An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made with the smallest amount of material. base height ft x ft ft

Q: and the present value of the given future amount. Assume 360 days in a year. $123,622 for 237 days…

A: Given query is to find present value .

Q: A 32 grams of a certain substance was initially poured and dissolved in an 18-liter container full…

A:

Q: Evaluate √ √R 6xy5 dydx R where the region is bounded by the curves y = = x² 1 and y = 1-². Sketch…

A:

Q: I → Question 2: Are the limits of these functions defined as a too? (please take this opportunity to…

A:

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A:

Q: -5-4-3-2-1 1 2 3 4 5

A:

Q: Find the integer that is represented by the following logarithmic expression. log2 48-log₂ 6

A:

Q: Consider the function f(x) solution, enter your answer as a comma-separated list (like "1, 3"). You…

A:

Q: Let f(x)= In (x^4) f'(x)=

A:

Q: A hot air balloon lifts off from ground rising vertically. From 100 feet away, a 5' woman tracks the…

A: Given that a hot air balloon lifts off from ground rising vertically. From 100 feet away, a 5 feet…

Q: A company that produces landscaping materials is du sand into a conical pile. The sand is being…

A: It is given that the sand is being poured at a rate of 5 ft3/sec. The physical properties of the…

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2…

A: Given Data : Two curves are given as, z=x2+y2 6 x2+4 y2+5 z2=30.   Required : We have to find…

Q: 3-8 Test the series for convergence or divergence. dhe tadt Hour 3.- + - + 1

A: 3. The given series is 47-48+49-410+411-....... We have to find the series is convergence or…

Q: 19-40 Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: 19. The given series ∑n=1∞n5n We have to check the convergence of the series by using ratio test.

Q: Samasin Fasin Bada

A: We have to find out

Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. X X +7 -dx…

A:

Q: Use implicit differentiation to find the points where the parabola defined by x² - 2xy + y² + 4x −…

A:

Q: Write the sum using sigma notation: -1/8 + 1/10 - 1/12 + 1/14 - ... = Σ η= = 0

A:

Q: If f(x)= e^2+In(9) then f" (x)=? Please answer asap and write neatly Thank You.

A: see below the answer and explanation

Q: Consider the graph 2 6 2 2 f(x)=√x² - 4 Where is the function positive?

A: function is given  this is the question of function we have to find domain of function where it is…

Q: find the first derivative for :Y=8-7x-7x^2+4x3

A: Given query is to find first derivative.

Q: Given: (2x³ — x − 1) ÷ (x − 1) = 2x² + 2x +1 - Therefore: (2x² + 2x + 1) ÷ (X − 1) = 2x³ O True O…

A: The statement is false .

Q: I= d. h(x) = H= e. h(x) = I 7(x-6)(x + 7) 3x² + 5 Preview Preview (x-7)²(x + 10) (x + 13) x(x-7)(x +…

A:

Q: Given: (x³ – 3x − 2) ÷ (x² + 2x + 1) = x − 2 Therefore: (x - 2) (x² + 2x + 1) = x³ - 3x - 2 True O…

A: Let P(x),Q(x),R(x) be polynomials such that, P(x)/Q(x)= R(x) Then doing cross multiplication we get,…

Q: x = 3t² + 3t 2t² + 5 The position of an object at time t is given by the parametric equations Find…

A:

Q: Find the curvature of the curve r(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 Give your…

A: The given curve is  r(t)→=4cos(2t), 4sin(2t), 2t

Q: 2. Solve the following integral (secx - tan x) secx dx O a. tanx + secx + C O b. secx - tanx + C O…

A: Solve the intregal

Q: Lim x>>9 [(6*sqrt x - 5) / (x - 22)]

A: Given query is to find the limit.

Q: Write the sum using sigma notation: cos(4) + cos(13) + cos(22) + cos(31) + ... = n=0

A: Let's write the sum using Sigma notation.

Q: Find the equation of the tangent line to the curve y = 10x -x^2 at the point x =1

A: To find the equation of the tangent.

Q: 51. 53. Soz z dz (a² + x²)³ dz LAVET A

A:

Q: Find the derivative using suitable differentiation rules: + 3x + ¹) J- = 5x + sin(x² + 3x + 1)…

A:

Q: Optimal Chapter-Flight Fare If exactly 180 people sign up for a charter flight, Leisure World Travel…

A:

Q: A curve is represented by the equation 4y³ + xy - 5x + 4 = 0. Part A: Determine Part B: Evaluate dy…

A:

Q: Use Fubini's Theorem to evaluate the double integral ff f(x,y) dA, where f(x, y) = 3x + 3x²y +9y and…

A:

Q: Which of the following are rational functions? Select all that apply. f(x) = = Of(x)= Of(x) = Of(x)…

A:

Q: x²-2x Find all pertinent information and sketch the graph of f(x) = x²-4 Find all asymptotes: HA:…

A:

Q: On the moon the acceleration due to gravity is 1.4 m/s2. A ball is thrown straight up at an initial…

A: we need to find out the differential equation.

Q: Find the equations of the lines tangent to the curve: 2e^x = y^2 − x, at x = 0.

A:

Q: 3. Show all work and solutions without use of a calculator: Consider the curve defined by the…

A:

Q: 1. Consider the function f(x)= x-x5 + sin(27(x - 1)). Use the MVT to prove that there exists a c…

A: Use mvt

Q: A bank features a savings account that has an annual percentage rate of r r = 4% with interest…

A: Topic - Compound interest  we are given, Present value: P=$9500Annual percentage rate =4%=0.04number…

Q: Find the slope of the line passing through the points (3,5) and (3,-2). a) The slope is b) Select…

A: The line passes through the points (3,5)  and (3,-2)

Q: Find the points on the cone z (x, y, z) = (x, y, z) = Need Help? Read It Show My Work (Optional) IE

A: Here we using the Lagrange multiplayer.

Q: For each of the following rational functions, determine the horizontal asymptote for the rational…

A:

Q: 1. Evaluate the limit. lim √x²+1 X-00 3x+2

A:

Q: An object is moving with a uniform acceleration a = 2ms ², determine the functions for: c) a)…

A:

Q: Suppose 4x² + 16y2 = 100, where x and y are functions of t. dx dy (a) If. = find dt dt 4' dx dt E…

A:

Q: 2x + 9 . For this function there are two important intervals: (-∞, A) Consider the function f(x) 3x…

A:

Q: Consider the function h(x) 2 x5 +3 Write h(x) as a composite function, f(g(x)), determine each of…

A: Given a composite function h(x).