# length

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. ### Triangle Question Regarding Altitude and Segment Lengths

RE is an altitude of triangle RST. Find the measures of MN, NE, and RT. I would appreciate it deeply if someone could help me figure out NE and RT. I already know that MN is 14, but I don't know how to find the two other segments.
3. ### Arc Length

Calculate the arc length of the curve y = ln(sin(x)) over the interval [pi/6, pi/2] f'x = cos(x)/sin(x) Integral [pi/6, pi/2] sqrt (1+((cos(x)/sin(x))^2) dx = -ln(2-sqrt3)????
4. ### Arc length of cardioid using line integral techniques

I've written out the question and my work thus far. If someone tell me if I'm on the right track or not, it would help a lot.
5. ### Scaling a vector to a known length

I did a bunch of browsing around online, and couldn't find the solution to a problem I'm looking to solve involving vectors. So, I figured I'd check around here. I'm a Computer Science major, but my university didn't have me take linear algebra, so this problem I've found has me stumped. Here...
6. ### Equally separated Arc Length

Hi guys, Say we have a smooth continuous real single variable function f(x) defined on a closed finite interval [a,b]. Lets say the Arc Length on that interval is L, then if I want to partition L into n equal segments (i.e. of length L/n) and solve for the values of x that correspond to said...
7. ### Parallelogram Help?

A parallelogram exists within a rectangle which measures 15 inches tall by 20.5 inches wide. A=15 inches B=20.5 inches C=1.5 inches (C makes a 90° angle with X) Solve for lengths X and Y and angle Z of the parallelogram and please tell me how you did it!
8. ### Graph theory: Prove that each cycle has minimum length of 5

Hi, I'm stuck with this proof. Given graph G How can I prove that each cycle in this graph has a minimum length of 5? Thank you very much for your help!
9. ### find arc length

how to integrate the integral that I gt ? I'm asked to find the arc length of the curve
10. ### arc length

i want to find the arc length of x= (y^4)/8 + 0.25/y^2 , the ans given is 0.609,but i gt 5/6
11. ### finding the arc length

i have problem of integrating the terms here , how to continue ?
12. ### Measuring the length of the sides of a triangle type problem?

I can't figure this out for the life of me(Crying). King Kong stands on the edge of the roof of a 62 foot high building. You poke your head out of a manhole and measure the angles of elevation to the top of King Kong's head and to his feet as 60 degrees and 59 degrees respectively.
13. ### Finding the directrix,focus, the length of focal chord, and a rough sketch.

x= 1/20(y-3)^2-7
14. ### Need a step by step explanation of how to solve this arc length problem

Hello, I would like a step by step explanation of how to solve the arc length problem below. I attempted to solve it myself, but there's no way my answer could be correct, which is why I am seeking the help of somebody more experienced. Find the length of the arc between x = 0 and x = 9 for the...
15. ### Arch Length of a curve

Find the length of the curve y=x^5/4 on the interval; [0,1]. Hint(write the arc length integral and let u^2=1+((5/4)^2)(sqrt(x)) -the whole u^2 substitution has me very confused
16. ### Arch Length of a Parabola

Find the length of the curve y=ax^2 from x=0 to x=10 where a>0 is a real number Arch length= So far I have found the derivative and got 2ax which I put into the formula and got integral from 0-20a (sqrt(1+(2ax)^2) dx I am confused as to how I solve this using a trig substitution: do I...
17. ### Curve Length - # 2

Find curve length 0 \leq t \leq 1 r(t) = 9ti + 12t^{3/2}j + 9t^{2}k r'(t) =<9i + \dfrac{3}{2}(12)t^{1/2}j + 18tk> [/B]r'(t) =<9i + 18t^{1/2}j + 18tk> |r'(t)| = \sqrt{(9)^{2} + (18t^{1/2})^{2} + (18t)^{2}} |r'(t)| = \sqrt{81 + 18t + 324t^{2}} \int_{0}^{1} \sqrt{81 + 18t + 324t^{2}} dt...
18. ### Curve Length

r(t) = <9t, 3 \cos t, 3\sin t> r'(t) = <9, -3 \sin t, 3 \cos t> |r'(t})| = \sqrt{9^{2} + (-3\sin t)^{2} + (3 \cos t)^{2}} |r'(t})| = \sqrt{81 - 9 \sin^{2} t + 9 \cos^{2} t} |r'(t})| = \sqrt{81- 9( \sin^{2} t +\cos^{2} t)} |r'(t})| = \sqrt{81- 9( 1)} = \sqrt{72} \int_{-5}^{5} \sqrt{72} t...
19. ### finding the length of the chord using info about cone surface area

A problem asks to find the length of a chord CB given chord AC length = 8 and the total surface area of a cone = 60 * pi and a slant height = 7. Please see attached file. I found the formula for the surface area of a a cone equals pi * r2 + pi * r * l where l is the slant height. I wasn't...
20. ### Finding the arc length problem

please see attached file The problem states OA = 4, measure angle AOD = 160 degrees and measure of arc DC = 88 degrees. What is the arc length of BC? The answer given is 8/15 * pi I found the arc length to be 88 degrees which I don't believe matches the answer. Can someone help?