Solve the following system of equations 2x + y = 1 3x + 1.5y = 1.5 Give a geometric interpretation of your answer.

Q: Find area of the region under the curve y = 4x³ - 2 and above the z-axis, for 3 < x < 8. area =

A: We know that the area of the function f(x) at x=a to b is  int_a^b f(x) dx

Q: (b) lim (4x) = 818 8 (c) lim -6x= 8118 (d) lim -6x = 818

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: =) f²4f(x) dx = [ =) f2f(x) dx =[ ☐☐ =) f₁5 f(x) dx = [

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: an = 3n 2n + 3

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Q: 12. Practice similar Help me with this Use the Integral Test to determine whether the infinite…

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Q: (iii) y = (3 + 2x)−5

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Q: First find f' and then find f. f"(x) = x³ + 8x² – 3x - 9. f'(1) = 10. f(1) = -10. f'(x) = 0 f(x) =

A: The given derivative function is:f''(x)=x3+8x2-3x-9The given condtions are:f'(1)=10      and…

Q: Find the average value fave of the function f on the given interval. sec²(2), [0,7] 2 fave = f(0) =…

A: The given function is: fθ=17 sec2θ2 ;             0, π2

Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

A: Give that marginal cost function C'x=0.0006x2-0.14x+25 and daily fixed cost is = $900

Q: r = 3 -4+2 sin 0

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the dot product of the vector pair. u = and v =

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Q: 3) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1, π,…

A: x=sin3t y=2t z=cos3t Point÷ -1,π,0 π=2t means t=π2

Q: Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has…

A:

Q: (c) Figure 4.1 shows the rough sketch of the function: y = x(x² - 6x + 8) y 0 A Figure 4.1 B X Find…

A: NOTE: Refresh your page if you can't see any equations. . to find the zeros of the function, take…

Q: Find the first term In a geometric sequence in which the common ratio is 5/4 and the tenth term is…

A: The general formula for nth term of a geometric sequence is given by tn=arn-1  Where, a is the first…

Q: Calculate all four second-order partial derivatives of f(x, y) = 4x²y + 8xy³. fxx (x, y) = fay (x,…

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Q: A volume is described as follows: 1. the base is the region bounded by x = y² +10y + 62 and x = y²…

A: equation are  (x-6)=(y-14)

Q: II. If f\x, y, z/ = ôf of of += e3x+2y+4z, then find x+y Ox Oy ôz

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Q: (2) g(x)) = f(z) g(z) + g(z) - f'(x). (a) For each of the following functions, use the Product Rule…

A: Note : As per our Guidelines , we can solve first part as your all parts are not small and also in…

Q: xp zx^x 0/ S (a)

A: The given integral is xsqrt(1-x2), limit from 0 to 1 to

Q: Use the standard Maclaurin series for sin(x) and cos(x) to find the first three non-zero terms in…

A: We have, Maclaurim series for sin x and cos x

Q: Determine x = f(t) for dx (t² + 6t). dt = 6x + 6, t> 0; f(1) = 9.

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Q: Find all four ways how to write point (3, 60°) in polar coordinates.

A: The point r,θ=3,60°

Q: Find the component form of vector with initial point (-6, 2) and terminal point (7, -3). O v = (-8,…

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Q: Recall the Chain Rule and how it can be applied to find the derivative of a composite function. In…

A: As per our guild line we are supposed to answer only 3 subparts of a question.

Q: 20. Practice similar Help me with this. Use the limit comparison test to determine whether For n ≥…

A: We have to to Check the convergence of given series.

Q: (a) The series For the following answer blanks, decide whether the given sequence or series is…

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Q: 8. Use the standard Maclaurin series for sin(x) to find the first three non- zero terms in the…

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Q: Determine all significant features (approximately if necessary) and select a graph. f(x) = 2 42-84…

A: We have to draw the graph.

Q: Evaluate the integral. (Use C for the constant of integration.) [7. 7z³e² dz

A: ∫7z3ezdz

Q: Determine whether the given point (x,y) is on the unit circle. Nin 21 No OYes

A: This is question of calculus  here one point is given  we have to verify that this point is on unit…

Q: Find the standard form of the complex number 6 (cos+ i sin). Round values to the nearest hundredth.

A: Standard form of the complex number is a+ib , where a ,b are real numbers.

Q: Express the limit as a definite integral on the given interval. 2 lim Σ 19(x;*)3 – 5xi]Δx, [2,7] i =…

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Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

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Q: Biologists have noticed that the chirping of crickets of a certain species is related to…

A: T=Temperature in degree FahrenheitN=Number of chirps per minute

Q: Refer to the figure. V 30° u 45° 15⁰ q 20° W Find the components of q = (91, 92).

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Q: You know that: ■ ■ ₁9(t) dt = 15 g(7) = g(9) = 5 Evaluate: +9 юст g'(x) √√25-(g(x))² Upload your…

A: Given:  ∫79gt dt=15g7=-52g9=5 To Find: To evaluate the integral ∫79g'x25-gx2 dx.

Q: 3) Curve Stretching Let F(x) = x 4-12x² +36x. use all significant Features (Domain, X and…

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Q: 2 1) Find the area bounded by the curves y = x² and y=√x.

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Q: ons, use your work (a) to help you the generar (Recall that general antiderivative of a function…

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Q: Create a limit evaluation problem that requires substitution with an answer of 1.

A: limit evaluation problem

Q: Consider a vector field F(x, y, z) = (2xz + y², 2xy, x² + 3z²) and a curve C given by r(t) = (t², t…

A: Consider a vector field F(x, y, z) = &lt;2xz+y^2, 2xy, x^2+3z^2&gt; and a curve C given by r(t) =…

Q: Find the value of the constant b that makes the following function continuous on (-∞, ∞ if x 8 PL {…

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Q: 11) An animal population oscillates over a 7 year period from a low of 800 in year t = 0 to a high…

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Q: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius…

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Q: Evaluate the integral. Jarctan arctan(3t) dt

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Q: 4) Find the curvature of y = e* at the point (0, 1). Then find the equation of the osculating circle…

A: Given:    y = ex  Point: ( 0, 1 )

Q: Consider the following vector function. r(t) = (8 sin(t), t, 8 cos(t)) (a) Find the unit tangent and…

A: To find unit tangent and unit normal vector and curvature. Given  r( t) =  { 8sin(t), t, 8cos(t) }

Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

A: The given equation is, x5+4=0