Find the total mass M and the three moments of inertia Ix, Iy, and I₂ of the solid with mass density e(x, y, z) = x² + 5 kg/m³ that occupies the unit cube in the first octant given by F = {(x, y, z) | 0≤x≤ 1,0 ≤ y ≤ 1,0 ≤zs 1). M = Ix = Iy = Iz = ✓kg kg-m² kg-m2 kg-m²

Q: The tangent line to the graph of some function f at x = 4 is y = - 2x + 5 corresponding normal line…

A: Given query is to find the equation of the normal line.

Q: solution

A:

Q: 2 If √3-2x² ≤ f(x) ≤√3-x² for -1 ≤x≤ 1, find_lim_ f(x). X→0 lim_ f(x) = X-0 (Type an exact answer,…

A: Given inequality is 3-2x2≤fx≤3-x2 for -1≤x≤1 We need to find the value of limit limx→0fx

Q: Evaluate

A: b) Given sinπ6π6=π6×180ππ6=30°sinπ6=sin30°sin(π6)=12

Q: b = |2 πχ + 1 π 2

A:

Q: The radioactive isotope potassium-40 is used to date very old remains. The proportion of…

A:

Q: Find the surface area of a sphere of radius 4 using integral. SHOW WORK ON PAPER PLEASE

A:

Q: Find all values of n such that y = xn satisfies: x 2 y ′′ − 12y = 0

A:

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A:

Q: Consider the following vector function. r(t) = (t, t2, 4) (a) Find the unit tangent and unit normal…

A:

Q: Find the General Solution of the following differential equations. If boundary conditions are given,…

A: The given differential equation, 1. x2+y2dx-2xydx=0, when x=1, y=2 Note: Multiple questions are…

Q: Using the substitution t tan can be written as of dx sin(x) - 60 cos(x) of dt +30-30 2 de 30²2²…

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

Q: E. DE with Linear Coefficients (x+2y-1)dx - (2x + 4y + 1)dy = 0

A:

Q: → Use the Table of Integrals to find the following antiderivatives. Be sure to cite the Formula…

A:

Q: Evaluate the following limit. Enter the exact answer. To enter √a, type sqrt(a). lim 1-0 √z+2-√2 I =…

A:

Q: Given P(theta) = (-8, 15). Solve for sin theta. a. -8/15 b. -15/17 c. -8/17 d. 15/17

A: To solve for sin θ

Q: K Given the function f(x) = 4x2-x+ 3, determine: f(z)-f(x) Z-X a) lim Z→X b) f(x) a) lim Z→X…

A:

Q: Which expression is equivalent to (sin 28) (csc)? O2sin 8 sin 8 2cos 8 cos 8

A: Please see the below answer. (sin 2θ)=2 sin θ cos θ csc θ = 1sin θ

Q: Find an equation of the tangent plane at the given point. g(x, y) = exly, (6, 1) (Express numbers in…

A:

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A: NOTE: Refresh your page if you can't see any equations. . here we have so the lower and upper…

Q: For what value of a is the following function continuous at every x? f(x) = a x+6a, x≥2 20, X<2

A: Given continuous function f(x)=a2x+6ax≥220x&lt;2

Q: If I(x)=g(g(x)), find l'(1) * I(x) = g(g(x)), find I'(1)

A: Given data

Q: Consider h(w) = = - 4w ( - 4 - w) Determine the intervals on which h is concave down. Oh is concave…

A:

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

A:

Q: At what points is the function y = x + 4 2 x -5x+4 continuous?

A: Rational function is continuous at all points where its denominator is not equal to 0. If its…

Q: Consider the function f(z) = 6 sin 6+ 5+ TH 3 (²) on the interval [0, 14]. 2- 2 4 6 8 10 12 Find the…

A:

Q: 3. Evaluate the following integral or show that they diverge. La dz €³r (er + 5)² ∞

A:

Q: Evaluate the following double integral over the region R. SS (x² - y²) ²dA; R={(x,y): 0≤x≤1, −1≤y≤1}…

A:

Q: 2 S² √√²*-*² √x² + y² dy dx 0

A:

Q: A tank contains 80 gal of pure water. Brine solution with 2 lb/gal of salt enters at 2 gal/min, and…

A:

Q: (b) y = tan-¹x (e) y = cotx (h) x5

A:

Q: The following table gives the percentage, P, of households with a television set that also have a…

A:

Q: A tank initially contains 200 gallons of water in which 50 lbs of salt are dissolved. A salt…

A:

Q: = - q³+ 270q² and its cost function is given by Suppose a company's revenue function is given by…

A:

Q: If x = f(0) cos(e) and y=f(0) sin(8) then the dy dx derivative with polar coordinates, where f(0) =…

A:

Q: 10 8 6 4 2 -6 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10- 1 2 3 4 5 6 From the function graphed above, find the…

A:

Q: A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying…

A:

Q: Find the value of the two realities x and y (x + y)² 3+1 3-i

A: Let's find value of two realities x and y.

Q: A. Using the definition of limit, show that lim-∞ 1/ n³ = 0 and that limm- 1 / n¹/5 = 0. 3. Using…

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: 16 16 Implicit Curves Consider the 2 implicitly-defined curves 5x+2y + x³ + xy² = 0 and 2x - 5y + y…

A:

Q: Using left endpoints, determine the value of the Reimann Sum S 2x² +5 dx using four partitions each…

A: Solution: The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: Graph the function. y = 2x O -10 -5 -10 y -5 10 5 The xy-coordinate plane is given. The curve enters…

A: Topic = Graph

Q: Evaluate the indefinite integral: [ sin (r) cos(x) dx

A:

Q: Express the area of the shaded region in terms of (a) an integral with respect to x and (b) an…

A: NOTE: Refresh your page if you can't see any equations. . given functions are first, we need to…

Q: The function below represents the number of people who have a rumor t hours after it has started.…

A:

Q: (a) Find the derivative. dy=[ y = In(4x - 8) - 3 In(x) (b) Find the derivative. = 1 (²x - ³) State…

A: here we have to find the derivative of function  a) y = ln(4x-8) -3lnx dy/dx = 4/(4x-8) - 3/x dy/dx…

Q: 0 √4-² 1 √4−x² 17x² + 17y² +1 dy dx

A: Given integral ∫02∫-4-x24-x2117x2+17y2+1   dy dx

Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

A:

Q: Find an equation for the ellipse whose vertices are at (-5,4) and (3,4), and focus is at (1,4).…

A: Since, the y values of the vertices are not changing, only the x values are changing , it means it’s…

Q: How many units are in beginning inventory if 20,475 units are budgeted for sales, 20,449 units are…

A: