The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is given by

Q: Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

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Q: Find the sum of the series. 1 - In(4) + (In(4))² _ (In(4))³ 2! 3!

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: Solve the following

Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: y = x(x2 – 4)

A: We have to find the area of the shaded region.

Q: り (2xy+y?) dx - 2x? dy = o 2) Yy dx - (メ+ 2y)? dy -0

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Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: Evaluate the line integral, where C is the given space curve. y dx + z dy + x dz, C: x = t, y = t, z…

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Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

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Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Find curl (3z i+ 4x j+ 5y k). curl(3z i+ 4x j + 5y k) = ( i )i + (i )j+( i )k

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Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Fit a second degree parabola y = ax² + bx + c to the following data %3D 3. y 1.8 1.3 2.5 6.3

A: Normal equations associated with y=ax2+bx+c are: ∑y = a∑x2+b∑x+nc ∑xy=a∑x3+b∑x2+c∑x…

Q: Solve the equation on the interval 0s0<2x. 50 = 2 sec 50 What are the solutions to sec T=2 in the…

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Q: The three basic trigonometric substitutions are in the table below. Integral Contains Try using…

A: We will solve the integration.

Q: 10 %3D1

A: Formula Given

Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: Use the Taylor series for f(x) = Vx, centered at a = 16, to approximate the numerical value of v17.…

A: This question can be solved using the concept of Taylor series centered at a.

Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: iF Zz fexiy) where R= ě- ě Gud ge ě- ě show That!- +y5= (e-ぎ)( - 24

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Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: 1. Find fa(x, y) and fy(x, y) given f(x, y) = (csc y) Arcsin(r2).

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Q: In(æ) -de (2)/ 1

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Q: Find a basis for the eigerspaca conesponding to the eigenvalue 12. 17 141 12 A basis for the…

A: We want to find the basis.

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: Determine if the point A(4, -7, 8) lies on the plane: T1 : [x, y, z] = [-3, 2, 9] + s [2, 3, –7] +t…

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Q: petdo eidj to noitom paidi b noit t no eog edt bnt Use the limit process to find the area of the…

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Q: sketch the given region R and then find its area. R is the region bounded by lines y=x, y=-x, and…

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Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

A:

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: o} (2xy+y?) dx - 2x² dy = O 2.) xy dx -(x + 2y)? dn

A:

Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: %3D Find the area of the region bounded by y = 5x² + 1, x = 0, x = 2,y = (

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Q: dx x?(4x++9)Z

A: Integration are simplyfied..

Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x? N(x, y) = x² - 2y (I): (2xy – 3x )dx…

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: If we apply Rolle's Theorem to the function f(x) = 2x? – 4x – 7 on the interval [ – 1, 3], how many…

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Q: Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln…

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Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

Q: Use the figure to evaluate the following function, given that f(x) = sin x. (Simplify your answer.…

A: Given diagram,

Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: 6. v(y) = In (y² – 8y – 1)

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Q: Evaluate the definite integral. i-ej+ k 7 O el - 1 7. O el - 1 i+ (e- - 1) j+ k i- (e-- 1) j+ k O e…

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Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

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Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: Find the minimum speed of a particle with trajectory c(t) = (t3 – 4t, t2 + 1) for t > 0. Hint: it is…

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