4. The temperature of a pan of hot water varies according to Newton's Law of Cooling: T-K(T-A), where T is the water temperature, A is the room temperature, and k is a positive constant. If the water cools from 90°C to 85°C in 1 minute at a room temperature of 30°C, how long (to the nearest minute) will it take the water to cool to 60°C? ܘ ܘ ܘ ܘ dt

Q: 17 c. Find the general solution of the D.E. 2 y" +4y'-8y = 8×-4e²* +4

A: We solve given DE by using method of undetermined coefficient.

Q: What is the degree and lead coefficient of the following polynomial? f(z) =−+52 = −x + 5x² − 6x³ +…

A: We have fx=-x+5x2-6x3+10 This can be written as: fx=-6x3+5x2-x+10 The degree is the highest power…

Q: Determine £¹{F}. s²-2s-12 (s+3)² (s+6) Click here to view the table of Laplace transforms. Click…

A:

Q: Joyce removes the pennies from her purse. Now her bag contains 12 nickels, 26 dimes, and 14…

A: We will use conditional probability  and multiplication theorem  If two events A and B associated…

Q: Solve x(1): dy/dt + x = 1; dx/dt -y + 4e¹ = 0; x(0)=0 and y(0)=0. O 7.88 O 3.78 O 9.02 -5.58 -6.75

A:

Q: 1847 In x 5)- b) Show that the ode (x + tan-¹ y)dx + y dy = 0 is exact, then find the general…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: Please Find the critical points, evaluate the stability of them and sketch the inn phase plane.…

A:

Q: Which of the following statements about a polynomial function is false? A polynomial function of…

A:

Q: 6 F(s) = ((28 + 3)² + 2)² + e7 S3

A:

Q: Find ||u||, |v||, and ||u + v||. u = (-1, 1, -2, 0), v = (4, 1, 0, 1) (a) ||u|| (b) ||v|| (c) ||u +…

A:

Q: For a given function f(x), the divided-differences table is given by: Xo = 0 X₁ = 1 X₂ = 2 X3 = 4…

A:

Q: O 30 18+ 12+ 6+ N -24 -30

A: Graph of the function

Q: M = 0 (+) 0 -1 1 1 1 Find an orthogonal matrix Q such that QM is upper triangular. Obtain Q as a…

A: As per the question we are given a 3×3 matrix M and we have to find an orthogonal matrix Q such that…

Q: 42 1. (Volumes of Solids with Known Cross-Sections). Sketch the solid bounded by the surfaces 2²…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 13. What is the maximum value of f(x) = 2 sin[3(x+T)]-8? A. -10. 14 MAGAL. B. -6. C. 6. D. 10.

A: 13

Q: Find the area bounded by the curve y = x³ − 3x and y + 4 = 0

A:

Q: Given: • tan a = 2√6, a € [0, π] • cos 3 = 3 5' Find the numerical value of the following: and sin 3…

A:

Q: 1 3-2 3 4 a) Find a basis for the kernel of T and a basis for the range of T. b) Is T one-to-one?…

A:

Q: Sequence of Subsets Let A₁, A₂,..., A₁00 be a se of Some set B. Suppose that all these subsets are…

A:

Q: Let A be the matrix below. Find the singular values of A and enter them as a Use the square root…

A:

Q: Od. A function f: Rm→Rª is continuous if and only if for every x in Rm and ɛ>0, there exists 8>0…

A:

Q: Find the exact arc length of the curve x = Enter the exact answer. L = (y² + 2)² from y = 2 to y =…

A: We need to calculate the exact arc length of the curve: x=13y2+232 from y=2 to y=7.

Q: 1 Given the matrix A = 2 3 3 2 3 1 6 5 4 5. 97 85 (a) Find a basis each for N(A) and C(A). What is…

A:

Q: IV. Let F be a vector-valued function such that 1 F'(t) = (te', ; 1 + 1.31²) and F(0) = (-1, 0, -2).…

A: Given information F→'t = t et,  11+t2 ,  3 t2 and F→0 = -1, 0, -2

Q: 1) Let T = la + 1b+5c+(-1)d -la+0b+ (-4) c+3d 7a+ 4b +32c +(-13) d 7a+ 4b +32c +(-13) d -la+(-2) b+…

A:

Q: Solve the following differential equation by dividing interval to 4 equal parts (1 + Ax)y" + By¹ +…

A: Given,              (1+Ax)y''+By'+Cy=Dxy(a)=0, y'(b)=1 Where             A=-3, B=2, C=-1, D=2, a=2,…

Q: Consider the matrices 4-17] ¹=[₁₂7], B = [1 2] ₁ A 5-7] [2] = i) Find A¹0 times vector b by writing…

A: Consider the given matrix A=1−111, B=0−212 and b→=−22. i We have to find the A10b→. We know that…

Q: What is the parent function of y = (x + 2)(x − 8) Oy=x² Oy=x4 Oy=x³ Oy=x

A:

Q: The quantity supplied of a good is the amount of product that a company is willing to make available…

A: Equilibrium price: The equilibrium price of a product is defined as the quantity supplied S(p) is…

Q: Prove the next arguments about normal matrix A € Cnx" and all of its eigenvalues EC 1. A*=A^-1…

A: As per the policy, we are solving three subparts. Please repost the question and specify which part…

Q: Let G be a group and let a e G have order pk for some prime p, where k ≥ 1. Prove that if there is x…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: 8. Given that B = {u, v, w} is a basis for a vector space V. Determine if the set 2u+v+w} is a basis…

A:

Q: Determine £¹{F}. F(s) = 2 4s - 18s +2 s(s-4)(s-6)

A:

Q: B. SOLVING. Answer each of the following. Write your solution as neatly as possible. Simplify your…

A:

Q: The approximation of the root x* of the function f(x) = ln(x + 1) -x +3 accurate to within 10-2…

A:

Q: ¡ cs] Demonstrate how any vector x E R¹ can be expressed as a linear combination of the following…

A:

Q: QUESTION 2 Is one half always greater than one fourth? Examine these figures and tell me when one…

A:

Q: This question examines your understanding of the Euclidean norm. Please tick all correct statements.…

A:

Q: •√ [F(x, Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

A: We need to calculate ∬Sf(x, y, z) dS. Here,  f(x, y, z)=x2+y2+z2S=x+y, x2+y2≤1

Q: 2x² + 2y² + 8x + 4y + 2 = 0 is the equation of a circle with center (h, k) and radius r for: h = and…

A:

Q: For the matrix 2 1 2 1 2 +40 A = 2 1 2 1 0 find the characteristic polynomial, the minimal…

A:

Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. (w²-2²-4z-1))dw + 2w(z + w + 2) dz = 0

A: Given : w2 - z2 - 4z -1dw + 2w z+ w +2  dz=0 To Find : Solution of differential equations

Q: 1. Sketch the z-domain root locus for the systems with following loop transfer functions (a) L(z) =…

A:

Q: D Question 33 Which of the following matrices is (are) symmetric? All the matrices are symmetric [12…

A:

Q: Determine the (x, y) co-ordinates for Leigh's and David's position at time s. which Find the…

A: Given that David is climbing the parabola y=x2-6x+14. (d) At time s, the position coordinates of…

Q: 15. If the interval under consideration is 0≤x≤ 2, how many solutions does the equation sinx(1 - cos…

A:

Q: Determine the inverse Laplace transform of the function below. 4s e -45 (3s +28) (s+ 6) (s+4) Click…

A:

Q: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

Q: 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is…

A:

Q: The matrix has eigenvalues −4, 1, and 4. Find its eigenvectors. The eigenvalue -4 has associated…

A: