# parallel

1. ### Trapezoid Question Regarding Congruent Segments

In trapezoid ABCD, AD is parallel to BC. Points P, R, and M cut AB into four congruent segments; points Q, S, and N cut CD into four congruent segments. If AD=12 and BC=18, then AD+PQ+RS+MN+BC=? Can somebody help me with this question? Thank you!
2. ### xyz-space

Sketch a graph in the xyz-space and identify the plane as parallel to the xy-plane, xz-pane, or yz-plane and sketch a graph. a) y = 4 b) x = -2 ------------------ I don't understand why the answer for (a) is plane parallel to xz-plane!

Decide an equation in general form for a plane that is parallel to the vectors u and v and goes thru the point P=(1, 0, 3). Vectors: u=(1, -2, 0) v=(3, -5, 1) --- If the terminology is incorrect it is because I have tried to translate it from Swedish: "Ange, på normalform, en ekvation för det...
4. ### Equations of a line through a point, intersects z axis, and parallel to a plane

A question on my review guide asks for me to find the parametric equations of the line through the point (3,6,4) that intersects the z-axis and is parallel to the plane x − 3y + 5z = 6 . The answer should be (x = 3t + 3, y = 6t + 6 z = 3t + 4) Any help is appreciated!
5. ### Parallel segments between 2 circles

Hello! I have an interesting task i am trying to solve. Given are two circles with centers. A segment a is given too. We have to find all parallel segments to a with same length as a, such that on end of these segments lies on Circle 1 and the other end lies on Circle 2. Kind of tricky for...
6. ### line of intersection between two parallel planes

How can I find the line of intersection between the planes 2x-y+2x+1=0 and -4x+2y-4x-2=0 I realize these are parallel as they are multiples of each other, but I'm not sure how to solve for the point. I also have to convert this line into parametric, cartesian and vector form. Sorry for the...
7. ### Find the Distance between two parallel Lines

how to use the equation D=c1-c2/(A)^2+(B)^2 in this given question : 4x+y=6 12x+3y=14 i know how to use it on same A and B like this 3x+12y-4=0 3x+12y+15=0 but in the another given im confused

Stuck again (Headbang)...not sure what this question is asking me exactly, I've looking over all my class notes and I'm pretty sure we were never taught this. How exactly do I solve the: Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 at x = 2 that is parallel...
9. ### Machines in parallel

Hey, I had this little optimization problem and I kinda feel like my solution was too simple - maybe someone here might want to check it out? We have two machines, each capable of producing a product A. Machine 1 takes 14 minutes to finish, machine 2 takes 15 minutes. If the machines can work...
10. ### Projection Transformation on x Axis Parallel to y=2x

Let $T \colon \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be the projection transformation on x axis in parallel to $y=2x$. Find the representing matrix of $T^*$ for the standard basis $B=\left(\left \{1,0 \right \},\left\{0,1\right\}\right)$. I have a solution which I don't understand. A basis for...
11. ### When grad f(X) is parallel to X

Let f be a differentiable function in n variables, and assume that there exists a function h such that grad f(X) = h(X)X. Show that f is constant on the sphere of radius a>0 centered at the origin. I can show it when n=2, but proving it generally seems quite challenging. Can anyone help me out?
12. ### Finding parallel lines

Question: Find the value of a so that the lines y=3-(1/2)x and ay+3x=4 are parallel So if the slope of y=3-(1/2)x is -1/2 then I know that the other line has to have the same slope in order to be parallel. Rearranging the equation I get y=(4-3x)/a. I was thinking that a should be 6, so I'd get...
13. ### Parallel line calculations???

I have a set of lines where I know the beginning and end coordinates (X1, Y1, X2, Y2). What I need to calculate is a set of begin/end coordinates for parallel lines that makes the line a set distance away. Example, if I have coordinates (0,0,50,0), which is a horizontal line, and the...
14. ### Tangent/parallel plane of another

Hello guys, me again. I need someone to explain me how to get this: I have to find the two tangent planes of \frac{x^2}{8}+\frac{y^2}{2}+z^2 and parallels to x+2x+3z=1

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16. ### Proof that parallel lings converge at a point

I was thinking about how can this be proved? I haven't ever tried to prove anything, but just thought I'd give it a try. This was my plan: 1) $\Delta x' = \left| \dfrac{d \cdot x_{n+1}}{z+d} \right| - \left| \dfrac{d \cdot x_{n}}{z+d} \right|$ 2) Prove that as $\gamma$ gets "bigger", $z$...
17. ### Triangles and parallel lines problem

The picture includes the question and my attempts, can someone help me?
18. ### Calculating the extent of a star's orbit on the sky - need parallel functions?

Hello! I wrote an N-body simulator that plots the orbit of stars and planets. I have set it up so that it plots the orbit, which is calculated at the centre of mass of the star, as well as parallel lines +- a stellar radii from the orbit, i.e. showing the extent of the star on the sky over...
19. ### vecctor- line parallel / in plane

for part b and part c, i shown my working in the photo below. The ans is just below the question . pease refer it. i cant understand why the ans explain. can anyone explain in a more detailed way ?
20. ### Linear function equation help please

I need help understanding the following: write the equations, in general form, for the lines that pass through point (4,3) and are parallel AND perpendicular to the line y+1=5/7 (x-4). HELP PLEASE?