6- If a,b,c,d>0, use the properties of logarithms to simplify and then Tnd the exact numerical value of 3log a/b+ log d?/ +log (abc) – log d if a'd- 10b?= 0 |

Q: Expand loge x in powers of (x- 1) and hence evaluate log, 1-1 correct to 4 decimal places.

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Q: Tx/2+sin(ix) f(x) = V2r then = (x).

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Q: 2 : 1+ai and w=2-i which of the following is equivalent to ū 9. I+i c. 1-i 6. - 3 +i d.1-3i

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Q: Use coordinate vectors to test the linear independence of the set of polynomials {1– 212 –t',t+21,…

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Q: 3 2 -1 Rank of the following matrix is A = 4 2 6 7 4 5

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Q: Let ø : Z25 → Ss be a homomorphism such that ø(1) = (12468). (a) Find o(22). (b) Determine kero. (c)…

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Q: 2. Given U = 7i – j+ k and W = -2î – 5j + 6k, compute a) Proj w V and b) Proj v W

A: To find  The projection of given vectors.

Q: In Exercises 1-8, show that the given set of functions is orthogonal with respect to the given…

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Q: Box Plots Use the following Box Plot about the height of boys and girls to answer these questions.…

A: The box plot is given about the height of boys and girls.

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A: We make an equation from given information and then solve that equation.

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Q: Sketch the region bounded by the given curves, then find the centroid of its area. 1. у%3D х*,…

A: (5) From Symmetry we can see that centroid of the bounded region is at (0, 0)

Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

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Q: Consider a, b ∈ R where a < b. Use Denseness of Q to show there are infinitely many rationals…

A: To prove: There are infinitely many rational numbers between a and b, where a,b∈ℝ, with a&lt;b.

Q: Problem 7. Let f : N→ N be the function such that f(n) = 1 if n is a perfect cube, and f(n) = 0…

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Q: Q7) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=5X+7Y…

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Q: [17] For each of the following equations, • find general solutions; • solve the initial value…

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Q: In Exercises 1-7, (X,M) is a measurable space. 1. Let f : X R and Y = f-1(R). Then f is measurable…

A: Given: Let's consider X,M is a measurable space.  Here f:X→ℝ¯ and Y=f-1ℝ

Q: 4n +1 5.

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Q: for x[z] given by z1 x[z]

A: Given xz=z-11-z-2 then we have to find x∞ xz=1z1-1z2

Q: Find the values of x,y and z using Gauss Jordan method.

A: We have given a system of equations ,  3x + 4y + z = 102x - 3y + 5z + 9 = 0x + 2y - z = 6 This…

Q: Problem 1: Given: -2,3,8, 13, ... Find the following: (a) 6th term of the sequence; (b) an formula…

A: Here we use arithmetic progression.

Q: f(t) = t? cos 6t 2s(108-s?) А. (s2 -36)3 2s(s? -108) C. (s2-36)3 2s(108-s2) В. (s2+36)3 2s(s?-108)…

A: Given function f(t)=t2cos6t. We have to find the Laplace Transform. Formula will use 1.…

Q: Use Gauss-Jordan Elimination to solve the following system. Identify the Gaussian Matrix and the…

A: We use Gauss-Jordan Elimination method to solve the given matrix.

Q: Cookie salon is celebrating their second anniversary. They are offering hair service for only ₱699…

A: Discount = 1699 - 699 = 1000.

Q: f(x) 2 4 8. 10 12 14 CO

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Q: f(t) = sin* 3t

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Q: Find the solution. (D2+4D+4)y=0; when x =0, y=1, y'=-1. Ay = (1 – x)e2r y = (2 + 3x)e- y = (1 +…

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Q: Let I and J be ideals of R. Prove that if I ∩ J = {0}, then rs = 0 for r e I and s e J.

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Q: Problem: A loan of Php 1500 at 12 % annual interest rate. The loan was made on June 22 and due on…

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Q: The manager of a store determines that a markup rate of 45% is necessary to make a profit. What is…

A: Given: Cost price = Php 800 Markup rate is 45% Concept: Markup price is the price that is imposed on…

Q: Prove that an algebraically closed field is infinite.

A: Let F be an algebraically closed  field.Suppose, if possible, that F is  finite, say, F = { a1 ,a2…

Q: 5. Compute sin a e + 3e¬z

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Q: 1 1 1 1 --1 2 1. A = -1 2 1 3. 3 2 1-10 0 -10 0. 6. -5 0 10 2. B = -2 4 -5 -4 -2 From the given of…

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Q: Let R = {(x, y) € R² | In y <r <1n1< y< e} and let S be the surface defined by the vector function…

A: First we find the region of (u,v) such that the projection of surface on xy-plane is R.

Q: x+y Value of 5x+4y 4x 2xis: 10x+8y 8x 3x (a) 0 (b) x (c) y (d) none of these Select the correct…

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Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: 5. Determine the Fourier cosine series of f(x) = n²– x² 0<x<1

A: We have ,  f(x) = π2 - x2 We need to find Fourier Cosine series of f(x). We know that , Fourier…

Q: 8) Use the Gauss-Jordan method to find the inverse of the matrix A %3D 23

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Q: Q2) Using Graphical Method to determine the optimal value of X1 & X2 that maximize value of Z, Max.…

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Q: Question 4 Given that EF is the midsegment of trapezoid АВCD, what is AB? 92 cm D 12.6 cm

A: Given that EF is the mid segment of the trapezoid ABCD. We have to find the value of AB.

Q: Given the following matrices, perform the indicated matrix operation. 1 7 8 [5 1 2 -2 -4 -6 1 -2 -3…

A: Solution

Q: Find the volume of the solid within the cylinder r2 + y? = 4 that is bounded below by the xy-plane…

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Q: [2 If x + 2y = [1 -31 and 2x + 5y = [7 51 , then y is equal to ? 2 3 [3 11] 1. 7 [3 2. -7] [3 11 -7]…

A: The given problem is to find the matrix y with given matrix equations. Given x+2y=2-315 and…

Q: Problem 5. Find all primes p such that 1+p: 2P is a perfect square.

A: We have to find all prime p such that 1 + p×2p is a perfect square.

Q: Find the future value, using the future value formula and a calculator. (Round your answer to the…

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Q: f(t) = te3t cosh 4t s²-6s+7 s2-6s-7 А. (s2-6s+25)2 С. C. (s2-6s-25)2 s2-6s+25 В. (s2-6s-7)2 s2…

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Q: If the order of A is 4x 3, the order of B is 4 x 5 and the order of C is 7 x 3, then the order of…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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