Can someone help me to prove this?
Let ABCD be a trapezium and AB||DC E and F are the mid=points of the oblique sides AD and BC respectively To be proved: EF is parallel to AB and DC Construction: After joining D and F,the line segment is produced to interect AB produced at a point P. Proof: In triangles CDF and BPF, CF=BF (given)
Can someone help me with a relation proof?
Is this a linear order on the natural numbers? Prove answer. V, where mVn iff m is odd and n is even, or m and n are even and m< or equal n, or m and n are odd and m< or equal n.
Can someone help me prove this identity: cos3x=4cos^3x-3cosx. Please show work. thanks?
Cos (3x) = cos(2x + x) = cos(2x)cosx - sin(2x)sinx Now substitute in your double-angle formulas and proceed from there. :)
Can someone help me prove this limit?
Use the Squeeze Theorem. The key idea is to use -1 ≤ cos t ≤ 1 for all t. Let t = 2/x: -1 ≤ cos(2/x) ≤ 1 for all nonzero x Multiply through by x^4 > 0: -x^4 ≤ x^4 cos(2/x) ≤ x^4 for all nonzero x. Since lim(x→0) ± x^4 = 0, we conclude that lim(x→0) x^4 cos(2/x) = 0. I hope this helps!
Can someone help me solve this trigonometry proof?
The proof is: (sin x + cos x) / (1 – cos x) = tanx. I've been trying to solve it, but I keep getting stuck. Can someone help me PLEASE?!
Can someone help me prove this identity cot-tan=cos2/sincos?
cot x - tan x = (cos x/sin x - sin x/cos x) = (cos² x - sin² x)/sinx cos x = cos 2x/sinx cos x
How can I prove someone wrong that left me when I needed her and told me I will never be able to reach my goal without her help?
Unless you paid her money and she r failed to deliverthere is nothing you can doand she does not act like a friend. Learn your lessonIf she told you you need herthen you don;t need herwalk away and carry on with your lifeIt’s your life
Can someone provide a hint to help me complete the proof that [math]f(m,n) = 2^{m-1}(2n-1)[/math] is bijective?
We’re considering a function [math]f:S\to T[/math] where [math]S[/math] is the set of ordered pairs of positive integers, [math]T[/math] is the set of positive integers, and [math]f[/math] is the function such that [math]f(m,n)=2^{m-1}(2n-1)[/math].One way to show that [math]f[/math] is bijective is to show that it’s one-to-one (injective) and onto (surjective).Onto (surjective)You need to show that a positive integer [math]k[/math] can be expressed as [math]2^{m-1}[/math] times [math]2n-1[/math]. Let [math]m-1[/math] give the highest power [math]2^{m-1}[/math] that divides [math]k[/math]. Note that [math]m[/math] is a positive integer. Then [math]k/2^{m-1}[/math] is an odd number, and every odd number is of the form [math]2n-1[/math] for some positive integer [math]n[/math]. Therefore [math]k[/math] is in the image of [math]f[/math]. Since that’s true for all [math]k\in T[/math], therefore [math]f[/math] is onto.One-to-one (injective)You need to show that a no positive integer [math]k[/math] can be expressed in two different ways as a product of a power of [math]2[/math] and an odd number. I’ll leave that to you.BijectiveTherefore [math]f[/math] is bijective. In the process of this proof, we’ve described the inverse function [math]g:T\to S[/math]. Here [math]g(k)=(m,n)[/math] where [math]m[/math] and [math]n[/math] are as described above. It’s the inverse function because it satisfies the two equations [math]f(g(k))=k[/math] and [math]g(f(m,n))=(m,n)[/math].Sometimes it’s easier to show a function by showing it has an inverse.
Can someone prove to me God isn't watching us?
I don't think anyone can prove to you God isn't watching you. Nanana, I have never met you, but I know what it's like to want to know the details of God. How over thinking some things is futile... and exhausting. I read an article a while back, and it made me think of you, and the many questions that swirl around in your head and heart. "your ocd is in your thoughts. You think about things to the point of obsessing about them." (to which, when the author of the article was told these things by a psychologist said, "well, that's just awesome." I just wanted to tell you not to fret about the things that have no obvious answers. One day, all things will be made known. In saying this, God did not leave us alone without any truth. Letter to John Hagee (click the link) It's a critique of John Hagee's sermon by L. Ray Smith. It explains who God really is, why we are here, and the final destination of all mankind according to scripture. It will also answer your question of WHY you ask "Can someone prove to me God isn't watching us?" At the bottom of the linked article is a "Home" link that will take you to the home site that answers many more questions in detail. I sincerely hope this article helps you find answers as much as it helped (and is helping) me.