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Polynomial Division Problem Calculate the following and state the remainder: 2x^3+x^2-22x+20 divided by 2x-3 Thanks!

Express [∑(n) (k=1) [3(1+4k/n)]*(4/n)] as a closed form (your answer will be in terms of n).

Given triangle with lengths a,b,c , prove that the sum of two random chosen lengths is larger than the other length.

i was looking at shor's algorithm and had a bright idea, square the numbers rather than multiply by a specific base. this idea however doesn't seem to work. for example, the followng code: def gcd(p,q): if p == 0: return q else: return gcd(q%p,p) N= 97*79 per = 1...

Circular track: Both are in same direction. A = 3m/sec, B = 1 m/sec. Circumference of track = 100m. What is the time taken by A & B to reach starting point for first time?

Hi all, Please take a look at the attached image of the problem and if someone could explain where the indicated value came from that would be so very helpful. I got everything but not quite sure why the sqrt2 was inserted towards the end.

Pentagon $ABCDE$ is inscribed in a circle. $AB \parallel EC$, $AE \parallel BD$. $AD \cap EC \equiv G$, $BD \cap EC \equiv F$ and $AC \cap BD \equiv H$. Prove that the area of $AGFH$ is equal to the sum of the areas of $DEG$ and $BCH$. --------

$T$ is the middle point of the segment $AB$ of the convex quadrilateral $ABCD$. The circle $\omega$, through points $C,D,T$, is tangent to $AB$. $K$ and $L$ are the intersection points of $AD$ and $BC$ respectively with $\omega$. $M$ and $N$ are the intersection points of $AC$ and $BD$...

A circle circumscribed to the triangle $ABC$. $D$ is a point on the circumcircle. Prove that symmetries of the point D according to the edges of the triangle are collinear.

A and B are racing at a 1 km track. A gives B a start of 100m and beats him by 15 sec. A, in his over confidence, now gives B a start of 90 sec, but loses by 500m. In how much time does A finish the race? Sol: 1st case: A does 1000m in t sec B does 900m in t +15 sec 2nd case...

A and B start from X and Y respectively at 10 am. They start moving towards Y and X respectively. If A reaches Y at 2 pm and B reaches X at 4 pm, then at what time do they meet? How to solve a distance problem ?

Given 3 random numbers x,y,z \in \mathbb{R}\;: (a) Find the number that is bounded by the two other numbers. Express it in terms of a function like \phi (x,y,z). (b) Express the largest number in terms of \phi(x,y,z).

Hi, I am not sure how to solve the problem as attached. Help needed. Thanks

(I'm not sure if this is the right sub-forum, but I didn't see a better fit.) I have a problem with an exercise in a machine learning text-book. Solving it doesn't require any knowledge of machine learning, though, just of advanced probability theory. It's a very simple exercise in principle...

Shatabdi express left Delhi 40 min late. After covering half of the distance it increased its usual speed by 1/6 of original speed and reached Chandigarh on scheduled time. Find usual time (in min) taken by Shatabdi express to cover complete journey. Solution: Speed Ratio; 6 : 7 Time ratio; 7 ...

Hello, my class has just started exploring rational equations. I have no problem solving the equations on their own but when I need to convert information into these equations I can confuse myself. If anyone can help me with turning these two problems into rational equations, I'd be really...

I'm listing a product for sale on Ebay, and wondering if someone can help solve this mathematical problem: If you sell a product to the US it costs let's say \$3 for the shipping, which we add into the overall sale price of the item. If we then sell the same product to the UK, it costs us...

What is the average speed of a man who works at 1kmph for 1 hour, 2 kmph for 2 hours........ till 10 kmph for 10 hours? A) Average speed = (Total distance)/(Total time) = (1*1+2*2+3*3…….10*10)/(1+2+3****+10) = {1/6 n(n+1)(2n+1)}/ {1/2 n(n+1)} = 2n+1/3; (n = 10) = 7...

What is the average speed of a man who travels 1/4th distance at 10kmph, 1/3rd the distance at 20kmph and the rest at 12.5 kmph? Solution: Remaining time = 1 – (1/4 + 1/3) = 5/12 Multiplying 12 to fractions to get whole numbers; 3, 4 & 5. After this how to proceed?

Dear My Math Forum Community: Could the n-body problem be a macroscopic manifestation of the Heisenberg and Born Uncertainty Principle? Thank you.:)