Find integers s and t such that 330s + 156t = gcd(330, 156).

Q: Find two positive real numbers x and y such that they add to 120 and x2y is as large as possible.

A: Oue Aim is to find two positive real nnumbe x and y such that theyadd to 120 and x2y is as large as…

Q: ind the three positive numbers I, y, and z with minimal sum whose product is 64.

A:

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

A:

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

Q: For every real m x n matriz mx m) and a diagonal m x n matriz

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Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

A:

Q: Find the number of ideals in Cx,y that contains both the polynomials y – (x – 1)³ +1 and p(x) in…

A: We have to find the number of ideals in ℂx,y that contains both the polynomials y-x-13+1 and px in…

Q: Find the value of the Conj uction g(+) ifya know that w(f.g)=3e" and fCo=et (Wronskain)

A: We will find out the required value of g(t).

Q: Find the zero(s) of f

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Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: F L (a) Given A = use the Cayley-Hamilton theorem to find (1) A¹-3A6 + A¹+ 3A³ - 2A² +31 (ii) A*,…

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Find a number t such that In(4t + 3) = 5 %3D

A:

Q: Prove that P(A) - P(3)| 4 P(AAB). where A is the symmetric difference.

A: The following identity can be proved after breaking the LHS and RHS into mutually exclusive events,

Q: inf f, is not measurable Vn. Isisn ulgn

A: False Statement

Q: Find the sum of f(i) = 2i +2 over the integers 1, 2, 3, ..., 20.

A: Given,           The sum of fi=2i+2 over the integers 1,2,3,...,20

Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

A:

Q: 5. For z=x2siny show that 332 332 = дудхду дугдх

A: Topic = Derivative

Q: nd the supremum and infimum of the set D defined by D:= :neN

A:

Q: 3. Prove that R² is Hausdorff. Is R²T3? Is R² T4?

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: c. Find all the points X1 x2 in R3 [x3. that are transformed to Explain.

A: Given, the transform spantial coordinates                               x1x2x3into plane coordinate…

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: Q3. Show that p = 1– x + 3x? and q = 9x + 3x? product in are orthogonal with respect to the inner…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: Use the inner product (p, q) = aobo + ab1 + azb2 to find (p, q), ||P||. ||9||, and d(p, q) for the…

A:

Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: test the conver gehre and dvelyence n coscnt)

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Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

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Q: Find the two positive integers x and y such that x + y = 60 an 2 xy is maximum

A: The equation is x+y=60 where x and y are two positive integers. The main objective is to find x and…

Q: 8. Triangle GHI with verlices G(O.-2). H7.-6), and (3,-8): 270 counterciockwise G H:

A:

Q: Find the value of a such that 1 0. 3 2 2 a- 2

A: I have solved the determinant

Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

A:

Q: For the pairs of integers a=13, b=32, find the gcd g and integers x and y satisfying g=ax+by. Attach…

A: Given that, the pair of integersa=13,b=32 The equation is: g=ax+by where g is the gcd.

Q: Q2) If f(x) = (x), and g(x) = (2- x)i find (gof) (x) and the domain of (gof)(x).

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Q: R. find he Corficient of

A: We need to find coeffiient.

Q: (P^Q)^(P = ¬(Q^R))^(S = R) = -S

A:

Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn|       ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: Find the standard basis B, of Eg for the polynomial q(s) = s + 4s2 – 3s – 18.

A:

Q: Find all pairs of consecutive even positive integers, both of which are larger than 5 such that…

A: We have to find all pairs of consecutive even positive integers, both of which are larger than 5…

Q: Find k such that P(k< T < 2.947) = 0.845 when T~t15

A: In this case, the random variable T follows t distribution with degrees of freedom of 15.

Q: Use the inner product (p, q) = a b + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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Q: Find all solutims in 15e interval T or 27) bele 2c05メー3c0sX = -

A: Given: Find all solutions in the interval [0, 2π). The equation is:…

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.