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If a,b,c and d is real numbers satisfy (a/b)=(2/3), (c/d)=(4/5), (d/b)=(6/7) then (a/c) =?

$${If}\:{a},{b},{c}\:{and}\:{d}\:{is}\:{real}\:{numbers} \\ $$$${satisfy}\:\frac{{a}}{{b}}=\frac{\mathrm{2}}{\mathrm{3}},\:\frac{{c}}{{d}}=\frac{\mathrm{4}}{\mathrm{5}},\:\frac{{d}}{{b}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${then}\:\frac{{a}}{{c}}\:=? \\ $$

Question Number 118825 Answers: 2 Comments: 0

I am thinking of a two−digit number .If i write 3 to the left of my number and double this three digit number the result is 27 times my original number. what is my number ?

$${I}\:{am}\:{thinking}\:{of}\:{a}\:{two}−{digit}\:{number} \\ $$$$.{If}\:{i}\:{write}\:\mathrm{3}\:{to}\:{the}\:{left}\:{of}\:{my}\:{number} \\ $$$${and}\:{double}\:{this}\:{three}\:{digit}\:{number}\:{the} \\ $$$${result}\:{is}\:\mathrm{27}\:{times}\:{my}\:{original}\:{number}. \\ $$$${what}\:{is}\:{my}\:{number}\:? \\ $$

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If α is a root of the equation 4x^2 +2x−1=0 . How do you prove the other root is 4α^3 −3α ?

$$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{1}=\mathrm{0}\:.\:\mathrm{How}\:\mathrm{do}\:\mathrm{you} \\ $$$$\mathrm{prove}\:\mathrm{the}\:\mathrm{other}\:\mathrm{root}\:\mathrm{is} \\ $$$$\mathrm{4}\alpha^{\mathrm{3}} −\mathrm{3}\alpha\:?\: \\ $$

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Given a transformation , T: C → C ; z → ω Show that if ω = ((z−i)/(z +1)) then z = ((ω + i)/(1−ω)). Hence the image of the line ∣z−i∣ = ∣z + 2∣ under the transformation T the ω−plane is a circle with center (−2,−i) and radius (√(10)) .

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{transformation}\:,\:\mathcal{T}:\:\mathbb{C}\:\rightarrow\:\mathbb{C}\:;\:{z}\:\rightarrow\:\omega \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\omega\:=\:\frac{{z}−{i}}{{z}\:+\mathrm{1}}\:\mathrm{then}\:{z}\:=\:\frac{\omega\:+\:{i}}{\mathrm{1}−\omega}.\:\mathrm{Hence} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mid{z}−{i}\mid\:=\:\mid{z}\:+\:\mathrm{2}\mid\:\mathrm{under}\:\mathrm{the}\:\mathrm{transformation} \\ $$$$\mathcal{T}\:\:\:\:\mathrm{the}\:\omega−\mathrm{plane}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{2},−{i}\right)\:\mathrm{and}\:\mathrm{radius}\:\sqrt{\mathrm{10}}\:.\: \\ $$

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∫x^x dx=?

$$\int{x}^{{x}} {dx}=? \\ $$

Question Number 106628 Answers: 0 Comments: 0

(((p−1))/p) where p=prime no. Remainder will always be (p−1) or −1 Que. find Remainder ((1!+2!+3!+........................1000!)/(10)) Que. ((1!+2!+3!+........................1000!)/(12)) Que. ((1!+2!+3!+........................1000!)/9) Que. What id the unit digit of below expression 1!+2!+3!+4!+......................1000! ANS. If we divide some number by 100,then remainder is last 2digit similary 1000----Last 3digit 10000 last 4 digit 100000 last 5 digits [(((1+2+3+4+0+0+0+..........+0)/(10))),() ] R=3 unit digit =3

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