Use the substitution method to solve the system -x+y=-2 4x - 3y = 9 Your answer is x= y =

Q: A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal…

A: The volume of the box is vx=4x3-48x2+140x on the interval 0,5 we have to find its maximum volume…

Q: A sales representative for a company that produces blenders can sell x units of their deluxe model…

A: To marginal profit is the derivative of the profit function, which is based on the cost function and…

Q: - Evaluate sin x dx using 3 i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

A: We have to evaluate ∫0π2sin x dx. Here a=0 and b=π2=1.570796 Given n=6 ∴ h = b-an = 1.570796-06 =…

Q: Calculate L6 for f(x) = √√7x + 3 over [1, 3]. (Give your answer to three decimal places.)

A: The given function fx=7x+3 over the interval 1,3 we have to the left Riemann sum using 6…

Q: What are the three cases we must consider for finding horizontal/slant asymptotes?

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Q: Parameterize the plane that contains the three points (-2,-2,-2), (-12, 2, 12), and (0, 35, 30).…

A: To find the parametric equation of a plane containing three points (-2,-2,-2,), (-12,2,12) &…

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

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Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: Approximate the integral with the approximation. (Round your answers to one decimal place.) x²y dy…

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Q: Consider the following equation. =(21+√51) f(x, y) = y^/x, P(1, 3), u = (a) Find the gradient of f.…

A: Given :fx,y=y4x

Q: An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth…

A: Solution of given question is written in below steps.

Q: Find the third degree Taylor polynomial T3 (x)centered at a O T3 (x) = 3 - 6x + 9x² - 12x³ O T3…

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Q: Differentiate from the first principle f(x) = x² +6x² + 3

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Q: Use the Ratio Test to determine whether an 15" n! Evaluate the following limit. an+1 lim n→∞ an an…

A: This question can be solved using the concept of test for convergence.

Q: Given the following function,f (x)= -x^2-10x-25 , use the second derivative test to decide whether…

A: Now the equation(function) given in the question f(x)=-x2-10x-25

Q: If y=-2x² + sin x solve for the differential of dy.

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Q: Consider a projectile launched at a heighth feet above the ground and at an angle with the…

A: The parametric equation of the position of the ball is given by…

Q: Suppose that f(x) is a continuous function on the interval [-1, 3] with f( − 1) = − 3 and f(3) = 3.…

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Q: (a) Find the area of the region bounded by the given curves I + y = 0, r = y² + 3y. (b) Let R be the…

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Q: b. (1) (x) c. (fog)(x) d. (gof)(x)

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Q: II) Let f be the piecewise function f(x) = x³ + 6x² + 8x x+2 1-x-2, -, x≤-1, x -2 -1 1 1) Sketch the…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi +…

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Q: Question 1 options:   A vector has initial point (-5, 8) and terminal point (0, 2). Write the…

A: let initial point A (-5,8)=(x1,y1) terminal point B(0,2)=(x2,y2)

Q: 1) For each of the following tests, give an example and explanation of a specific series formula…

A: We have to explain the series and give an example.

Q: Let y = (2x + 3 sin(x))4. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

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Q: Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is…

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Q: Find f'(x). f(x)= ex+ 5x 3 Inx f'(x) =

A: We have to find the derivative.

Q: 9 outside cardioid r = 1 + cos 0 inside circle r = 3 cos ( 10 lemniscate ² = 4 cos 20 outside r = =…

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Q: Find the missing coordinate of the point, given that the point is in quadrant IV (₂ Oa). 5 √61 Ob)…

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Q: If x > y and a are a negative real number, this always applies

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Q: Find the area of the segment cut from the curve y=x (x-3) and the ordinates x=0 and x=5

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: Follow the procedure given below.

Q: 1. S x² (x+1)4 - dx

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Q: Compute the gradient vector fields of the following functions: A. f(x, y) = 1x² +10y² Vf(x,y) =i+j…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: (1 + 2.6) ² an = (1 +

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Q: 7. Given f(x)=√x² + 3, determine p(x), q(x), and r(x) such that f(x) = p(q(r(x))). ✓✓

A: We need to find p(x),q(x),r(x)

Q: If g = xy + yz + zx and Ē = x²yī+ y²zī+ z²x k, find F. grad g and cross product of F and grad g at…

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Q: The radius of a spherical balloon is increasing at the rate of 0.6 cm / minute. How fast is the…

A: Topic - Application of derivatives Volume of sphere=43πr3 where r is the radius of sphere

Q: Question* An equation of the tangent plane to the surface x² + xy +22²-3-0 at the point P, (1,1,1)…

A: Basic differentiation is used along with the stated formula

Q: Shown to the right is a graph of f(x). (a) Describe the transformation for h(x) = -f(x + 1) +2. (b)…

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Q: an = (1 + 2,60) ² =

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Q: Determine whether the following series converges or diverges. Σ k=0 2k 2 k +1

A: To determine the series convergence or divergence.

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1) and R (1, -1, 1). Find the perpendicular…

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Q: = xn For the function f(x) = cos(x), write Newton's formula as n+1 = F(xn) = solving f(x) = 0. Type…

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Q: Evaluate the following: 1. [cos 3xdx

A: We can solve the integration as below.

Q: IV. Determine whether the following series converges or diverges. Show your complete solution. +00 3…

A: To determine whether the following series converges or diverges.∑n=2+∞ n4-234n3+5

Q: Calculate the arc length of the indicated portion of the curve r(t). r(t) = (3 − 2t)i + (1+6t)j +…

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Q: rticle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4…

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Q: Given three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1) Find a vector perpendicular to the…

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