A rectangular box with no top is to have a square base and a volume of 30 ft. The material for the base costs 27 cents/ft2 and the material for the sides costs 12 cents/ft2. If x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used constructing the box in cents. Total Cost, as a function of x = Determine the domain of the total cost function. Enter your answer using interval notation. Domain of total cost function=

Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

A:

Q: 5-6 FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE. What's the future value of a 5%, 5-year ordinary…

A:

Q: 3 3. y' for y² = x²y³

A: to find out the derivative

Q: Q4: Solve the following integrals:- dx ³-2x² (1) dx (2) √ √2√9-1² (3) fx² sinxdx (cos-14x)² 1-16x²…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Q2: Find dy/dx for the following functions:- (1)y=x'Inx (2) y = √sinh √tanx (3)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: A differential equation is an equation A that contains a derivative like y'(x) as well as the…

A:

Q: Use the spreadsheet to answer the following questions. 83 1 2 Put m Hein 5 x fx 57 C GP Answer: B 47…

A: Here, not that 82 value is at the intersection of the B column row 2.

Q: Express the repeating decimal as a fraction. 4.717171...

A: Given,            4.717171....To find : Express the repeating decimal as a fraction.

Q: Solve the differential equations 1. (3x²2y²)y' = 2xy 2. (y² - xy)dx + x²dy = 0

A:

Q: In Exercises 5–8, determine whether the graph of the function is symmetric about the y-axis, the…

A:

Q: If f(x) = (cos(√) - In (x²))³, then f'(x) = 3

A:

Q: 3 1 1 Evaluate Inverse Matrix A¹ = -1 = -1 2 2 1 2 -1 1

A: We can apply  A-1= 1/det.of A *(Adjoints of A)

Q: For the homogeneous equation (y² + 2xy) dx -x²dy = 0, which is a better substitute: letx=vyory=vx?…

A: The given equation is; (y2+2xy)dx -x2dy=0.

Q: 1. Which of the following matrix multiplications make sense? Evaluate the ones that do make sense.…

A:

Q: (d) +ỷ =0 dy dt (e) (f) d²y dt² d³y dt3 + sin(t + y) = sin t +t + (cos² t) y = t³ dy dt

A: To find out the order of the differential equation and also we need to write down that the…

Q: 1. fx² sec x³ tan x³ dx

A:

Q: Define R as the region bounded by the graphs of f(x) = 6x - 5x² and the x-axis. Which of the…

A:

Q: Add. 7 9 2 (x+8)² x²+x-56 + 7 9 2 (x+8)² x²+x-56 (Simplify your answer.) +

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or…

A:

Q: The rate of change of the variable y with respect to x is equal to the expression 5x*-3e***. What is…

A: rate of change of variable y with respect to x is =dydx

Q: X- 1.Find the area bounded by y=sin(sin x), the and x = π 2. axis and the lines Find the area…

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

Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: Solve ydx + (dy - 3dx)√(1-x²) = 0

A:

Q: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

A:

Q: (2) S dx x²√9-x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: List the x-values where the function is not continuous: f(x) = -x+ 3 if ex if if 3 – x x < - 3…

A:

Q: -1 Using Doolittles method for the following matrix A = 0 L-2 L- matrix and U - matrix. 2 11 86 0 51…

A: Given, A=-121086-205

Q: Prove the identity. sin (x-y) = tanx-tany cosx cosy Note that each Statement must be based on a Rule…

A:

Q: Find the differential equations for each family of curves under the following conditions: c)…

A:

Q: 5. Sketch a graph of a function of that satisfies each of the following. (Feel free to use the…

A:

Q: Solve the following system by using Gauss-Seidel method when the initial value is X(0) = 0, & = 5 x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: You borrowed money and need to pay interest on the loan. You must pay 5% of the $6700 loan to remain…

A:

Q: The function f(x) is continuous on the interval [-1,3]. The table below gives some of its values.…

A:

Q: L- matrix and U

A: The objective of the question is determine the L- and U- matrix.

Q: Question = 2 and v(y) Define as the region bounded by the functions u(y) around the y-axis, what is…

A: We need to find volume.

Q: Find the Differential Equation to the given Solution x sin y - xy² = c

A: To find the differential equation corresponding to given function.

Q: So 1 x²+7x+10 3ln 2-ln 2 dx

A:

Q: Refer to the images, then Choose all descriptions that apply of how the tank filling on Tuesday…

A: Given information Function for Monday:- Mx = 5 x3 Graph is   Function for Monday:- Tx = 5 x-153…

Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

A:

Q: ZSM-5, a catalyst material, has a surface area of 425 m³/g. What is the surface area of this…

A:

Q: 6. Write the following power functions in the form f(x) = kx² a. f(x) = -³/3 x3 b. f(x) = ³² c.…

A:

Q: (b) Let f(x)=√x and g(x) = 2x+5, find: (1)fog(x) (2)gof(x)

A:

Q: 2. Eliminate the arbitrary constants of the equation below, where ß is a parameter. 4 x = C₁eßt + C₂…

A: To find- Eliminate the arbitrary constants of the equation below, where β is a parameter. x = c1eβt…

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: Q10.IN R², let A(0,2), B(2,2),C(4,0),D(0,0). Then the quadrilateral ABCD is a: A) convex set B)…

A:

Q: For the function f(x) = 6x² *, evaluate and fully simplify each of the following. f(x + h) =…

A:

Q: 2. Make up a differential equation of the form dy dt that has the function y(t) = e²t = 2yt+g(y) as…

A:

Q: Find dy/dx fc (1) y = x³ Inx ,,2

A:

Q: Prove that B (xX+1; y ) + B (x,y+1)=B (X,Y) let П (х+1) = ХГ (Х)

A: We have the formula for beta function interms of gamma function is that B(m,n)=Γ(m)Γ(n)Γ(m+n)As we…