The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1,536 cm², find the dimensions (in cm) of the poster with the smallest area. WW

Q: Consider the function f(x) = 2x3 - 6x² - 18x + 54. a. Find the first derivative. f'(x) b. List any…

A:

Q: Concept check: Evaluate the following integrals: 1. dx (6-x²)z OIL

A:

Q: Given an interest rate of 1.0% compounded continuously and starting principal of $5000, determine…

A: Continuous Compounding Formula: A = P·er·t where A is the Accumulated Amount. P is the Principal…

Q: For the function, do the following. f(x) = + from a 1 to b = 2. \) Approximate the area under the…

A: The given curve is  f(x)=4x

Q: Suppose f(x) is continuous on [4, 6] and −4 ≤ f'(x) ≤ 3 for all x in (4, 6). Use the Mean Value…

A:

Q: 8 A communication signal is given by the function sint t The task is to: y=- a) Derive and equation…

A: To find the derivative of given function

Q: Visually estimate the location of the centroid of the region shown. Then find the exact coordinates…

A:

Q: An objective function and a system of linear inequalities representing constraints are given.…

A: see below the answer and explanation

Q: Given z = x² + xy², x= uv¹+w², y=u+ve" дz ?u then find: when u = -2, v = -1, w=0

A:

Q: What is the degree and order of the given differential equation? d²y dx2 5 + degree 1 and order 3…

A:

Q: answers to three decimal places. Find the critical numbers of the function f(x)=-3x5 + 15x¹ +25³ +4…

A:

Q: π 3 H|3 Evaluate the integral 2 cos (u + v + w) du dv dw. 元 π F|3 3 wla 3 3 000 SS S 000 (Type an…

A: This question is related to definite integration, we will solve it using given information.

Q: 0 A B (5, 1) C (2y+1,2-y)

A:

Q: f(x) = 6e9x³-9x

A: Given    find first derivative

Q: A particle moves along a horizontal line. Its position function is s(t) for 120. Find the velocity…

A:

Q: Set up a triple integral in spherical coordinates that would determine the exact volume outside the…

A:

Q: The present value of a sum of money is the amount that must be invested now, at a given rate of…

A:

Q: If the angle is in standard position and P(x, y) is a point on the terminal side of 8, and r is the…

A: If the angle θ is in standard position and Px, y is a point on the terminal side of θ, and r is the…

Q: 1. a) Solve the following differential equations: ydx x i) -1 (tan-¹x) dy = ydx x² +1 (In x)dy, b)…

A:

Q: 1. f'(x) and ƒ' (7). Show all work, no decimals allowed in your final answer y -Cos (x) Tan(x)…

A: Given query is to find indicated derivative.

Q: (l+h)³41 allimpro h th b) limpo Sin+h

A: Here we have to use the concept of limits

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A:

Q: For the function f(x, y) = 3x² — 5xy — 5y² + 4x − 3y + 5, find a unit tangent vector to the level…

A: The given curve is: f(x,y)=3x2-5xy-5y2+4x-3y+5

Q: A fence 7 feet tall runs parallel to a tall building at a distance of 2 feet from the building.…

A: Let the length of the building be:  x Let the distance between the foot of the ladder and fence be:…

Q: 20. To apply the root test to an infinite series Σ an the value of n P = lim (an)¹/n 818 has to be…

A:

Q: Find three angles which are coterminal to -575°.

A: Coterminal angle

Q: Given a nominal interest rate of 4.0% compounded quarterly, determine the starting principal…

A:

Q: Concept check: evaluate the integrals using the appropriate method: 2. [ xsecxtanxdx

A: To evaluate the given integral

Q: How do you take the indefinite integral of ln(3x2)?

A:

Q: Let U = {a,b,c,d,e,f, 12, 13, 14, 15, 16, 17), X = {a,b,c,13,14,15), and Y = {b,d,f, 12,14,16}. List…

A:

Q: In order to find the area of an ellipse, we may make use of the idea of transformations and our…

A: The region R is bounded by the ellipse:(x-4)216+(y-2)21=1

Q: Function g is graphed. -3 -2 -1 4 g A -1- S²90 Y 3- di -2- -3- T Find S g(x) da. Give an exact…

A:

Q: (x+10)² 144 2. Express the equation draw its graph. in its general form, find its elements and…

A:

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

A:

Q: Given a nominal interest rate of 1.5% compounded daily (ie: compounded on each calendar day),…

A: Solution- Given Accumulated value after 9 years (A)=$20,000 Rate(r)=1.5% or 0.015 (annually)…

Q: Given an interest rate of 4.5% compounded quarterly, determine the effective rate of interest.…

A: Given rate of interest is:  4.5%  compounded quaterly

Q: How did you get the (2n+1)(2n-1)? I just don't know where the (2n+1) came from. thanks in advance

A: use the general principle of mathematical induction.

Q: Find the critical point of the function: f(x, y) = 3 + 7x + 2x² - 8y + 3y² (x,y)= This critical…

A: The solution to find critical points of given functions are as follow.

Q: 1) An antiderivative of a function f (x) is a function F (x) such that F ′(x) = f (x). Find any…

A: Note:-     Given functions:- a) fx=12x2+8sec2x b)gx=x+6sin2x

Q: K Use the quotient rule to find the derivative of the given function. Then find the derivative by…

A:

Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

A:

Q: places. Find the direction in which the maximum rate of change occurs for the function f(x, y) the…

A: we will find the required

Q: In each part, a point is given in rectangular coordinates. Find two pairs of polar coordinates for…

A:

Q: Evaluate the following sums. 9 (2) Σ 3 k=1 500 (b) Σ 9 k = 1 264 (c) Σ k = 2 20

A:

Q: 2. A rectangular plot of land is to be fenced in using two types of fencing. Two opposite sides will…

A: Let's find heavy duty and standard fencing should be used so it gives maximum area.

Q: Calculate the moments Mr and My and the center of mass (x, y) of a lamina with the given density and…

A:

Q: Consider the function f(x)= lim X→∞0 a. Evaluate lim f(x) and lim f(x), and then identify the…

A:

Q: If t= -pi, evaluate (if possible) Part 1. sin (t) Part 2. cos(t) Part 3. tan(t)

A:

Q: that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find…

A: Given query is to apply rolle's theorem.

Q: Given y=pq, find dp/dt when p=30, q=250, dq/dt=-200, and dy/dt=-5250.

A: