A rectangular sheet of metal of length=30cm and width = 28cm has a square of side x cm cut from each corner. The ends and sides will be folded upwards to form an open box. Determine the value of a that will maximise the volume of this box. Input the value for a correct to one decimal place. x = X

Q: 2. Let C be the parametric curve traced out by the equations a √t and yt² - 2t. Find an equation of…

A:

Q: (ii) 8 ΣΕ n=1 X

A: To find the sum of the following series.

Q: Find the directional derivative of f(x, y, z) = z³ — x²y at the point (-5, 4, -2) in the direction…

A:

Q: If sin(x) tan(2x) = = 3 26 (in Quadrant-I), find (Please enter answer accurate to 4 decimal places)

A: Sin(x)=3/26 (in quadrant - first) Find tan(2x).

Q: A car is traveling along a flat road. The position function is given by a(t) = sin(3t). a.)…

A: According to bartleby guidelines , we supposed to the first three subparts of multiple subparts…

Q: Evaluate (x+y)ds, C: x = 3t, y=-3t+3, for -1 ≤t≤ 2. Check Answer

A:

Q: Given f(x, y) = 4x² - 6xy5+ 2y¹, find the following numerical values: fr(2, 2) = fy(2, 2) =

A:

Q: Let f(x, y) = x² + 2yª + 40xy. List the critical points: The critical point at the origin is a…

A:

Q: 39. f(x) = x³ – 6x² + 9x and g(x) = x² – 3x

A: The region is bounded by the curves  and  .The aim is to find the area of the region bounded by…

Q: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: The Computer Password As you enter the spacecraft, you look to connect your computer. To your…

A:

Q: Evaluate 16120 (x + y)ds, C: x = 2t, y=-2t + 2, for 0 ≤ t ≤ 2.

A:

Q: Find a Taylor polynomial of 3rd degree centered at a=1 for the fuction f(x) = = 01- (x-1) + 2(x -…

A: Solution- The formula of Taylor polynomial is,here n=3 ( because we are calculating for 3rd the…

Q: Consider the following. A = Write the above using cylindrical coordinates. (Choose 0 < A. Choose 0 <…

A: The given integral is

Q: Solve the following differential equations of y"-9y= X 3x

A:

Q: If sin a = 0.844 and sin ß= 0.181 with both angles' terminal rays in Quadrant-I, find the values of…

A: Trigonometric formula

Q: Use L'Hopital's rule to evaluate the following limit. Enter your work in the answer fields below. If…

A: The given limit is; Limx-0(x3+4x2)/(1-cos(pi x)).

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(2x + 3y +6z). F(x, y, z) = 2 Check…

A:

Q: Evaluate the limit, and show your answer to 4 decimals if necessary. Iz² - y²z xyz - 1 lim (x,y,z)…

A:

Q: Estimate the area of the region under the curve y = In(x) for 1 ≤ x ≤ 4. Use the left-hand rule with…

A:

Q: Consider the vector field on R2. The associated one-form is: 3 || F(x, y) = (xy + 5x + y, x³y¹4)

A: .To write the associated one-form.

Q: Use the Ratio Test to determine whether the series is convergent or divergent. k=1 k!

A:

Q: Find the Cartesian coordinates of the given polar coordinates. Then plot the point. -(C (x, y) = 1.0…

A:

Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1),…

A: Solution is given below in step 2.

Q: Suppose that g is continuous and 7 that g(x) dx = 3 and 2 10 7 g(x) dx = 17. Find g(x) dx. 2 10

A:

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of in…

A: Given the polar equationr=θ

Q: Find the area of the parallelogram shown below I 10+ 0

A: Here we have, h=2 (Height of the Parallelogram)b=8 (Base of the Parallelogram)

Q: Find the area between the regions y=sinx and y=1-sinx from [0,1/6] (2.5)+sqrt(3) O (π/6)+sqrt(3) - 2…

A:

Q: 5. Identify the focus of the parabola given by Y= 3(x − 2)² +6 (2, 1) 12 O (-2, #1) O (-2, 11) ○ (2,…

A:

Q: (d) farctan x dx

A:

Q: Determine wether the following series converge or diverge. State and explain the test you used to…

A: The given series is

Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

A:

Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = e¯¼i — xe¯½j;…

A:

Q: Evaluate p4 sin(x) ln(1+x²)) SA 4 ex dx

A: Evaluate ∫44sin⁡(x)ln⁡(1+x2))exdx

Q: 1. Another way of writing 5-³ = A. log 1 5-3 125 13 is: B. log-35 = 1 125 C. logs 125 =-3 D. log5-3…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: 5 17. The marginal profit function for a company can be modeled by P'(x) = - 5x+3 thousand units…

A:

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Givenfind x interceptFind y intercept

Q: find the unit tangent vector T. r(t)=(4tsint+4cost)I+(4tcost-4sint)j-

A: r(t)=(4tsint+4cost)I+(4tcost-4sint)j-5kFind the unit tangent vector.

Q: Find the values of x for which the series converges. (Enter your answer using interval notation.)…

A: The given series is summation of (x-4)n/5n, n from 0 to infinity.

Q: 19. A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length…

A:

Q: Find cos (x² + y²)dA where D = {(x, y) | 9 ≤ x² + y² ≤ 36 Round your answer to four decimal places.

A:

Q: Evaluate the integral. 1/4 S 0 √36-x 5x dx

A:

Q: webassign.net Graph the function showing all relative extreme points and inflection points. f(x) =…

A: The given function

Q: -2 ..) Find the eigenvalues and corresponding eigenvectors for the matrix P = -6 A₁ = V₁ = , and λ₂…

A:

Q: Evaluate the definite integral using the Fundamental Theorem of Calculus, Part 2. Enter the exact…

A:

Q: = z² + 5. Below is the graph of y= 401 30 U 20 10 -3-2-1 0 1 2 3 4 5 6 The area bounded by y = z² +5…

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 9.…

A:

Q: □ O O O 5. Select the graph of the parametric equations. x=t+7, y = 1+ t 0 4 #

A:

Q: 16. Solve. a) log (²x) = Text 2 b) log4(x²7x − 18) - log4(x + 2) = 3

A: a) log3⁡(2xx−7)=2

Q: (c) Σ 2 (−1)n 1 sin (7) η √n η

A: