Find an explicit solution of the given initial-value problem. dx dt 8(x² + 1), ×(Z) = 1 4

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A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where m is the…

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Q: Solve the given initial value problem. dx dt 7x+y; x(0) = 3 dy dt = - 6x +2y; y(0) = 0 The solution…

A: To solve the given initial value problem.dxdt=7x+y;  x0=3dydt=-6x+2y;  y0=0

Q: Question 1. Find the parametric equations of the line through (-3,4,2) that is perpendicular to both…

A: The line through -3,4,2 that is perpendicular to both u=1,1,-5 and v=0,4,0

Q: Indeterminate Form 1 1 6. lim x-0 sin 2x

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: What is T₂(x) centered at a = 3 for a function f(x) such that f(3) = 9, f '(3) = 8, f "(3) = 4, and…

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Q: A hyperbola has aymptotes y=+-3x/2 and vertices at (0,+-6). Find an equation of this hyperbola.

A: Given Asymptotes   ;   y=3x2   ,   y=-3x2Vertices         :     (0, 6)    and    (0,-6)

Q: 10. Solve each of the following systems; a) 2x+3y-z=-2 x - 2y + 3z=13 4x + y + 3z = 9 c) x + 2y + 72…

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Q: A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling…

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Q: Find an explicit solution of the given initial-value problem. x2 dy = y − xy, y(-1) = -3 dx y =

A: We can solve as follows

Q: The plane with equation = (6,-2,3)+a(1,3,0) + b(2,2,-1) intersects the y- and z- axes at the points…

A: Vector equation of line is r'→=a→+αb→-a→where, a→ is the position vector of the point A.…

Q: 4. For the relation explain the transformations, y-intercept, asymptote, domain/range, show at least…

A: The given function is y=2-x+2-1 ............................................. (1)

Q: solve using laplace transform 69= y" + y = f(t) where: (0)=0 y 1 1 0, 0≤t≤介 f(t) ] 1. π 2π y'(0)=1

A: Let's solve diffrential equation by using laplace transform.

Q: Simplify the difference quotient. f(x) = 3x2 + 4x — 2 show ALL of your work in order to receive…

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Q: 2) The diagram shows two squares. Name a single vector equivalent to each expression. B M F E D a)…

A: Given

Q: find the volume in the first octant under the plane z=y and inside the cylinder y²=4-x.

A: Given that, the cylinder is y2=4-x and the plane is z=y. y2=4-xy=±4-x Note that, the volume is in…

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Q: Suppose that F(x) is a power series with radius of convergence R = 12. Which of the following is…

A: Here, given that F(x) is the power series with the radius of convergence R=12. Therefore, the…

Q: Find the area of the region between the curves y=x and y=x^3 on the interval [-1, 1]

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Q: Find the derivative of fx Fx=8x3 cot x

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Q: 3 -6 -4 -3 4 Let y = ,V1 = 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁1…

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Q: Find the derivative f(x) = |x-21= X-2 -(x-2) ×22 x 22

A: To find the derivative and then to evaluate each intervals with derivate.fx=x-2=x-2,  x≥2-x-2,…

Q: A tank contains 210 liters of fluid in which 40 grams of salt is dissolved. Pure water is then…

A: Given the volume of the fluid initially = 210 lsalt dissolved = 40 gpure water is pumped into the…

Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

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Q: Given that f(z)=z-z where does f'(z) exist

A: Concept: f(z) is differentiable at a point z0 if it follows two conditions: (1). ux , uy ,vx ,vy all…

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Q: 6 + 5 4 3 2 1 What is the least possible degree of the polynomial graphed above?

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Q: Use the elimination method to find a general solution for the given linear system, where…

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Q: 1 dx x(x - y²) separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y…

A: We can solve this as follows:

Q: 4. Find the derivative of f(x) = 7. A. 7 B. 0 5. What is the derivative of In(x)? B. 1/x A. xln(x)…

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Q: A Venn diagram is used to illustrate the relationship between sets R, S, and T. The regions of the…

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Q: 123 Evaluate the integral [[[x²y³ (x²y + xyz + y²²) dxdy dz 001

A: Topic = Integration As per guidelines , At a time only one question can be answered. Please repost…

Q: Q3/Solve the differential equation (0²2 - 2x + 5 = e²xsinx)

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Q: Find the derivative of f(x) = 7. A. 7 B. 0 What is the derivative of In(x)? A. xin(x) B. 1/x C. 7x…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find the arclength of a parametric curve given below for 0 ≤ t ≤ π (x(t) = 3 cos t (y(t) = 3 sin t

A: Find the arc length of given parametric curve

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: Find the equation of the curve that passes through the point (0, 3) and has a slope of 2 x+1 O y =…

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

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Q: (k) y dx + x dy = 0 separable exact linear in x linear in y Ⓒhomogeneous Bernoulli in x Bernoulli in…

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Q: Find the area of the region enclosed by the curves 4x² + y = 4 and x - y = 1.

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Q: 4. Determine a value of k for which the line L₁ : x=2s, y = 1+ks, z = 2-s, se R and the line…

A: Topic = Geometry As per guidelines , At a time only one question can be answered. please repost for…

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √√₁-x² dy = 0, y(0) = 1/2…

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Q: The count in a bacteria culture was 200 after 10 minutes and 1700 after 30 minutes. Assuming the…

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Q: if the birth rate of a population is b(t)=2200+52.3t+0.74t^2 people per year and the death rate is…

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