1. A rectangular page of unknown dimensions is to contain 24 square inches of print. The margins at the top and bottom of the page must be 1.5 inches, and the side margins must be 1 inch each. Use calculus to determine the dimensions that minimize the total size (area) of paper required.

Q: prove v(x1) = v(xn) → x1 injective if x1 ‡xn → v(x1) ‡ v(xn) v →x1 = xn ⇒

A: To prove: vx1=vxn→x1=xn⇔x1≠xn→vx1≠vxn

Q: Deliymine the Pripes Tua yectangle the 715 Nil lineay by any Z₁ = 0, 2₂ = 1/2₁ 2₂ = 1 and ²4=1+ N₁ =…

A: HINT : USING CROSS RATIO METHOD  w1-w2w3-w4w1-w4w3-w2 = z1-z2z3-z4z1-z4z3-z2

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A: Given Data: F =xi  +yjTo Prove:∫C F . n ds =∫R∇·F dA where R is the disk of radius ''a'' and centre…

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Q: Question 6 Solve the differential equation y' = (A) 2x + e^xy - y^2 = c 2+yey 2y-xey

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Q: -6 -2 4 2 6 -2 4 -6 y 2 4 6 ww X

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Q: 2- Consider the matrices A = [₁²1], B = [₁ J₁ C=__=₁} K₁ = [50], K₂ = [₁²2] Solve AX + BY = K₁ CX +…

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Q: the determinant and inverse of the following matrix. You must clearly explain all steps of how you…

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Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

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Q: 100. In a topological space, which of the following statements is correct? Sisianoge (A) a compact…

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Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Q: Consider the set of francti of the complex plane with where how S a Ta, b; c, d (z) = az+b Cz + d…

A: consider the set of function linear transformations of the complex plane with ∞ adjoined.…

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Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

A: Given Data: H^ =hω03i0-i30002 , B^ =b07i1-i-i71+i1+i1-i6D^= 002α02α02α0-3αψ0=e1ψ0e2ψ0e3ψ0=236

Q: Consider the two functions given below: Function 1: f(x) = −7x² + 2x + 28 Function II: 30 20 10

A: Function -I f(x)=-7x2+2x+28 Function -II

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Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

A: If the function is injective , then the above statement is true.

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Q: (P→Q) ^ (P → R) = (~P V Q) ^ (~P V R) =((~P V Q) ^ ~P) v ((~P v Q) ^ R) How do you produce the next…

A: Introduction: If two logical statements have the same truth value in all circumstances, they are…

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Q: Please, expert, I want to solve all these questions Homework: Evaluate the following integrals: 8.f…

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Q: Write the Maclaurin series for f(x) = 7cos(4x²) as Find the following coefficients. Co= C₂= C4= C6=…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 3. (a) If f: X→ Y and g: Y→ Z are functions and go f is one-to-one, must g be one-to- one? Justify…

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Q: Determine the average rate of change of f(x)=3(2)" on the interval 0<x<2. a) 4. Ax b) Ax d) = 45 c)…

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Q: Consider the problem: Min 10+ x² + y² subject to 2x² + y² ≥ 2, x ≥ 0 and y ≥ 0. x,y 1. Suppose that…

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A: Here the given vectors are u→=a-1-1, v→=2b2,w→=0-1c. We shall find values of a, b and c so that the…

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Q: -4 y=름 (x+3)2 3 -2 -1 4 3 2 1 。 -1 -2 -y=3 ↑ y=0 1 -y=큼(X-3)- 2 3 A

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Q: The rate at which water flows into a tank, in gallons per hour, is given by a differentiable…

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Q: Exercise 2. Plot the graph of the function given in polar coordinates tanh0 r=2- 0>1 0-1' Write…

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Q: Question No. 5) Show that a partition of a set S determined equivalence Relation on set S.

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