Find the equation of the line joining the points (2, -8) and (5, 6)

Q: Find the value of (a, b) so that sin 12x lim x+0 x³ cos 12x Write your answer in the form of (a, b)…

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Q: Determine the equation of the polynomial that pass though the following points: X Y 0 5 1 8 2 7 3 6…

A: Given: X 0 1 2 3 4 Y 5 8 7 6 9 To find: The equation of the polynomial.

Q: Working with the solid E bounded by z = 0, z = 5y and x2= 36−y, use Mathematica to: (a) graph the…

A: Given : A solid E bounded by z=0, z=5 and x2=36-y, To Find : a) Graph the solid E bounded by z=0 ,…

Q: The graph of the derivate F' of a function F is shown JA 2 (a) on what intervals is I decreasing?…

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Q: 3. Find the area of the region bound by the z-axis and the curve y = 8r²(6 — 2) y = 8x² (6-x) n

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Q: Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of…

A: Any point on the polar coordinate system is represented using the ordered pair: r, θ. A graphing…

Q: 1. (Theorem 2.1, Eq. 2.4) By employing change of variables r = ax +y and s=x, prove that the PDE: A…

A: Auxx+Buxy+Cuyy=0 A≠0B2-4AC=0

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 200 + 1000t - 150t², where t…

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Q: Suppose a 7 ×9 matrix A has six pivot columns. What is nullity A? Is Col A = R6? Why or why not?…

A: In a 7×9 matrix having a six pivot columns that means rank of matrix  A is  6 now by using  rank…

Q: Let f(x, y) = (x³y², x²y). Obtain a linear approximation of f(x, y) at the point (-1,1) and use this…

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Q: Given f: [] → R where f(x) = sin x Is it a function or not? If function, identify whether it is…

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Q: fo* sin(y²)dy to places. You need to use Fundamental Theorem of Calculus and L'Hospital rule…

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. (Enter the…

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Q: Find the matrix A of the quadratic form associated with the equation. 9x² - 6xy +9y² + 24z²31 = 0 A…

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Q: Q8 An elliptical culvert located underground with the total height is 4.0 ft and width is 8.0 ft,…

A: The elliptical culvert has height of 4ft, width of 8ft and water is filled up to 1 ft depth. The…

Q: Question 5 Textbook Y Videos [+] Use Newton's method to approximate a root of the equation 2x7 +8¹…

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Q: Construct a homogeneous transformation matrix with the provided rotation and trans In 1

A: Introduction:   The plan is to employ loops like those in the software for spirally printing a…

Q: e the given integral equation or integro-differential equation for y(t). t y'(t)+ 125 (t-v)y(v) dv =…

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Q: we will use the method of separation of variables and Fourier series to derive a solution formula…

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Q: 8. Approximate 3.9996 using linearization.

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Q: II. You want to build a rectangular cardboard box with no lid. If the cardboard of dimension…

A: Given the dimension of the box is 10 cm ×16 cm The length of the box is 10-2l and the width of the…

Q: For each function, state whether it is linear, quadratic, or exponential. Function 1 X 4 5 6 7 8 y…

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Q: de − 7 √(1-k² sin²0) 2F₁ ( ½ ‚ ½ ; 1;^²), \K[<1

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Q: 4. Let S be the surface in R³ defined by x² - y² +22² = 9. (c) For what value of the real number t…

A: If S be a surface given by f(x,y,z)=0 then every point (x,y,z)=(a,b,c) of the surface satisfying the…

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 500 + 900t - 90t², where t is…

A: Given that the traffic flow rate is    rt = 500 + 900 t - 90 t2      The time taken 6 A.M. as t = 0,…

Q: For the given rational function, (A) Find the intercepts for the graph. (B) Determine the domain.…

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Q: Suppose y is a function of x, i.e. y = y(x), and -15 x·y+5.ex+y= -18. a. Find in terms of x and y.…

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Q: dy -1- -y=0, y(0) = 4 dt Use Y for the Laplace transform of y. (not Y(s)). So Take the Laplace…

A: The initial value problem is given by:  -1dydt-y=0 , y0=4 We have to use the Laplace transform to…

Q: Solve the given initial-value problem. The DE is a Bernoulli equation. y1/2 dy +y dx y3/2 = 1, y(0)…

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Q: a. Find Ztt Ztt = b. Does for z(x, y, t) = cos(√36 + 4t) sin(6x). sin(2y). ab sin (a) O Yes ə əx…

A: The given problem is to find the double partial derivatives of the given function and also to check…

Q: Exercise 5.9.7 Write the solution set of the following system as a linear combination of vectors 2…

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² R²:…

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Q: Determine the dimensions of Nul A, Col A, and Row A for the given matrix. A = 164 4 - 1 0 0 0 -1 0…

A: The matrix is given by :  A=1644-1000-100000000000 We have to find the dimensions of Nul A, Col A,…

Q: Letz € C² be any complex vector, and 1 3 3-3i). 19 3+3i Show, that "Az is a real number for all z €…

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Q: Problem 3: Let f: A -> B be a function. Prove that if f has a right inverse g1 and a left inverse…

A: Solution:

Q: Estimate the percentage change in the function f(x) = x² + 2x - 1 as x increases from 1 to 1.25.…

A: We know : ∆f≈ f'(x)*∆x Here f(x)=x²+2x-1 And so f'(x)=2x+2. Also ∆x= 1.25-1=0.25 Thus,the eqn will…

Q: a. Find fax. fxx (x, y) = absin (a) b. What is fyy? 8 dx 8 f(x,y)= In -In (√Br² + 5y²). a Ω E

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Question -x₁+3x₂ = 2 2x1 + x₂ + 4x3 = 3 x2 + 2x3 = 4 (a) Using [IA] [A¹1], Find A-¹. (b)Find Adj A.…

A: Given the system of equations                                -x1+3x2=2,2x1+x2+4x3=3,…

Q: Evaluate the line integral (3ry² + 6y) dr, where C is the path traced by first moving from the point…

A: The given problem is to evaluate the given line integral over the given path C traced by moving in a…

Q: Consider the semicircle r(t) = a cos(t)i + asin(1)j with 0 ≤ ≤ and a > 0. For a given vector field…

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Q: Find the orthogonal trajectories of the family of curves x² + y² = cy A B с D x² + y² =c x² + y² =…

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Q: The quadratic function  f(x) = a(x − h)2 + k  is in standard form. (a) The graph of f is a parabola…

A: A function fx is said to be a real-valued function if the function gives real values for all the…

Q: Let n = p₁¹p². does n have? Pk pak, where the p; are distinct primes, and the a¿ are positive…

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Q: Let P be a convex n-gon in which no three diagonals intersect at a single point. How many…

A: The idea is to select 4 points.

Q: Prove that 1 1 16 ≤ (a+b+c+d) = + = + b + ax (²=²+ + + + + + + ² + 1 = 0) d for all positive numbers…

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Q: Find a rational and an irrational number between 71.8094 and 71.8095

A: Let a=71.80940       b=71.80950  Clearly a&lt;b  Here c=71.80942 is a rational number lies between a…

Q: we will use the method of separation of variables and Fourier series to derive a solution formula…

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Q: 6 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute. The base of the ladder…

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Q: Find the directional derivative of f(x, y, z) = ((x+y+z)e², (x² + y²)e-²) at c = (1, 0, 1) in the…

A: The given problem is to find the directional derivative of the given vector function at point…

Q: [a+(b-c)x]F=a(1-x) F(a+)_ (c-a)(c −b)x F (c+) C

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