a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

Q: d the mass of a wire in the shape of helix r(t) = cos лti+sin лtj+8tk, ≤t≤1, where the density of…

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Q: II. Use the differentiation rules to solve for the derivative of each function. Show your complete…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 4. Find the length of arc of the curve x3 + y = 1 in the first quadrant from the point where x =…

A: Let's find arc length of given curve in first quadrant.

Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

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Q: Determine whether the statement is true or false. If it is true, explain why it is true. If it is…

A: Here we have to choose the correct option.

Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure  water is then…

Q: 3 -6 -4 -3 4 Let y = V1 = 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁ and…

A: Let, W be the subspace spanned by v1 & v2 . Now, calculate the distance:…

Q: Given an acute angle Cosx=2/7, find the exact value of cos(x/2). (Use a half-angle formula)

A: As we know from the half angle formula; cosx2=±1+cosx2   Given; cosx=27

Q: Fx 4x2cos x find the derivative of fx

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Q: ddy /dx for the following functions: _y².cot x = [sin(x. y)]¯¹ b) y = (Inx+x)tan x

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Q: 1) Write a differential equation that models this situation. Let V represent the volume (in gallons)…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next…

Q: the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with…

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Q: Evaluate the integral. 1 √x(1+x)” 1 x(1+) dx = dx

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Q: Which of the following describes the graph of g(x) = -In(4 — x)? 8 7 5 4 2 2 -30-9-8-4 -6 -10 6 8 9…

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Q: 6. Find the derivative of y= 2x² (3x-4). A. 6x³ - 8x² B. 18x² - 16x C. 15x² - 6x D. 6x-4

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Q: Evaluate the integral. sin dx Se √1-x² 2

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Q: B) Let F(x,y)=√√y-x, then answer the following (For four only): (1) Find the function's domain (2)…

A: According to Bartleby guidelines I can only answer the first three sub questions.

Q: A function f(x) is continuous on the real numbers and has the following features about the point x =…

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

Q: 0=yج - - لا

A: Follow the procedure given below.

Q: Q5. Check whether the given points A (1, 2, 3), B (3, -1, 4) and C (-2, 3, -4) are collinear.

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Q: 1. Find the area of the region that lies inside the cardioid T-1+ sin 0 and outside the circle r -…

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 sin(x) + 7 cos(x),…

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Q: 5.) (ya+yx) dx -x ² dy = 0 ny Simplier) + xbx = vbe+bv=xb. Y = VX keta dy=vdx + xdvo (v²x²+xx²) dx…

A: We want to solve the given homogeneous differential equation.

Q: Find the intersection of the line 1₁: x-6 2 || y+2 1 with the plane p: x-6y - 2z - 10 = 0

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Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: Find the value of the following derivation y = x ln x sin x

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Q: Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of…

A: Given problem:- Graph of y = ex   Transform it to make the graph of y = - ex + 5   Give the domain…

Q: . Using the diagram below, fill in the blanks. B A D F G E Column A: a) AB+ BC b) FE+FG c) HG+FB H…

A: Follow the procedure given below.

Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

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Q: (iii) Find the directional derivative of f at the given point in the direction of v. f(x, y, z) =…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 15. Solve the following limits (if possible): 1 1 5+x 5 a) limx→o x x³ - 27 b) limx→3 x² − 9

A: Simplification of limit

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Consider the following polynomial function. f(x) = (x+2)²(x-1) Answer the questions regarding the…

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Q: Solve the initial-value problem y"+5y'+6y=0, y(0)=2, y'(0)=3

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Q: News s the followinouation sutisfied Cauchy - Rieman. equation w = Z₁ W 4

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Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: topic- average value of function over interval

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

A: The given sequence is ∑n=0∞-1n+1n+6xn=∑n=0∞an

Q: Find the vector standard a Ā= (-3.4.5)

A: we know that if v=<a,b,c> then its standard form is v=ai^+bj^+ck^

Q: Calculate the operational determinant of the given system in order to determine how many arbitrary…

A: Concept: Elimination method: We can now and again combine equations as we do in linear algebra to…

Q: Graph the rational function. -5x-15 f(x)= x²+2x-15 Start by drawing the vertical and horizontal…

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Q: find the limit lim x->6 -1/(x-6)^2

A: Solution

Q: True or False: 6. If the limit exists at x = a then the function is continuous at x = a. 7. A…

A: This question can be solved using the concept of limit, continuity and differentiability.

Q: 8. Determine a vector equation for the plane with Cartesian equation: 2x -y + 3z-24 = 0

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Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y =S₁ dx (x-1)².…

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Q: 28. Which pair of lines are parallel? a. x+7y-2=0, 7=(2,5) + s(1,7), s € R b. 3x-4y-2=0, 7 = (1,4) +…

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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Q: For each function, determine whether it is a polynomial function. Function (a) v(x)=3x² +0.6x4 (b)…

A: polynomial can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2),…

Q: 2 Within x² - y² = 16, y = 0, x =

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Q: Use GEOMETRY to compute the value of the definite integrals. Report EXACT answers - not decimal…

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