Assume the X NY are both differentiable functions of tea find the required value X squared plus Y squared equals 25 find DY divided by DT when X equals 3Y equals 4DX divided by DT equals 16

Q: Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii)…

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Q: 2. Given the following data: X -20 12 4 f(x) -11 1 -2 5 97 Newton divided difference polynomial…

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Q: Q2: Find the area inside r = = 2(1 cos0) and outside r = = 2. O find th

A: The given problem is to find the area of region formed by given curves. Given curves r=2(1-cos(θ))…

Q: 4 The remainder when the expression x³ + x² - 5x-3 is divided by x-2 is 5 times the remainder whe…

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Q: -1 3 -6 -4 -3 4 Let y = ,Vi= " 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

A: The distance of a vector from a subspace can be evaluated using the norm. For this, we have to find…

Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

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Q: The norm of the matrix A = O True False [3 1 1 1] is equal 4. 3.

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Q: 5. i) A population of yeast cells can triple every 4 hours. Assume an initial population of 20…

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Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

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Q: e linear approximation of the function of the function O, then use it to approximte f(5.9, 2.06).

A: Introduction: The formula of linear approximation of two variables function f(x,y) is given by,…

Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: The diagram shows part of a logo design. There is one known angle of 142°. Calculate the sizes of…

A: Law of sines for the triangle △ABC. sin Aa=sin Bb=sin Cc

Q: -1 The point A has coordinates (4, 1), AB = 9 5 BC= . Find the coordinates of B and -4 the column…

A: Let B=a,b Now,  A=4,1AB→=-19 So,  AB→=-1 , 9⇒B-A=-1 , 9⇒a,b-4,1=-1 , 9⇒a-4,b-1=-1 , 9⇒a-4=-1…

Q: 9. Find the numerical Integration of cos(x) + sin (x) where n = 4 using trapezoidal rule.

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Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

Q: 3: The cubic interpolation method with two points has converge rate with order three. True False

A: Solution

Q: 4. Classify the type of the equation as elliptic, parabolic or hyperbolic. Uxx xuy+xu 0 =

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Q: (1) Construct an example for three distinguish points A, B and C in a 3- space for validating the…

A: For every three-dimensional vector a→=ai^+bj^+ck^, the corresponding point has the coordinate a,b,c.…

Q: Consider the equation sets below; x + 3y + 2t = 1 z + 4t = 6 x + 3y +z+ 6t = 7 a) Write the system…

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Q: 17: Which of the following directions is descent direction for f(x) = 2x1 + x² - 2x₁x₂ + 4 where Xo…

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Q: 3) You deposit P 12,780.00 in an account paying 93% simple interest. Find the future value of the…

A: simple interest formula A=P1+rt where A is accumulated amount P is principle amount r is rate of…

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

A: This is a question from vector analysis.

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)+¹k! (2k -…

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Q: PAPER 1 N2010 5 Solve the equation 3x³ +7x²-22x-8 = 0. 5. FACTORS OF POLYNOMIALS

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Q: Find the measure of the arc or angle

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Q: 5. Interest rate. A 2-year loan of $4650.25 accumulated $269.75 in simple interest. Calculate the…

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Q: Given that f(z) = z where does f'(z) exist

A: The given function is,  f(z) = z. We have to find those points where f'(z) exists.

Q: the inverse Laplace transform of the following function: 68²-50 s+92 f(s) = (S-2)(8-3)(8-4)

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Q: In a certain Region, about 7% of a city’s population moves to the surrounding suburbs each year, and…

A: We have to Set up a difference equation that describes this situation, where x0 is the initial…

Q: If NG and both G and G/N are soluble, show that G is soluble.

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Q: X = 1 + 6t y = 2 + 4t, ter z = 2t A line is defined by the parametric equation L : If the point (a,…

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Q: the centroid z of the frustum of the right-circular cone.

A: The diagram is given as,

Q: Find the orthogonal projection of -10 14 11 V = 15 onto the subspace V of R4 spanned by -1 2 1 X1 =…

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Q: ber ? Find its for

A: Nusselt number is a dimension-less number used in study of heat transfer between solid body and…

Q: QUESTION 9 A group of 12 students have to decide among three types of pizza: sausage (S), mushroom…

A: We need to compare them pairwise and if one beats all other options in pairwise comparison then by…

Q: X = 1 + 6t y = 2 + 4t, t ER z = 2t A line is defined by the parametric equation L : If the point (a,…

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Q: O Consider the following matrices 0 ^- (-¹2 ~) -- († ;) -- (1 ¹/² : ;) -- (:) --( : ) 1/2 3 A = D= 1…

A: We will use property of matrix multiplication  Two matrix can be multiplied only when number of…

Q: ne blanks and b = -2x+9y, write

A: Given: a⇀=3x⇀-5y⇀ and b⇀=-2x⇀+9y⇀ We should write the given vector5a⇀-8b⇀in terms of x⇀ and y⇀

Q: oblem 5. Let P; be the vector space of all polynomials of degree 2 or less, and let I be the…

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Q: Evaluate the z transform Evaluate the z transform of x(n) = a^(-n) u(n). of x(n) = c^n u(n).

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Q: Given the following data. 1 1.5 2.2 2.5 3 Y 4.5 5.501 11.248 15.625 26 i. The relationship of x and…

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Q: 3 -1 -6 -4 -3 4 Let y = D-B V1 = 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

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Q: Let (-3, 8) be a point on the terminal side of 0. Find the exact values of sin 0, csc0, and cot 0.

A: Here we use basic trigonometry to solve this

Q: Consider the function xy f(x, y) x²+xy+y² k if (x, y) = (0,0) if (x, y) = (0,0) State, with…

A: Given :  f(x, y) = xyx2+xy+y2if (x, y)≠(0, 0)kif (x, y) = (0, 0) To find : The value of k if it…

Q: 6. Find the derivative of y= 2x² (3x-4). A. 6x³ - 8x² B. 18x² - 16x 7. Find the derivative: f(x) =…

A: 6. The derivative,  y=2x23x-4or y=6x3-8x2 ......1

Q: Investor Dan has $119,000 to invest in bonds. Bond A yields an average of 9.4% and the bond B yields…

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Q: If f(X) is a convex function, then ef(x) is also convex function. O True

A: We have to check whether if f(x) is a convex function then ef(x) also convex. As per policy…

Q: 22. Represent the graph of the following functions using a sine and cosine function. 323 124 10 8 m…

A: The general form of the function is f(x) = Asinkx+M or f(x) = Acoskx-π2+M Where M is the midline, A…

Q: temperature T of a heated circular plate with the origin being at the center 64 T(x, y): = x² + y² +…

A: The given problem is to find the rate of change in temperature T from given point within given…

Q: The Hessian matrix for f(x) = x³x3 + x2x3 at the point [1 2 3] is given by: [6 0 31 [18 0 31 [3 0 6]…

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