 # Analytic geometry questions and answers

Recent questions in Analytic geometry skystasvs 2022-09-04

### The sum of the infinite geometric series $\left(x-1\right)+\left(x-1{\right)}^{2}+\left(x-1{\right)}^{3}...is...1/3$ . Determine the value of x. Kailey Vargas 2022-09-04

### The general term for a geometric sequence is given $by{t}_{n}=0.5\left(4{\right)}^{n+1}$. Determine the first fourterms. Leroy Gray 2022-09-03

### The length of a rectangle is 5m more than twice its width. Find the dimension of the rectangle, assuming that its perimeter is 28m. embelurildmixjm 2022-09-01

### The second term of a geometric sequence is 2 and the fifth term is250. What is the seventh term? Belen Moses 2022-08-20

### Please, help. People refer to the dimensions of things as ''2 by 4'' etc. I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). enseignement20 2022-08-19

### Write the coordinates of the vertices after a translation 9 units right.  assuolareuz 2022-08-16

### Some textbooks define a trapezoid as a quadrilateral with exactly one pair of parallel sides, while other textbooks say that a trapezoid has at least one pair of parallel sides.a. What are the consequences of choosing one of these definitions over the other? Which is correct?b. Is a parallelogram a trapezoid? Why or why not? Ebone6v 2022-08-06

### The sides of a tringle have lenghts X1=X+4 and 20 if the lengths of the longest side is 20, what Values of X make the triangle acute? Jaxson Mack 2022-08-05

### How many segments can be drawn using four points no three of which are collinear ganolrifv9 2022-07-30

### Suppose P and Q are two distinct points. Prove that there exists exactly one translation which sends P to Q Cristofer Graves 2022-07-29

### Consider the curve . Show that this curve passes through the points and find its arc length between these points. Raynor2i 2022-07-29

### TRUE OR FALSE? The law of sines and law of cosines can be used to find angle and sides measures in any triangle? Ishaan Booker 2022-07-27 capellitad9 2022-07-25

### Find the slope of a line a. parallel and b. perpendicular to the line x+2y=2. posader86 2022-07-25

### Show that lobachevsky's basic triangle formulas transform into standard formulas of spherical trigonometry if one replaces the sides a,b,c of the triangle by ia, ib, ic, respectively. Assume that the angle C is a right angle.Formulas: sinAcot(productb)=sinBcot(producta), cosAcos(productb)cos(productc)... pablos28spainzd 2022-07-15

### Let $\mathrm{△}ABC$ be a triangle of sides AB, AC and BC which has the following equations$AB\equiv {a}_{1}x+{b}_{1}y+{c}_{1}=0\phantom{\rule{0ex}{0ex}}AC\equiv {a}_{2}x+{b}_{2}y+{c}_{2}=0\phantom{\rule{0ex}{0ex}}BC\equiv px+qy+r=0$Then an angle $\mathrm{\angle }A$ is acute if$|\begin{array}{cc}{a}_{1}& {b}_{1}\\ p& q\end{array}||\begin{array}{cc}p& q\\ {a}_{2}& {b}_{2}\end{array}|\left({a}_{1}{a}_{2}+{b}_{1}{b}_{2}\right)<0$And the angle $\mathrm{\angle }A$ is obtuse if$|\begin{array}{cc}{a}_{1}& {b}_{1}\\ p& q\end{array}||\begin{array}{cc}p& q\\ {a}_{2}& {b}_{2}\end{array}|\left({a}_{1}{a}_{2}+{b}_{1}{b}_{2}\right)>0$But I absolutely have no idea how to prove this theorem. Caleb Proctor 2022-07-12

### Let ABCD be a convex quadrilateral, with $AC\cap BD=\left\{O\right\}$ , and $OB>OD$ , $OC>OA$Let E and F be the midpoints of (AC) and (BD), $EF\cap AB=\left\{J\right\}$ , $EF\cap CD=\left\{K\right\}$ , $CJ\cap BK=\left\{L\right\}$ . If M is the midpoint of (KJ), show that O-M-L are collinear. lilmoore11p8 2022-07-10

### How can I generate equations for 3D objects beyond the basics like spheres, cubes and pyramids? For example, how about a diamond? Janet Forbes 2022-07-10

### I want to find the general equation of the two lines of intersection of a one sheet hyperboloid to its tangent plane for the function$F\left(x,y,z\right)={x}^{2}+{y}^{2}-{z}^{2}=1$at$\left({x}_{0},{y}_{0},{z}_{0}\right)$The equation of the tangent plane is${x}_{0}x+{y}_{0}y-{z}_{0}z=1$ Kolten Conrad 2022-07-08

### Calculate angle between two vectors, given their rotation w.r.t. a third vector.I have three vectors, $\stackrel{\to }{a},\stackrel{\to }{b},$ and $\stackrel{\to }{c}$ in n-dimensional space. I know the coordinates of all three vectors and their dot products. Both $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$ are rotated away from $\stackrel{\to }{c}$ by an angle $\alpha$, in their own respective directions, obtaining ${\stackrel{\to }{a}}^{\prime }$ and ${\stackrel{\to }{b}}^{\prime }$ . What is the angle between ${\stackrel{\to }{a}}^{\prime }$ and ${\stackrel{\to }{b}}^{\prime }$ ?

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