Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) = z(t): %3|

Q: The relationship between the number of decibels B and the intensity of a sound I in watts per…

A: a)β=10ln(10)lnI10-16β=10ln(10)lnI10-16β=10ln(10)ln(I)-ln(10)-16β=10ln(I)ln(10)+16ln(10)ln(10)β=10log…

Q: 10. Maximize f(x, y) = 25 – ² - y² subject to 2x + y = 10

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Q: x2 1. Let f(x) = 3Vx² – 1 and g(x) x4 – 81 (a) Determine the domain of f and g. (b) Compute gof and…

A: Find domain.  According to guidelines we solve only first question.

Q: Compute the length of the curve r(t) = (41² + 1, 81² - 5,1) over the interval 0 < t < 2. (Use…

A: To find the length of the parametric curve  r(t)=4t2+1,8t2-5,t3 over the interval 0≤t≤2. Here, let…

Q: Eind the conorel ond norticulor solution of the linoor first order oguot

A: Given query is to find the solution of the differential equation.

Q: Find a formula for the nth partial sum of the series and use it to find the series' sum if the…

A: The given series, 91.2+92.3+93.4+......+9nn+1+.......

Q: r = 3 cos 0

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Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Write the first five terms of the geometric sequence a, based on the given information about the…

A: Given query is to find the first 5 terms of the sequence.

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A: Given query is to find the parametric and symmetric equation.

Q: Ans: y' + y2 - y = 0 ae* 5. y= 1+ae*

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Q: 05 1 15 2 25 3 3.5 1.5 0.5 -0.5 -1 -1.5 -2 Identify the equation of the surface. Oæ = y? O r = 2 y =…

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Q: Given: a, =4, d=-1 Answer the following questions. Part: 0 / 2 Part 1 of 2 (a) Write the first five…

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Q: Find the area between the curve ​f(x)=x^2​+15 and the​ x-axis from x=3 to x=5.

A: Given query is to find the area under the curve.

Q: Set up iterated integrals for the scenarios described below. a. Set up, but do not evaluate, an…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Question Find the absolute maximum and absolute minimum of the function f(x) = over the interval[-4,…

A: Use critical point to evaluate the absolute maxima and minima .

Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) x²…

A: The given curves are y1=x2+2x+5  &amp;  y2=2x+15

Q: Solve the differential equation. dy = 5 ex-y dx Choose the correct answer below. O A. y= 5 e* +C O…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: x dx (7x2 + 3)

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Q: A piece of wire 5 m long is cut into two pieces. One piece bent into a square and the other is bent…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 1. (3y²+ 2x²)dy + 2xydx=0

A: Ode

Q: Given that Vƒ(4, – 15) = 4i – 2 j, find the directional derivative of the function f at the point…

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Q: Use the Integral Test to determine whether the infinite series is convergent. Σ -4 n=1 Fill in the…

A: Let the function f(x)  is a continuous, positive and decreasing function on the interval  [ k,∞)…

Q: Compute the gradient of f(x, y) = 9 - 5x² – y² and evaluate it at the po (4, – 1). %3D - The…

A: Use gradient formula for finding at given value .

Q: Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal…

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Q: 9. Evaluate the following definite integrals. S" V5x – 1 dx 10 а. b. J sin 2x dx

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Q: Use spherical coordinates to show that the volume of a sphere of radius R is V = *nR³.

A: Given the radius of sphere is =R  Then equation  of sphere is                      X2 + Y2 + Z2 = R2…

Q: average cost per gigabyte of RAM can be approximated by the function C(t)= 8,500,000(0.65)^ t, where…

A: Given query is to find the the average cost of ram for the given time.

Q: 1 8 - Find an equation of the plane containing the Point P (2,1, -1) and having the normal vutor N :…

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Q: (x³ +2x)" Find dy/dx, given the following: y = V2x-4 (2³ +2x)“ V(2r–4) 17 -36a²+10x-24 %3D (2x–4)²…

A: Quotient Rule of differentiation :  ddx (uv) = v.dudx-u.dvdxv2. dxndx=n.xn-1

Q: xx+x dx

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Q: Find the directional derivative of f at Pin the direction of a. f(x, y) = 3x³y*; P(5, 1); a = 7 i –…

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Q: Assume that ū. i = 3, |ū| = 5, and |õ| = 6. What is the value of 5u. (4ü – 87)?

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Q: Determine whether the function is​ one-to-one. If it​ is, find a formula for its inverse.…

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Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: y" + 4y' + 6y = 1 + e¬2t , y(0) = 0, y'(0) = 1

A: We need to solve the differential equation.

Q: Evaluate using Integration by Parts. (Use symbolic notation and fractions where needed.) xeSx+6 dx…

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Q: Find the area, if it is finite, of the region under the graph of y = 5x* e over [0,00). Select the…

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Q: 2. Given that arcsec 2) + (x² – y²)² = 2. (a) Find dy using implicit differentiation. dx dy usino…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges giver 1 by the vectors u, v and w…

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Q: The students at Prairiewood Elementary plan to make a pyramid out of plastic cups. The bottom row…

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Q: f(x) = |x + 1| (-1,0) Prove that has no tangent line at

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Q: Find the area of a triangle PQR, where P = (2, – 3, – 4), Q = ( – 6, – 2, – 6), and R = (5, 6, – 6)

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z²; _P(-3,3,1);…

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