A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a straight line cutting the rectangle without cutting any domino.

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

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Q: 15, Find a) fxedx b). dx using the substitution of x- cost.

A: We have to evaluate the integrals

Q: A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach…

A: Given: A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to…

Q: What is the number of pathways of getting from A to C travelling along grid lines and moving only to…

A: Given pathway Either we move to right or move up. The number of right moves needed to reach to…

Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

A: Family of lines contains parameters.

Q: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points…

A: Given that receiving station x = (15,7)   ,  y = (-9 , -3) &   z = (-9 , 7)Now, let coordinate…

Q: Construct a clamped cubic spline passing through the points 9, 13 and 22 with fx=x3+1

A: f(x)=x3+1y0=f(9)=730y1=f(13)=2198y2=f(22)=10649 Here h0=4h1=9 For given set of points (x, y) that is…

Q: QUESTION 1 Is y-Vy a polynomisl?

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Q: prove the parallelogramequlity:

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Q: Given: mTRV = 60° M2TRS = (4x)° %3D Prove: x = 30 Z. 60° R (4x)° W

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Q: 2) Find the area of triangular ABC of points (4,6,12), (2,7,6) and (-2,5,6).

A: From the given data:

Q: 2. Find the desivative ofy= Binx

A:

Q: is the find the areas of the other regular polygons listed on the chart, (Show your work) and then…

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Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

A:

Q: A cube has four diagonals. Show that no two of them are perpendicular.

A: Given: A cube has four diagonals.

Q: Conotrut a onatn'x whode Columu 8pure (leli2) & whole cli5) 10 is spanned by now &pale in Bpanned by

A: Column space is spanned by 3-dimensional vector. Row space is spanned by 2-dimensional vector.…

Q: Suppose that you want to evaluate point (8,3): Compute w:(18- al+ 13 - bil) = K For each contour…

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Q: 1. A bowl contains 10 red and 10 yellow balls, how many balls must be selected to ensure 5 yellow…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Sketch ler=qcose

A: The given curve is  1-r2=9cos(θ)

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: The graph of the corresponding equation of a linear inequalityis a line that separates the xy-plane…

A: We have complete the missing word/words.

Q: Use Lagrange multipliers to find the dimensions of a rectangular box with largest volume if the…

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Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Assume that a circular pizza is being cut into pieces. If there are C cuts and I points of…

A: It is a counting problem .

Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

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Q: Evaluate ff xydxdy over the square with corners (0,0), (1,1), (2,0) and (1, –−1) (u + v) (u - v) 2 2…

A:

Q: If the interval [1, 9] is partitioned into 4 subintervals of equal length, what is ∆x? List the grid…

A: Since n = 4 on the interval 1, 9 then                                               ∆t=b-an=2 where…

Q: Show that K, is not planar.

A: To prove: K5 is not a planar graph. Proof:  This is proved by the method of contradiction. We use…

Q: 17. Find two positive integers such that their sum is 10 and maximize and minimize the sum of their…

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Q: and such that the sum of their squares is as small as possible. Give the sum of the squares.

A: Given problem:- 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such…

Q: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: Find the maaimum and miniryem Valiaes of e feencteon Cif exits) feny) Luž-3ary

A:

Q: A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach…

A:

Q: Find all points where fex)= |21x-131 fails be be differenbiadle

A: Given:- f(x) = |21x-13| To find:- All points where function non differentiable

Q: Solve the BVP on interval Lo, nJ) 2 %3D 2.

A:

Q: 10. If mLTSV = (6x + 17) and mSV = (15x + 13)", find mSUV. %3D T

A: Property used is (11) An exterior angle of a triangle is equal to the sum of the opposite interior…

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: Since a line segment is defined by two distinct points, therefore the total number of line segments…

A:

Q: Show that the equadion Can also be obtaind from the fellowing squation 4(一 20 where and

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: HW.12 Describe in your own words, what is Limear tram furmatim" How the' concept of meant by n…

A: Linear Transformation:      A linear transformation of matrix is changes the original value to the…

Q: 10. If mZTSV= (6x + 17) and mSV = (15x + 13)', find mSUV. %3D T

A: A circle

Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: FIND THE APEA POONDED BY THE CUPVES y"=x"(4-x

A: We have to find the area bounded by the curve.

Q: Suppose the product of x and y is 49 and both x and y are positive. What is the minimum possible sum…

A:

Q: A river flows between the lines x = 3 and x = 4. Where should a bridgebe constructed to minimize the…

A: A river flows between the line x=3 and x=4. Bridge constructed to the path from O(0,0) to P(5,4).

Q: Find mZ1 in circle O. mAB = 42x, and 6x2. %3D mCD = %3D

A: Clearly we can see that chord BD is bisected by the radius OC. Hence,  mBC = mCD  mBC  =  (6x2)°…