Translate the following exponential expression to radical form √64 √6⁹ $6.9 √67

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Q: 2. F(t)= 41³ +21²-7 t³-1 7 tan-¹t, Int Evaluate lim F(t).

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Q: 1. Let S = {[] [] []} (a) Show that S is a basis for R³.

A: Here, it is given by S=22-1,2-12,-122. It has to be proved that S is a basis for ℝ3.

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A: Given that, f(x,y) = 4xy2 - x2y2 - xy3 and a triangular  region D with vertices (0,0) ,(6,0) and…

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Q: By the alternating series test, the series 3(-1)+1 k(k+8) 3 k(k+8) First find the partial fraction…

A: Given that the series                          ∑k=1∞3(-1)k+1k(k+8).

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Q: Using the Maclaurin series e² -> [²4-2 -² dt 71-0 3 find the general term of the Maclaurin series of…

A: Given: The Maclaurin series is given by ex=∑n=0∞xnn!. To Find: We have to find the general term of…

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A: Here we have to find the equivalent expression of the given one.

Q: Express the following vectors in Cartesian coordinates: a) A = pzsinó a +3p cospa + p coso sino a₂

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A: Using the given Euler approximate solution:

Q: S4.6 Area Inside a Polar Curve Find the area of the interior of the cardioid: r = 3 + 3 cos (0) Area…

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Q: Use Euler's Method to solve numerically. 4. Solve y'=x²- 2y, with y(2) = -1, numerically, using a…

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Q: Let z = x+iy. Verify each of the following identities: sin 2₁ sin 2₂ 1. cos(21 +22) = COS Z1 COS Z2…

A: Let, z=x+iy, where i=-1. 1) cos(z1+z2)=cos(z1)cos(z2)-sin(z1)sin(z2)

Q: c) Given (2 + ax)(1+ bx)7 = 2-41x +357x² ... where a and b are integers. Determine the value of a…

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Q: a) Express (-√3+32) in the form rei, where (radians) lies in the second quadrant. Give your answer…

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Q: 1. Is the set R\ {0} under multiplication abelian?

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Q: Compare the advantages and the drawbacks of the theoretical (analytical) and experimental approaches…

A: Theoretical (Analytical) Approach to Mathematical Modelling: Advantages: Theoretical Basis: The…

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Q: Compute the matrix of partial derivatives of the function f : R² → R², ƒ (x, y) = (4x, 8y) and…

A: Let  f:ℝ2→ℝ2  be a function defined by f(x,y)=(f1,f2) .  The matrix of partial derivative is defined…

Q: A pomegranate is thrown from ground level straight up into the air at time t=0 with velocity 67…

A: The given height function is ht=-5t+67t. We have to find the time it hits the ground and the time it…

Q: An industrial system with three industries has the input-output matrix D and external demand matrix…

A: The given matrix is, D=0.10.30.20.00.20.30.40.10.1,E=6000700017000. The equation is X=DX+E. The…

Q: (b) Find a matrix Q that converts from S to the standard basis for R³. Find a matrix P that converts…

A: Note: As per Bartleby guidelines, we are supposed to answer first three subparts. You can ask the…

Q: Suppose the curve C is the graph of the function f(x) = (x-1)(-5) ER, 2/1, *#5. Write down the…

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Q: 3. Show that the following graph is planar: Without changing the vertex-set, what is the maximum…

A: We are to show that the following graph is planar: Without changing the vertex-set, We find the…

Q: Maximize p = 10x + 10y + 15z subject to x − y + z ≤ 12 2x − 2y + z ≥ 13 −y + z ≥ 5 x ≥ 0, y ≥ 0, z ≥…

A: Maximize p = 10x + 10y + 15z subject to x − y + z ≤ 12, 2x − 2y + z ≥ 13, −y + z ≥ 5, x ≥ 0, y ≥ 0,…

Q: Solve 6 []-[20 -20 Q- 131: = Y x(0) = 4, y(0) = −18 -181

A: Finding eigenvalues of Coefficients matrix:

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Q: The finite-duration sequence x[n] = [-4, -1, 2, 0, 3] has a Fourier transform X(w). Determine X(0).…

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Q: Transform each of the following vectors to spherical coordinates at the point specified. a) A = 5a,…

A: Given: The following vectors into cylindrical co-ordinates a) A=5ax at  p4.120°,2b) G=4ax-2ay-4az at…

Q: Suppose A € M3 (R) and that A is diagonalizable. Suppose that A₁, A2, and A3 are the three…

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Q: Refer to the Venn diagram below. How many elements are in the set A'? n(A)= A 28 9 20 B 40

A: The given Venn diagram, We have to find the number of elements in the set A'.

Q: Complete the square to write the equation of the sphere in standard form. x² + y² +22² + 5x - 2y +…

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Q: Given sinP= Answer: 13 and cosQ = where 0<P<. 5 <a and 0<Q< 1/₁ to the nearest hundredth, sin(Q-P) =

A: Given that sinP=513, cosQ=45, where 0&lt;P&lt;π2,0&lt;Q&lt;π2. The value of the sinQ-P has to be…

Q: Suppose that µ(E) < ∞ and suppose that {n} is a sequence of non-negative μ- integrable functions…

A: μ(E)&lt;∞: This implies that the measure of the set E is finite. hn is a sequence of non-negative…

Q: Determine the first 3 terms in the Maclaurin expansion of y = esin² T + X + x²

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Q: 11. Consider the ODE y (8) - 2y (6) - 7y(4) – 4y" : = x 2 cos x + 3 sinx. The auxiliary equation for…

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Q: A homogeneous rubber string of length 5 has its initial points displaced by x/2 and then oscillates…

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Q: Calculate the cross products of the unit vectors i x k and jx i. (Give your answers using component…

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