# length

1. ### How can I relate the arc length to the acceleration of an object with rotation?

The problem is as follows: A spheric strawberry candy is spinning inside a centrifuge in a confectionery. Find the magnitude of the acceleration in $\frac{m}{s^{2}}$ of the candy after $4\,s$ from the beginning of its rotation. It is known that the arc length follows the function $s(t)=1+t^3$...
2. ### General expression for the total length

i want to derive an expression to calculate the total length of the green lines in the following figure. 1. Firstly we have a L-shape frame of green lines. 2. Horizontal green lines are places inside the frame starting from the bottom, each "D" distance apart. 3. Vertical green lines are...
3. ### Can the length of this triangle be solved using congruence?

I found this riddle in my book. Supposedly it should be solved without requiring trig. The problem is as follows: A CTV broadcasting tower is resting atop a square flat base in the highest hill of Taipei. The tower is supported by five cables which are held tight to the ground by four...
4. ### Calculate third point of triangle given angle and line length

I have a triangle with the three points named A, B and C. I know the coordinates of A and B and need to calculate C. I also know the angle a and that |AB|=|AC|. Unfortunately the only formulas for triangles I remember, are about calculating an unknown length or angle, and I need the coordinates...
5. ### The length of an edge of a cube

Dear Forum Members: Can anyone give me an algorithm for finding the length of an edge of a cube, given the volume of that cube? Thank you.:) Best regards, Carl James Mesaros
6. ### Finding Chord length given arc length and arc height?

I'm not sure this is possible but I'm in the process of building a tent and am trying to get two curved surfaces to meet. How can I find the length of a Chord of a circle if I have the Arc length and Arc height? I'm not sure this is possible without the radius but maybe there is...
7. ### How to find the smallest length in a triangle when the angles aren't known?

I am confused on how to find the answer for this problem. So far what I believe would apply is the triangle inequality but I'm not sure on how to use it. The figure $ABC$ is a triangle so as $BDC$. It is known that the length of $AB = 8$ inches and $\angle BAD = 2\,\angle BCD$ and...
8. ### How to find the length of an iron bar when it is given as a function of its size but

I'm not very sure how to solve this problem, but it looks to be related with division of polynomials. Can somebody give me some help with this?. The problem is as follows: In an auto factory in Hsinchu, a technician is in charge of a robot which its function is to cut steel bars for a coupÃ©'s...
9. ### How to do the computation of a spiral length in a disk using college algebra?

I have found this riddle in my book and so far I've not yet come with an answer which would require the use of college precalculus. In a research facility in Taiwan a group of technicians built a new optical disk which stores information in a spiral engraved in its bottom face named "lecture...
10. ### what is the length

What is x in the attached? All I can think of is to draw a line from A to E, but that doesn't seem to help much either. Answer is 2 * sqrt 6, but I do not know how they obtained this.
11. ### tower of length n of finite number fields of odd class numbers?

Hello Let $n$ be any positive integer. Did anyone before construct a tower of length $n$ of finite number fields of odd class number? Do you have any idea about how to do that?
12. ### sector length. and resultant load

https://imgur.com/a/wNbIEES Hi for the geometry shown in the attached How to calculate the total load q/cos(beta) (force/meter) on a circle sector (Radius= R), with an angle of (delta) as shown in the attached (need to find the length of the curve (L), not sure how to find it, I reckon...
13. ### Find ellipse sector line length?

So if I know a and b of the ellipse and also the angle of it. How can I calculate the curved line from the point of b to the point of a? I want the length of the curved line. For example: In a circle you can calculate the circle sector by knowing the angle and the radius.. If possible using...
14. ### Working the height out

You want to get out of the sun and look for some shade. There are some trees by the side of the lake. You know you are just below 2 metres in height. Estimate the height of the tree. m This answer will be marked within a reasonable range.
15. ### Need to calculate the length of an arc

Hello, Need to make an arc that is 16' wide at the base, and rises 12" in the centre. It'll be a perfectly curved arc. I need to know what the length of the beam for the arc should be. I looked up formulas online, but they all want the degree of the arc, but I won't have that until I build...
16. ### Length of vectors

Hey! I need some help with this task: Suppose that u1,u2 is an orthonormal basis of R2, that means u1*u2=0 and ui*ui=1, i=1,2. Let y=[<y1,y2>] be a vector in R2 and v = y1u1 + y2u2. Show that the vectors y and v are equal in length. The v vector is a sum of two scalar products. I don't...
17. ### Can you find side length of a triangle given three angles?

Can you mix dimensionless function or angles to find length in triangles? For example, two sides are composed of a distance of $0.85+0.4=1.25$ and at the same time $0.4=\cos\theta$and the base is $1$? For consecutive numbers or non-consecutive numbers $x<y<z$, I have the following example...
18. ### Finding the factor with which length increases

I want to prove that if there is a change in angle, length in y changes with the factor: sec Ï†. A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length...
19. ### How do I work out the maximum area of a right triangle with a fixed length hypotenuse

How do I work out the maximum area of a right triangle given a fixed length hypotenuse? I have watched several YT videos and ALL are based upon the ASSUMPTION the other two angles are 45 degrees - and whilst this may be true, this is exactly what I need to prove - so I'm looking for a formula...
20. ### Length of curve

I am given the curve x^2=3y, 2xy=9 and I need to find the length but between A(0,0,0) and B(3,2,2). I'm kinda stuck..no idea how to start.