Daniel is to print texts on a piece of paper. The area of the printed text is 20 square inches. All sides of the paper would have a margin of 1 inch A. What should be the dimensions of the pagr that will use the least amount of paper B. What is the area of the paper to the nearest whole?

Q: Evaluate x³ + €

A: On solving this we will get

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A:

Q: A horizontal trough is 1600 cm long and its ends are isosceles trapezoids with an altitude of 4 m, a…

A: I am attaching image so that you understand each and every step.

Q: 04) Find dy /dx for the following functions: a) y².cotx= [sin(x.y)]-¹ b) y = (lnx + x)tan

A: See the answer below

Q: If ā= 3x - 5y and b = -2x+9ỹ, write the vector 5ã-85 in terms of x and y

A: Given vector are a→=3x→-5y→   and b→=-2x→+9y→. We have to find the vector 5a→-8b→. Now, 5a→=53x→-5y→…

Q: (iii) Find the directional derivative of f at the given point in the direction of v. f(x, y, z) =…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 2. The sum of the roots of the quadratic equation x²-x-6=0 is given by 2 O

A:

Q: if Find: A = sin(u)i + was (u)j + (u)k B = cos(u) i - sin (u) j C = 2 i + 3j -K - 3K du [ A x (B x…

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Q: The value of integral [(cos(4x)+cos(8x)) dx

A: We have to find out integration

Q: Q7) Calculate AC. BC and (A + B)C. Also, verify that (A + B)C=AC + BC 0 6 7 [0 1 1] If A = -6 0 8,B=…

A:

Q: Given the initial condition y(0) = 1, find the particular solution of the equation y' = e3x - 2y

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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…

A:

Q: Find the x-values of all points where the function has any relative extrema. Find the value(s) of…

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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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A: The given equation is;  y'''-y''-6y'=ex.

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A: We have to find out the weekly average sales amount

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A: Using application of integration

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

A:

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Q: For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length of…

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Q: 14. The Integral:√4-3x² a. cos²0.de dx, can be transformed into : b. 2f cose.de c. 2 f tano.de d. 4…

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Q: 3. (3y² + xcos xy) sh a) d) al + (3x2 + ycos xy) = 0 dx y + sen xy + x³ = 0 y2 + sen xy + x³ = 0 y²…

A: The given equation is;  (3y2+xcosxy) dy/dx +(3x2+ycosxy) =0

Q: Solve the given initial value problem. x³y² - y³ = 45 ³y² + xy³ = 18 x²y² + xy³ = 90 x¹ y² + y² =…

A: Here we have to solve the differential equation.

Q: 6. Evaluate the inverse z-transform of x(z)= 2z-1 (1-2z-¹)²

A:

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

A: The objective of the question is determine the area bounded by the given curves.

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A: Solve the following

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A: The given sequence is ∑n=0∞-1n+1n+6xn=∑n=0∞an

Q: 4) √₂° e¯*dx = 5) S- dx = 4x+5 x²+x-2

A: Given, ∫2∞ e-xdxLet I=∫2∞ e-xdxI=e-x-12∞I=-1ex2∞I=-1e∞--1e2I=-1∞--1e2I=0--1e2I=1e2Therefore∫2∞…

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A:

Q: What is the present value of the firm’s revenue stream given that the time path for a firm’s revenue…

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Q: Sketch a graph f(x) = 2 sin [-2(x+1)]-3 for two cycles. ✔✔✔ 5. List 3 key points below. >

A: Concept:  The sine function's general form: y=Asin(Bx-C)+D Where A represents the amplitude Period:…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Given problem:- The population of a community is known to increase at a rate proportional to the…

Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 1/1/22 4 12 a. b. ³/1 3 2) The Volume…

A: Given

Q: Q1): Find the point (x, y, z) that lines on the plane x + y + 2z = 4 that is near origin.

A:

Q: Find the vertical shift of the sinusoidal function. fx -3πT -2T Simplify any fractions. T 6 5 ★ تلا…

A: Concept: The sine function's general form: y=Asin(Bx+C)+D The vertical shift: This is the vertical…

Q: 5. A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53°…

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Q: . Evaluate cos 3x sin² 3x dx

A:

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: solution:-the weekly online sale s(t)=600et in dollarsthe formula to find the average value of a…

Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

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Q: 9y=x²,0 ≤ x ≤ 2 ; x-axis

A:

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Q: b) 42x + 4 = 6 (HINT: use substitution)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: %VII. १:०. By using the differential operator D and it's inverse, solve this equation: y"+y=sin(x)

A: The objective of the question is determine the "yc".

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A: We need to solve Helicopter task.

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Q: calculusssss please

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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: Determine if the following operation on the two given matrices is defined, and if it is, determine…

A: I am attaching image so that you understand each and every step.

Q: A radioactive substance decays in such a way that the amount left after t years is given by A=100e…

A: Follow the procedure given below.