A document is to contain 80 square centimetres of print. The margins at the top in bottom of the document are each 2 centimetres wide and the margins on each side are 3 centimetres wide. What should be the dimensions (in centimetres) of print so that a minimum amount of paper is used? 11 cm by 7.3 cm 12 cm by 9.3 cm 11 cm by 5.3 cm none of the above

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

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A: Let's find speed of boat.

Q: T 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

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Q: 5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001…

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Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

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Q: Let f(x) f-¹(-2) = x + 3 x + 6

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Q: QUESTION 12 Which method of apportionment always satisfies the quota condition? OA. Hill-Huntington…

A: Topic = Algebra Correct option = C

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Q: Find the min and max of (f)

A: This question can be solved using the concept of maxima and minima.

Q: Find the absolute maximum and minimum values of the following function over the indicated interval,…

A: To find the absolute maxima and minima  of a function f(x)(i) find x such that f'(x)=0(ii)  find the…

Q: (-3², what values should "a" take to ge c. a> 3 d. a 0

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A: Given

Q: 14. Determine the constraints a and b such that f(x) is continuous for all values of x. ax - b x ≤ 1…

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Q: Q1: solve the equations below: 1) S dx Jellt vast (1+

A: Given, ∫1x(1+x)2dx

Q: Write an equation (any form) for the quadratic graphed below 15 3 2 1 5 -4 -3 -2 -1 2 3 4/5 -1 -2 -3…

A: We have to find out graph

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Q: Find an equation of the form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

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Q: evaluate the derivative of the function at the given pointf(x)=-4/(2x2-3x)4 , (1,-4)

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Q: Find the second derívate of x Fx=-8/square root of 3x+6

A:

Q: 4. With the fact of 1² +2²+...+ n² = n(n+1)(2n + 1)/6, prove that n n n(n −1) ΣΣ(i-j)² 6 i=1 j=1…

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Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: First we find the limits of integration.

Q: find the volume in the first octant under the plane z=y and inside the cylinder y²=4-x.

A:

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b…

A:

Q: 1- Evaluate the limit a-Limx²-4/(x²-x-2) X-2 b- lim [In(cos(x))]* c-2-(X²+4) ¹/2²/sin²x x-0 x →0

A: L'Hospital rule:- If a function is of the form p(x)q(x)   then if limx→a p(x)q(x)  is of 00 or ∞∞…

Q: 7. Evaluate a root using Muller's method from the function. Terminate if Es < 0.0055% f(x) = 0.5x4…

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Q: // لاح - لا - لا -4

A:

Q: Daniel is to print texts on a piece of paper. The area of the printed text is 20 square inches. All…

A: Find out the dimensions of the page that will use the least amount of paper.

Q: Use GEOMETRY to compute the value of the definite integrals. Report EXACT answers - not decimal…

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Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = ·S dx (x - 1)².…

A: The integral is y=∫ 2x2-3x+2(x-1)2(x-2)dx

Q: Explain why the integral is improper. 49 1 dx 1.6 1.4 1.2 Y 0.81 0.6 0.4 0.2 10 20 O At least one of…

A: The objective of the question is evaluate the improper integral.

Q: 4) The area under the curve defined by the positive function f (x) on the interval [2, 6] is known…

A: We are allow to solve first question only Thank you

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A: Concept: If a solid is formed through a wire then the perimeter of the solid is equal to the length…

Q: For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line r = (2,−1, −2) + t(3,1, −2)…

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Q: Evaluate using u-substitution j²x²√x²1 x²1 dx Evaluate using u-Substitution (Inx) 3 St dx x

A: 1. ∫12x2x3-1dx2. ∫ln x3xdx3. ∫2θ-5 cos2θ dθ

Q: 00 15. The sum of the series : Ek=0 a. m (-1) ()2k+1 (2k)! b. 픔 C. -2 T 3 d. 5 T

A: First I have arranged the series and then using power series representation of cos(x) evaluate the…

Q: 5. Interest rate. A 2-year loan of $4650.25 accumulated $269.75 in simple interest. Calculate the…

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Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: 4x+5 x2+x-2 5) 6) 2=1 +1 7) fx.tan-1x.dx dx =

A: To evaluate the given integral.

Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx y = S₂ 9x² +9

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Q: the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with…

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Q: What is the domain of this function? (assume there are arrows at the ends of the graph The answer…

A: We have to find the solution

Q: Ceq = 25.35nf Се

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Q: The growth rate of a town's population after t years is P'(t) = 420 t². If the town's current…

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Q: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

Q: Q1// prove one only: tan²x-1 tan²x+1 = 1-2cos²x

A: Topic = Trigonometry

Q: Find the nth Maclaurin polynomial for the function. f(x) = e-x, n = 5 2 4 P5(x) 1-x+ 2! 5! X 3 3! x…

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Q: 10. Solve each of the following systems; a) 2x+3y-z=-2 x - 2y + 3z=13 4x + y + 3z = 9 c) x + 2y + 72…

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Q: 15. Solve the following limits (if possible): 1 1 5+x 5 a) limx→o x x³ - 27 b) limx→3 x² − 9

A: Simplification of limit