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Question Number 9732 Answers: 1 Comments: 0

Find equation of an ellipse whose major axis is vertical, with the center located (− 1, 3) at the distance between the center and one of the covertices equal to 4, and the distance between the center and one of the vertices equal to 6.

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ellipse}\:\mathrm{whose}\:\mathrm{major}\:\mathrm{axis} \\ $$$$\mathrm{is}\:\mathrm{vertical},\:\mathrm{with}\:\mathrm{the}\:\mathrm{center}\:\mathrm{located}\:\left(−\:\mathrm{1},\:\mathrm{3}\right) \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{center}\:\mathrm{and}\:\mathrm{one}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{covertices}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{4},\:\mathrm{and}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{center}\:\mathrm{and}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vertices}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{6}. \\ $$

Question Number 9731 Answers: 1 Comments: 1

Find the asymptotes of the hypebola whose equation is given by. (x/(24)) − (y/(29)) = 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{asymptotes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hypebola}\:\mathrm{whose} \\ $$$$\mathrm{equation}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}. \\ $$$$\frac{\mathrm{x}}{\mathrm{24}}\:−\:\frac{\mathrm{y}}{\mathrm{29}}\:=\:\mathrm{1} \\ $$

Question Number 9727 Answers: 0 Comments: 6

Find a x integer: [Σ_(k=1) ^∞ ((sin(2Πkxπ))/k)] + [Σ_(k=1) ^∞ ((sin(2Πkxe))/k)] = 0 Where: 𝚷 represents 180° ; 𝛑 represents 3,14159265358... .

$$\mathrm{Find}\:\mathrm{a}\:\boldsymbol{{x}}\:{integer}: \\ $$$$\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kx}\pi\right)}{{k}}\right]\:+\:\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kxe}\right)}{{k}}\right]\:=\:\mathrm{0}\: \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Where}}: \\ $$$$\boldsymbol{\Pi}\:\mathrm{represents}\:\mathrm{180}°\:; \\ $$$$\boldsymbol{\pi}\:\mathrm{represents}\:\mathrm{3},\mathrm{14159265358}...\:. \\ $$

Question Number 9723 Answers: 0 Comments: 0

If ∫_0 ^x f(t) dt = x+∫_x ^1 t f(t) dt, then the value of f(1) is

$$\mathrm{If}\:\:\overset{{x}} {\int}_{\mathrm{0}} {f}\left({t}\right)\:{dt}\:=\:{x}+\underset{{x}} {\overset{\mathrm{1}} {\int}}\:{t}\:{f}\left({t}\right)\:{dt},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{1}\right)\:\:\mathrm{is} \\ $$

Question Number 9722 Answers: 0 Comments: 4

If the roots of the quadratic equation x^2 +px+q=0 are tan 30° and tan 15° respectively, then the value of 2 + q−p is

$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:\mathrm{are}\:\mathrm{tan}\:\mathrm{30}°\:\mathrm{and}\:\mathrm{tan}\:\mathrm{15}° \\ $$$$\mathrm{respectively},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{2}\:+\:{q}−{p}\:\mathrm{is} \\ $$

Question Number 9715 Answers: 1 Comments: 0

Vector A^→ of magnitude 20 unit, lies in the direction 45°S of E while vector B^→ of magnitude 30 units in the direction 60°W of N. calculate the scaler product A^→ ∙B^→

$$\mathrm{Vector}\:\overset{\rightarrow} {\mathrm{A}}\:\mathrm{of}\:\mathrm{magnitude}\:\mathrm{20}\:\mathrm{unit},\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{direction}\:\mathrm{45}°\mathrm{S}\:\mathrm{of}\:\mathrm{E}\:\mathrm{while}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{B}}\:\mathrm{of}\:\mathrm{magnitude} \\ $$$$\mathrm{30}\:\mathrm{units}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{60}°\mathrm{W}\:\mathrm{of}\:\mathrm{N}. \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{scaler}\:\mathrm{product}\:\:\overset{\rightarrow} {\mathrm{A}}\centerdot\overset{\rightarrow} {\mathrm{B}} \\ $$

Question Number 9717 Answers: 0 Comments: 0

((0.ba^− +0.ab^− )/(1/(ab−ba)))=3 ⇒ a^(2 ) − b^(2 ) =?

$$\frac{\mathrm{0}.\mathrm{b}\overset{−} {\mathrm{a}}+\mathrm{0}.\mathrm{a}\overset{−} {\mathrm{b}}}{\frac{\mathrm{1}}{\mathrm{ab}−\mathrm{ba}}}=\mathrm{3}\:\Rightarrow\:\mathrm{a}^{\mathrm{2}\:} −\:\mathrm{b}^{\mathrm{2}\:} =? \\ $$

Question Number 9709 Answers: 1 Comments: 0

A vertical pole 3m high is 2m south of a wall which runs directly east and west. The sun is south west at an elevation of 35°. Find to the nearest centimeter the height of the shadow of the pole on the wall.

$$\mathrm{A}\:\mathrm{vertical}\:\mathrm{pole}\:\mathrm{3m}\:\mathrm{high}\:\mathrm{is}\:\mathrm{2m}\:\mathrm{south}\:\mathrm{of}\:\mathrm{a}\:\mathrm{wall} \\ $$$$\mathrm{which}\:\mathrm{runs}\:\mathrm{directly}\:\mathrm{east}\:\mathrm{and}\:\mathrm{west}.\:\mathrm{The}\:\mathrm{sun} \\ $$$$\mathrm{is}\:\mathrm{south}\:\mathrm{west}\:\mathrm{at}\:\mathrm{an}\:\mathrm{elevation}\:\mathrm{of}\:\mathrm{35}°. \\ $$$$\mathrm{Find}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{centimeter}\:\mathrm{the}\:\mathrm{height}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{shadow}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pole}\:\mathrm{on}\:\mathrm{the}\:\mathrm{wall}. \\ $$

