Q1 Pick a number A number is chosen at random from the whole numbers 1, 2, 3, ..., 25. Work out the probability that the number is: an odd number or a factor of 8 a square number or a factor of 10 a multiple of 4 or a multiple of 6 18 5 23

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

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Q: Congratulations! You won a contest sponsored by a local radio station. If you were given the choice…

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Q: The slope of the tangent line to a curve is given by f'(x) = 7x² + 9x - 8. If the point (0,5) is on…

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Q: The one-to-one function fis defined below. 3 f(x)=√√/2-x+7 ¹(x), where f¹ is the inverse of f. 1…

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Q: 0. Given the following functions, make a sign sign diagram for • the first and second derivative and…

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Q: The Taylor series expansion of 2 |z| < 1 is (solve) Z-2¹ −(¹ + ² + ² + ² …..) X Option 2 O…

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Q: True or False: Suppose k is constant. Then 5 [² is equal to 10k. Select one: True O False kdx

A: Solve the given intregal

Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: 1. Stretching a spring A spring has a natural length of 10 in. An 800-lb force stretches the spring…

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Q: a) Find all values of x where the function is discontinuous, and (b) graph the given function f(x) =…

A: Here, the given function is: f(x)=2x+2            if x≤0x2-2x+2   if x&gt;0

Q: . Find the absolute the following functions on f(x) = x² - 6x + 5 minimums the and maximums of given…

A: As per our guideline we are supposed to answer only first question of a multiple type of questions.…

Q: Let a = (5,4, 2) and b = (-1, -2, -3), th 3a - 5b = (10, 2, -9). Select one: O True

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Q: Solve DU 112 dx 4x+3 x³ + 2x² + x

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Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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Q: The value ff*(x+y+z)dzdydx is (solve) 3/5 O 5/8 O 2/7 O 7/8 O

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Q: The Eigen value of matrix p is (solve) ГО 0 Lo 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [ (42³1 + (4t³i + 14tj…

A: We need to find integral.

Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: Find | 22 x²z ds, where C is the line segment from (0,4,-6) to (2,9,-5)

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Q: 5 Laplace transform, solve y" - 4y' + 7y = 0 y(0) = 3 , y'(0) = 7

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Q: (a) Find Maclaurin expansions for sin 2x, cos 2x and e³ up to and including the term in x³. I (b)…

A: Maclaurin Series for f(x) :       f(x)≈ f(0) +f'(0)x +f''(0)x22!+f'''(0)x33!+... Note : As per our…

Q: determine the interval of increase (in interval notation) b) determine interval of decrease

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Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: Solve the initial value problem y" + 5y' - 24y = 0, y(0) = a, y'(0) = 80. Find a so that the…

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Q: The equation x² + y² +10y + z² = 6z - 18 represents Select one: O a sphere with center (0, 5, -3)…

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Q: If v=3i+2j+ k,w=3i+ 4k and the angle between v and w is 90, find v.w (solve) 10 8 0 O Option 3 O

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Q: im →0 In[(x + h)² + 1] + ln(x² +1) h

A: Given: limh→0lnx+h2+lnx2+1h

Q: Convert the rectangular equation to polar form x² + y² = 9 (solve) rsino = 9 Option 4 O r=3 Option 2…

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Q: The two vectors a = (-1,2,-4) and b = (2, -4,-8), are not parallel but are orthogonal. Select one: O…

A: Given vectors:- a=-1,2,-4 b=2,-4,-8

Q: This is the approximate time right ? Making the no. of days from feb to aug into 30, by that logic…

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Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 5x²,…

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Q: Question [ a) [1 b)' 1. : Evaluate 6 1₂° ₁x + 2 ): If Show all your work. then find f(x). c) [ graph…

A: a)∫26 (x+2)x-2 dxLet    x-2 = z2      implies     dx =  2z dzx=2   ⇒ z =0x=6  ⇒ z= 2The integral…

Q: The equation of the plane that passes by P(2, 0, -1) and that is perpendicular to the line x-5 2-y Z…

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Q: Find dy/dx, given that xy^3 -3y^2 +xy=1-3x

A: We have given a function y in term of x, and finding the derivative of that

Q: Sketch the space curve represented by the vector-valued function and give the orientation of the…

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Q: Use the information given below to find sin (a-ß). 12 5 12 tana= with a in quadrant III cos ß= 13 I…

A: Find sin(alpha-bita)   When tan(alpha)= 12/5 in third quadrant  And cos(bita) = 12/13 in first…

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: Part 1 Basic Integration Solve the following integrals through video presentation. 1. f(4x²-3x²+) dx…

A: I can solve it but i can't explain like video presentation. It's a basic integration. Just apply…

Q: 46. A triangle with sides 5,5 and 6 feet is submerged vertically in water (p=62.4 lb/ft³) with the 6…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: Given the function f(r. y) = 1² + y² + 1 • For every point (r. y) = R², compute the gradient and the…

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Q: Find the function F that satisfies the following differential equation and initial conditions. F'(x)…

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Q: Write v as a linear combination of u and w, if possible, where u- (3, 2) and w(2, -1). (Enter your…

A: Given :- u =(3,2) , w=(2,-1),v=(-6,-4)  Write v as linear combination of u and w

Q: y = 3 2 x²/3 + 1, 8 < x ≤ 1 (3)

A: The objective of the question is determine the length of the given curve.

Q: (6xy - 3y² + 2y)dx + 2(x − y)dy = 0; when x = 0, y = 2

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Q: Find the area between the curve and the x-axis over the indicated interval. y = 6 x 10 [1, 10] The…

A: See this solution in below

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: Put the following program in standard matrix form: Z = X₁ + X₂ X1+ 5x2 <5 2x₁ + x₂ ≤ 4 maximize:…

A: see below the answer and the explanation

Q: Find the average value of f(x) = Enter the exact answer. fave = x (6x² + 5)² over the interval [0,…

A: Avg value is given by below

Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: x-1 0…

A: This question can be solved using the concept of lines in three dimensional geometry.

Q: Problem 2. Find the area between these curves: (a) f(x) = 5x-2 and g(x) = 4x + 1 on the interval…

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