Given that log(5) ≈ 0.6990 and log(4) ≈ 0.6021, find the value of the logarithm. log(5/4)

Q: Find the scalar and vector projections of b onto a. a = i + j + k,   b = i - j + k

A: Given vectors, a = i + j + k,   b = i - j + k

Q: Consider the following graph. y -5 -4 3 1 1 2 3 4 6. (a) Find the interval(s) on which f is increasi...

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Q: Find the area of the triangle with vertices P(1,2, –2), Q(0,0,0) and R(2,3, 1). NOTE: Enter the exac...

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Q: y" + 2y' + y = 7 + 75 sin 2x

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Q: Q4 Calculate the volume of the solid obtained by rotating the region bounded by the parabola 4py = x...

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Q: Find the area under the curve 2x+3y-6%3D0 from x+63D0 to x-19%3D0

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Q: Evaluate the following integral using partial fractions: 2x2 + 1 (x – 1)(x - 2)(x - 3)

A: Topic:- integration

Q: In a local art museum, a moving spotlight projects geometric figures on the wall in front of it. The...

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Q: Iff (x) is a polynomial with real coefficients and zeros of 4 (multiplicity 3), -5 (multiplicity 1),...

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Q: Evaluate the integral i- te*j + VTk] dt 0,

A: ∫03t2i - tet2j + t7/2k dt [t3i/3 - et2j/2 + 2t9/2k/9 ]03 9i - e9j/2 + 2*35/2k (9 , -e9/2 , 235 )

Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and ...

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx - (...

Q: 15-30. Working with parametric equations Consider the following parametric equations. a. Eliminate t...

A: We have to eliminate the parameter eqaution of x, y and indicate the positive orientation

Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

Q: Evaluate the integral. 3* dx 3* +4 Solution:

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.  (1−x)y′= ?2

A: (1 - x)y' = 2 y' = 2/(1 - x) dy/dx = [2/(1 - x)] dy = [2/(1 - x)] dx Integrating : y = 2 ln(1 - x) +...

Q: p + q N = p = u + vw, q = v + uw, r = w + uV p + r aN an aN when u = 4, v = 3, w = 5 au' av' aw ƏN 1...

A: We have to find the derivative by chain rule As per guidelines we have to solve one question

Q: Consider the following planes. 5x + 6y – z = 66 x - 12y + 2z = 0 (a) Find the angle between the two ...

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Q: C.Logarithmic and Exponential Functions

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Q: 3 The 9 ft wall shown below stands 30 feet from a building. Find the length of the shortest Straight...

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Q: Calculate L4 for f(x) = 42 cos () over L4 = %3D

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Q: The vector v and its initial point are given. Find the terminal point. = (4, -9); Initial point: (9,...

A: Given

Q: Let f(x, y) = 4x² + y². Using Lagrange Multipliers, how many critical points are there for f subject...

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Q: 5x2 dx et

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Q: b.y = x100 ; find dx100 d'100y (100th derivatives)

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Q: az az Use the chain rule to find and əs at z = tan(x° + y°), x = s In(t), y = tes az as az at II II

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Q: 12. Construct an algorithm that has as input an integer n> 1,n + 1 points and xo, X1,…· Xn ... and a...

A: INPUT: n, x0,...... ,xn, x OUTPUT: ∏i=0n (x-xi)

Q: Determine whether the subset W={(a,b,c)|b=a+1} is a subspace

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Q: OLVE THE FOLLOWING: What is the derivative of.6x* – 7x3 + 5x² ? What is f'(x) if (x) = (2x² + 1)(x² ...

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Q: Help

A: Topic:- simplification

Q: Use algebraic and/or graphical methods to solve the inequality. 10x° -x* <0 Select the correct choic...

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Q: Determine which of the vectors is (are) parallel to z. Use a graphing utility to confirm your result...

A: Given :  z = &lt; 3, 2, -7&gt; Let's find the parallel vector-    

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = 9i – 6j+ 3k, v = –...

A: We will calculate the dot product and the angle  between these vectors to solve this question.

Q: Alice will use all of the last 24 hours before her exam to study two different ways. Without any pre...

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Q: a power series representation (Give yo power series representation centered at x 8 + X f(x) 1 -X f(x...

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Q: Find a unit vector e, where v = (4,2, 5) ey = %3D

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Q: Let the function f be defined by tan(x) - 1 f(x) = sec(x) (a) Use the Quotient Rule to differentiate...

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Q: 3x (g) lim x +1

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Q: Prove the identity. (Recall sinh(a + b) = sinh(a) cosh(b) + cosh(a) sinh(b).) sinh(2x) = 2 sinh(x) c...

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Q: Find the linear approximation of f(x)=sin(x) at x=2π3 and use it to approximate sin(121∘). Give you...

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Q: question Let f: {0, 1} * -→ {0, 1} * be a function that maps each string u = abc where Ja| = |b| = |...

A: Given that f:0,1 →0,1u=abc where a=b=c fu=aSolution :one-to-one function ( injective )=A function f ...

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: rectangular box without cover has a volume of 12 m?. The width of the base is half Hhe length. Mater...

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Q: 3. For h(x) = (2x+3)2 find h' (1). (3-x)4

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Q: If r = 26 cm, what is the area of this sector? Express your answer to the nearest tenth of a centime...

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into ...

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. (R...

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Q: Consider the following function and express the relationship between a small change in x and the cor...

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Q: Find the derivative of the foll owing functions. Show complete solutrons, including trigonometrie id...

A: As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   And ddxcoshx=sinhxddxtan...