Question Number 9704 Answers: 1 Comments: 0

Question Number 9707 Answers: 1 Comments: 1

How many paving stones each measuring 2.5m×2m are required to pave a rectangular courtyard 30m long and 16.5 m wide?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{paving}\:\mathrm{stones}\:\mathrm{each}\:\mathrm{measuring} \\ $$$$\mathrm{2}.\mathrm{5m}×\mathrm{2m}\:\mathrm{are}\:\mathrm{required}\:\mathrm{to}\:\mathrm{pave}\:\mathrm{a}\:\mathrm{rectangular} \\ $$$$\mathrm{courtyard}\:\mathrm{30m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{16}.\mathrm{5}\:\mathrm{m}\:\mathrm{wide}? \\ $$

Question Number 9699 Answers: 0 Comments: 3

Question Number 9698 Answers: 1 Comments: 0

a^2 +ab+b^2

$${a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \\ $$

Question Number 9690 Answers: 1 Comments: 3

Question Number 9686 Answers: 1 Comments: 0

Question Number 9683 Answers: 0 Comments: 2

Question Number 9678 Answers: 0 Comments: 1

Question Number 9677 Answers: 1 Comments: 2

Question Number 9675 Answers: 0 Comments: 2

Question Number 9662 Answers: 1 Comments: 0

I have 2 buckets. Each bucket contains green and blue balls The first bucket contains 3 green balls and 7 blue balls. Second bucket contains 7 green balls and 8 blue balls. I want to take those balls with coin toss. If head, I will take 1 ball from each bucket. But if tail, I will take 2 balls from each bucket. What is the propability if all the balls that have been taken have the same color? (sorry for my grammar)

$$\mathrm{I}\:\mathrm{have}\:\mathrm{2}\:\mathrm{buckets}.\:\mathrm{Each}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{green}\:\mathrm{and}\:\mathrm{blue}\:\mathrm{balls} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{7}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{Second}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{7}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{8}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{take}\:\mathrm{those}\:\mathrm{balls}\:\mathrm{with}\:\mathrm{coin}\:\mathrm{toss}. \\ $$$$\mathrm{If}\:\mathrm{head},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{1}\:\mathrm{ball}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{tail},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{2}\:\mathrm{balls}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{propability}\:\mathrm{if}\:\mathrm{all}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{that}\:\mathrm{have}\:\mathrm{been}\:\mathrm{taken} \\ $$$$\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}? \\ $$$$\left({sorry}\:{for}\:{my}\:{grammar}\right) \\ $$

Question Number 9661 Answers: 0 Comments: 3

a) 2^i = b) (a_1 + b_1 i)^(a_2 + b_2 i) = Powers of complex numbers ???

$$\left.{a}\right)\:\mathrm{2}^{{i}} \:=\: \\ $$$$ \\ $$$$\left.{b}\right)\:\left({a}_{\mathrm{1}} \:+\:{b}_{\mathrm{1}} {i}\right)^{{a}_{\mathrm{2}} \:+\:{b}_{\mathrm{2}} {i}} \:=\: \\ $$$${Powers}\:{of}\:{complex}\:{numbers}\:??? \\ $$

Question Number 9658 Answers: 1 Comments: 5

Experiment shows that the viscous force, F on a spherical body of radius, r moving with angular velocity, n is, F = Kr^a n^b ω^c . Where K is a dimentionless constant. using the method of dimentional analysis, determine the values of a, b and c

$$\mathrm{Experiment}\:\mathrm{shows}\:\mathrm{that}\:\mathrm{the}\:\mathrm{viscous}\:\mathrm{force},\:\mathrm{F} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{body}\:\mathrm{of}\:\mathrm{radius},\:\mathrm{r}\:\mathrm{moving}\:\mathrm{with} \\ $$$$\mathrm{angular}\:\mathrm{velocity},\:\mathrm{n}\:\mathrm{is},\:\mathrm{F}\:=\:\mathrm{Kr}^{\mathrm{a}} \mathrm{n}^{\mathrm{b}} \omega^{\mathrm{c}} . \\ $$$$\mathrm{Where}\:\mathrm{K}\:\mathrm{is}\:\mathrm{a}\:\mathrm{dimentionless}\:\mathrm{constant}. \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{dimentional}\:\mathrm{analysis}, \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c} \\ $$

Question Number 9654 Answers: 1 Comments: 0

lim_(x→4) ((ax+b−(√x))/(x−4))=(3/4), a+b=...?

$$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}−\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}},\:\:\mathrm{a}+\mathrm{b}=...? \\ $$

Question Number 9653 Answers: 0 Comments: 0

Question Number 9648 Answers: 1 Comments: 0

Question Number 9642 Answers: 0 Comments: 0

Question Number 9637 Answers: 2 Comments: 0

A body starts from rest and move with uniform acceleration of 6m/s^2 . what distance does it covered in the 3rd seconds.

$$\mathrm{A}\:\mathrm{body}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{move}\:\mathrm{with}\: \\ $$$$\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{6m}/\mathrm{s}^{\mathrm{2}} .\:\:\mathrm{what}\: \\ $$$$\mathrm{distance}\:\mathrm{does}\:\mathrm{it}\:\mathrm{covered}\:\mathrm{in}\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{seconds}. \\ $$

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