Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

Q: Check the differentiability of the function f(x, y) = √xy | at the point (0,0). Also check the…

A: As per the question we are give a bivariate function : f(x,y) = √|xy| And we have to check for its…

Q: A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The…

A: Given: Time (x) Number (y) 0 25 2 36 4 52 6 68 8 85 10 104 12 142 16 260 To…

Q: 3. A student had 93% in Chemistry which had a class average of 85% and standard deviation of 8%. The…

A: Solution

Q: i can't understand your solution. (step 3)

A: The expert has answered the answer using double derivative. If you are not able to understand double…

Q: -6 -5 -4 -3 -2 -1 Equation: 9 5 ✦ 3 +4 or 0 + 2 -3 + -5 2/3 ➜X

A:

Q: (a) Assume that g(x, y) is a function of the form g(x, y) = {" 0 if (x, y) = (0,0). (i) Show that…

A:

Q: Solve the exponential equation e* = x² - 3 graphically:

A: Let us consider the equation f(x)=g(x) To solve the equation using graphical method  Draw the graph…

Q: Using the least squares approximation, the best fit an exponential curve y = ea(x-b) to the given…

A:

Q: Use the power series = (-1)^x, x < 1 1 + x n = 0 to find a power series for the function, centered…

A:

Q: Discuss using appropriate mathematics the properties and assumptions underlying the OLS technique,…

A: We need to discuss the properties and assumptions underlying the O.L.S.(Ordinary Least Squares)…

Q: 1. Evaluate the following limits: x³-1 if x < -1 5x²-x-4' 3. Let f(x)=4x² + 3x-2, if-1<x<2 √5x + 6,…

A: a) Consider the given piece-wise function, fx=x3-15x2-x-4,    if x≤-14x2+3x-2,…

Q: Find the generating function for the sequence (a,), where a, is the number of (a) partitions of r…

A: Given:   Find the generating function for the sequence (a,), where a, is the number of (a)…

Q: 3. Evaluate 5 sin rdx

A: We know, sin2x = 1-cos2x Also, ∫ xn dx = xn+1/(n+1) + C   Given, ∫ sin5x dx = ∫ sin4x.sinx dx…

Q: Suppose S is the lower hemisphere S = {(x, y, z) x² + y² + z² = 9, z ≤ 0}. Further, define a vector…

A:

Q: 3) By changing the independent variables x and y to u and v by means of the relations u xay, v = x +…

A:

Q: Solve the system' = -4y + 2z y' = 2y + z using the elimination method. Show a complete and detailed…

A:

Q: Determine the Fourier series of the following functions. (a) f(x) = { 3 -2 ≤ x ≤0 0 < x < 2 (b)_ƒ(x)…

A:

Q: Let G be the simple graph on the vertex set V(G) = {a, b, c, d, e, f} with adjacency matrix: 011101…

A:

Q: All vectors are in Rn. Check the true statements below: A. If I is a line through 0 and if ŷ is the…

A: Solution

Q: Let FCK be fields, and let u # 0 in K be algebraic over F. If ceF, then cu is algebraic over F. O…

A: We have to check whether the following statement is true or not : Statement : Let F⊆ K be fields and…

Q: In a 24-hour period, a human's body temperature will vary ab When at rest (usually at night), the…

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: Find the quotient of B/A. Use pivotal method in solving for ALL (3x3, 2x2, ...) determinants. 3 1 3…

A: given, A=3137077468328491, B=45675678678978910 B/A=BA-1A-1=1Aadj(A)let adj(A)= C for get the…

Q: Find the sum of the series: n=0 (-1)"64"-2 n!

A: The given series is                                     ∑n=0∞-1n64n-2n! We know that    ex=∑n=0∞xnn!

Q: Evaluate the following integral by reversing the order of intgeration: √ 2π [²² 1²² cos(7x²) dxdy…

A:

Q: If f(x)=x², 0<x< , find the Fourier sine series and draw a graph of the function with its periodic…

A:

Q: Use the mid-ordinate rule with four intervals to evaluate the integral Type your final answer below…

A:

Q: Question 6 (a) Write down the augmented matrix of the following system of simultaneous equations:…

A: # As per the guidelines we are entitled to solve one question at a time, Since (a) and (b) are…

Q: A = 5 0 0 0 -6 -1 -1 0060 0 0 -11 -5 - 11

A:

Q: 7. Given the function f(x)=x²-x_and_g(x)=x-1, determine an equation for the combined function g(x)…

A:

Q: 2) Perform the following index shifts: i. Write y = no anx" as a series that starts at n = 2 ii.…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Find the general solution of the following differential equation. (D4 + 4D3 + 9D2 + 8D + 5)y = 0

A:

Q: CORRELATION ANALYSIS Determine the relationship between the number of hours students spent per week…

A:

Q: Number of voters 10 16 1st choice C B D 2nd choice B A B 3rd choice D C A 4th choice A D C Find…

A:

Q: Sketch and describe, in your own words, the surface S parametrized as follows: r(u, v) = (3 cos v,…

A:

Q: 3. Consider the functions_f(x)=(x-a)(x−b), g(x)=(x−p)(x−q)_and_h(x)= g(x) If a‡b‡p‡q, then a) which…

A:

Q: 1. How many grams of a drug are there in 850 ml of a 1 in 130 w/v solution ? state andwer to 3…

A: Note: according to our guidelines we can answer only first question  1)   Given solution is 850 ml…

Q: Ju udv-uv- 1 [vdu to Explain why the substitutions below are inappropriate. Let dv <=x x dx 1.…

A: Here we will find how to use integration by parts

Q: LP Model Minimize: subject to: z = x-y 4x-3y ≤0 x+y ≤ 10 x.y 20

A: We have given a LP model ,  min z = x - ysubject to,         4x - 3y ≤ 0         x + y ≤ 10…

Q: 4. In Chebyshev polynomials form, the value cos 20 = ... a) (T₂(x) + T₁(x)) c)(T₂(x) - T₁(x))) O b O…

A: Solution

Q: Q3. a) Solve the following first order differential equations, clearly showing all calculation steps…

A:

Q: (2) Explain why the rational numbers are those having periodic representation or with- out infinite…

A:

Q: Let 2= R, and suppose S₁ consists of intervals including Ø, the empty Ω set: S₁ = {(a,b]: -∞ <a ≤ b…

A:

Q: (a) Write the sum: using E-notation. 21

A: Note: since you have posted multiple problems. As per our guidelines we are supposed to solve only…

Q: Maximize z = 4x + 2y, subject to the following constraints. (See Example 8. If an answer does not…

A:

Q: Q2: Use Linear Least-Squares Regression to fit the following variables: Xi 1 2 3 4 5 6 7 8 9 10 yi…

A: Given

Q: Suppose F(2) = 1, F(8) = − 1, and F'(x) = f(x). - 10 [ f(x) dz = 10

A:

Q: Q2. a) Calculate the 4th roots of (5-j3)

A:

Q: Solve the equation using Variation of Parameters (D² + 1) y = tan x

A:

Q: Question Three Let f(x) be a function given by 0 f(x) = { sin (a) Prove whether f(x) is a Dirichlet…

A: Given: Let us consider the given function, fx=0-π≤x&lt;0sinx0≤x≤π a) Let's show the given fx is a…

Q: Let f(x) be a function given by f(x) = { (a) Prove whether f(x) is a Dirichlet function. (b) Find…

A: