1. A mouse wheel is 16 cm in diameter and the base of the wheel is 2 cm off the ground. If the hamster can spin the wheel 4 times each second, what is the sine function that describes the movement of the wheel if it starts at its lowest point?

Q: How many ways are there to select 6 people to form a committee in a group of 10 men and 8 women, if…

A: A combination is  number of ways to select r items from n items. It is denoted by Crn. The formula…

Q: Let P₂ represent real polynomials of degree 2 or less. Define a linear transformation T: P₂ → P₂ by…

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Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: 9. Give a proof of F (Vx)(Vy)x = y → (√Y)Y

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Q: Calculate {te® sinh(4t)}

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Q: (t, 0≤t <3 Express f(t) = 0, 3 ≤t<5 in terms of unit step functions. et, t≥5

A: A unit step function can be defined as; u(t)=0t&lt;01t≥0 where u is the unit step function which is…

Q: (a) (y + 2)y' + ty = cos(2t) is (b) 3yy' + 4y = 0 is

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Q: Solve the following recurrence relation: hn = 3hn-1 + 2n, where n is greater than or equal to 1 with…

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Q: Find the Green's function for with homogenous Dirichlet b conditions in the half cylindr < R, 0 < <…

A: The impulse response of an inhomogeneous linear differential operator defined on a domain with…

Q: (c) Let C be the vector space of continuous real-valued functions on R. IfT: C → C is defined so…

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Q: Find the smallest positive integer solution for the given system. x=37(mod 52) x=14(mod41) You must…

A: Given system x≡37 mod 52x≡ 14mod 41 We will solve it by Chinese remainder theorem. Here,…

Q: Verify Stokes's Theorem by evaluating line integral S.F. F(x, y, z) = (-y + z)i + (x − z)j + (x -…

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Q: (a) Set up (but do not evaluate) an integral that calculates the volume of that part of the solid E…

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Q: FORMULA FROM EXPONENTIAL GRAPH The figure shows the graph of an exponential function. The dots on…

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Q: Solve the given differential equation by undetermined coefficients.

A: Given,              y''-2y'+2y=e2xcos(x)-4sin(x)

Q: Consider the following Extended Form Game: A' (9,5) O {A, A'] A O {A, (A', B')) O (B,B,B) O {(A, B),…

A: Given below clear explanation

Q: Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 =…

A: I am attaching a picture where you will get step by step solution first I write the formula of euler…

Q: Let be the transformation f : R → R given by f(x) = 3x − 3x^2  Check if it has periodic points with…

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Q: Verify the Divergence Theorem by evaluating [/F. F. N ds as a surface integral and as a triple…

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Q: Which of the following graphs is NOT planar? II. III.

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Q: Which of the following characteristics do the two given graphs share? -5-4-3 -2 - 5 4 3 2 + 1+ -1 -2…

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Q: Determine is the given series is a p sin(4x) x(3+5) Select the correct answer below: n=0 O a) Yes,…

A: Given series is ∑n=0∞sin(4x)x(3n+5)

Q: Determine if X is an eigenvalue of the matrix A. 22 -19 Select an Answer Select an Answer 1. A = 2.…

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Q: [³] 2 0 [[ = ܕV ܕ 4 ܗ ܗ 7 ܗ ܘ ܘ and v₁ = Use the Gram-Schmidt procedure to produce an orthogonal set…

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Q: 1. Prove cos 8-sin 8 cos 8 + sin e = sec 28 tan 20.

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Q: transform of log (S²112) 1- Find the inverse of Laplace transform of log

A: Sol:- L-1log10s2+1s-12Use Inverse Laplace Transform table:   L-1Fs=-1tL-1F's

Q: If f(x) = logz and g(x) = s, what is the domain of (ƒ × g)(x)= O{x € R/x -8 and x ‡ 1} O{x € R/x>0…

A: Given functions are f(x) = 1log x ,   g(x) = 18 + x

Q: Consider the following Extended Form Game: O True A' (9,5) O False A P2 P1 B' A' B (5,2) (8,5) A P2…

A: Given below clear explanation

Q: Given that cos(8√t) √nt find the Laplace transform of√√cos (8√t). {√² cos(8√7)} = 0 = e-16/s √s

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Q: Let be the transformation f : R → R given by f(x) = e^x  Check all your periodic points

A: A function f(x) is said to be a periodic function if f(x+T) = f(x)

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

A: To solve given question first of all we use the trigonometric identity and then use the Laplace…

Q: 3. Write out in set notation: a. The set of all integers divisible by 3 b. The set of all primes…

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Q: -6 (Click on graph to enlarge) What is the Domain? What is the Range? Enter your answer in interval…

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Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

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Q: (VI) (VII) (VIII) integer?) Find A¹07 by writing as linear combination of eigenvectors of A. b Find…

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Q: Consider the set that consists of the following six matrices 10 -6) :) I 0 1 C = (3) 0 1 A = D = 1…

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Q: Let B₁ and B₂ be orthonormal bases for an n-dimensional vector space V. Let A = JB₂B₁ be the…

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Q: Carbon-14 is used by scientists to estimate how long ago a plant or animal lived. The half-life of…

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Q: Verify the Divergence Theorem by evaluating [/F. F. N ds as a surface integral and as a triple…

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Q: Suppose set A={1,2,3,...,50} is divided into exactly two disjoint, nonempty sets. For example, one…

A: My approach is the I break into 2 disjoint part and take cardinality(number of element) of every…

Q: An open-top box is to be constructed so that its base is twice as long as it is wide. Its volume is…

A: Volume of cuboid is V=LWH Here,  L=lengthW=widthH=height Surface area of cuboid with open top is…

Q: 24 If csc(z) 23 Give exact answers. sin (1) (-) = ¹(²-) = ( COS tan (in Quadrant 1), find Submit…

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Q: Question 5 Calculate _{te® sinh(4t)}

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Q: A ball is dropped from the top of a building. The height of the ball in metres above the ground at :…

A: The equation of the height of the ball is provided as h(t)=-4.9t2+19.6. We need to determine the…

Q: Evaluate (any way you want) the integral fF.dr, y² x=3 4 9 oriented counterclockwise, and F(x, y, z)…

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Q: Consider the initial value problem (sin y)y' (t) = +¹⁄2, y(3): = −1. The largest open rectangle in…

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Q: A particle a of mass m moves inside a bowl. If the surface of the bowl is given by the equation Z m…

A: As per the question we are given the 3d equation of a surface in cartesian coordinates as :  z =…

Q: Find the curvature of the curve r(t) = (cost, sint, sin t) at the point P(1,0,0).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Q13. Suppose a connected graph, G, has 9 vertices. How many edges must there be in a spanning tree…

A: Sol:- No. of Vertices = 9