, 0, −1, 4, 0, 1 and 2. Calculate the mean and standard deviation of the numbers.

$$\mathrm{The}\:\mathrm{deviations}\:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{numbers} \\ $$$$\mathrm{from}\:\mathrm{12}\:\mathrm{are}\: \\ $$$$\:\:\:\:\:\mathrm{3},\:−\mathrm{2},\:\mathrm{1},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{4},\:\mathrm{0},\:\mathrm{1}\:\mathrm{and}\:\mathrm{2}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\: \\ $$$$\mathrm{deviation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}. \\ $$

Question Number 176094 Answers: 0 Comments: 0

Question Number 176022 Answers: 0 Comments: 0

Question Number 176005 Answers: 0 Comments: 2

Question Number 175976 Answers: 1 Comments: 1

Question Number 175954 Answers: 0 Comments: 0

Question Number 175953 Answers: 1 Comments: 0

Question Number 175925 Answers: 1 Comments: 1

1^x +6^x +8^x =9^x find x ? Mastermind

$$\mathrm{1}^{\mathrm{x}} +\mathrm{6}^{\mathrm{x}} +\mathrm{8}^{\mathrm{x}} =\mathrm{9}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 175888 Answers: 1 Comments: 0

Solve the differential equation (dy/dx)=((1+y^2 )/(y(1−x^2 )))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }{\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)} \\ $$

Question Number 175746 Answers: 1 Comments: 0

Solve the differential equation 2(2xy+4y−3)dx+(x+2)^2 dy=0 Mastermind

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{2}\left(\mathrm{2xy}+\mathrm{4y}−\mathrm{3}\right)\mathrm{dx}+\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \mathrm{dy}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 181509 Answers: 1 Comments: 0

Solve: (dy/dx)=((y^2 −3xy−5x^2 )/x^2 ) y(1)=−1 M.m

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}^{\mathrm{2}} −\mathrm{3xy}−\mathrm{5x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{1}\right)=−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

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