Determine the x-intercept of the plane: [x, y, z]= [3, 1, 3]+[1, 1, -1]+[0, 1, 3]

Q: Differentiate the function. f'(x) = f(x) = log₁0(x⁹ + 7)

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Q: Consider the following vector function.. r(t) = (2√2t, e²t, e-2t) (a) Find the unit tangent and unit…

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Q: Show that the equationy/= -9y is satisfied for y = cos 30.

A: We are required to check that y=cos3θ satisfies the equation y''=-9y.

Q: If f(x) = 3x5 - 10x³ +5, on what intervals is f"(x) > 0? Enter the (disjoint) interval(s) below…

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Q: Q14 Find the equation of the tangent line to the curve f(x) = 2x²(x − 3) at x = 1.

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Q: Find lim f(x) if, for all x > 1, x → 00 4 12ex - 24 4ex X 3√x √x-1

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Q: In (1 + x²) x-0 1 COS X 37. lim - x² - 4 x→2 ln (x - 1) 38. lim

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Q: If 3 A = -4 -4 8 1 x 4 1 1 Is a singular matrix, then x is 1

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Q: A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the…

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Q: Let y = f(x), where f(x) = (5x² + 6)1/3. Find the differential of the function. dy =

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Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

A: Given, f(x, y) = e-xyRegion, x2 + 4y2 ≤ 1   Finding the critical points, ∂f∂x = -ye-xy∂f∂x = 0, y =…

Q: Write a rational function whose graph is shown below. -1 + 2 0 -2- T 1 1 + 2 F L 3 + 1 (4,0) 4 1 -10…

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Q: Consider the ellipse 9x² + 64y² = 576. Consider the point P(16,3). Find an equation for both lines…

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Q: Use differentials (or equivalently, a linear approximation) to approximate sin(56°) as follows: Let…

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Q: Let f be the function given by f(x)=sin(2x)cos(1+x). What is the average value of fon the closed…

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Q: Q16 A helicopter is rising straight up in the air. The distance from the ground t seconds after…

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Q: [1-R] [CLO 12] What is the slope of the line f⊥, where f⊥ is a line perpendicular to the line f,…

A: The given line is: 4y-3x=5

Q: The temperature in a hot tub is 103° and the room temperature is 75°. The water cools to 90° in 10…

A: Here we apply the Newton's law of cooling

Q: Find the derivative of the functio y = sin ¹(6x + 1) y' =

A: Given: y=sin-16x+1

Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 4y and y³ = x with y…

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Q: Consider the following. Find r'(t) and r"(t). r' (t) r"(t) = K= r(t) = (4t², In(t), t In(t)) = Find…

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Q: The position of an object with respect to time is given by the following function: d(t) = t³ + 2t² -…

A: Derivative

Q: Given the vector u = (-5,4), find the magnitude and angle in which the vector points (measured…

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Q: The cost of producing x bags of dog food is given by C(x) = 900+√700 + 50x²-x where 0≤x≤ 5000. Find…

A: The cost of producing x bags of dog food is given by Cx=900+700+50x2-x, where 0≤x≤5000. To find the…

Q: Find all the first order partial derivatives for the following function. f(x,y,z)=x²y+y²z+xz² O A.…

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Q: Find the volume of a pyramid with height 28 and rectangular base with dimensions 5 and 7 using…

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Q: [5-A] [CLO 12] The line ℓ passes through the points (−3, −4) and (5, 1). Give an equation for the…

A: Given: The line l passes through the points -3,-4 and 5, 1. The objective is to find the equation…

Q: Sketch the region of integration and convert the polar integral to a Cartesian integral or sum of…

A: Please see the below picture for detailed solution.

Q: Find the directional derivative of the function f(x, y) = ln (x³ + y³) at the point (2, 3) in the…

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Q: Solve the initial value problem for x as a function of t.. (t²-19t+90) dx dt x(t) = (Type an exact…

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Q: The area under the curve of the function f, using the Riemann sum, will be exact if we let the n or…

A: Solved below

Q: Use the theorem given below to find the curvature of r(t) = √62²i + 2tj + 2t³ k. k(t) = Theorem: The…

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Q: A computer is purchased for ​$5000. Its value in dollars after t years can be approximated by…

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Q: Given u = 2 – 8j and d =−8+3j, find | + ả| and || + ả Give EXACT answers. You do NOT have to…

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Q: Consider the function f(x) Enter an antiderivative of f(x). Do not enter +c as part of your answer.…

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Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: The given function is;  f(x)=sqrt(4-34x).

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.

Q: Express the integrand as a sum of partial fractions and then evaluate the integral. 10x² - 1 S 4 X X…

A: Given integral : ∫-10x2x4-1dx To find: The value of given integral using partial fraction. Let I =…

Q: Sketch-the-graphs-x = 4y - y² and x = y

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Q: A student drew the graph of y = f (c), y = f' (x), y = g(r), and y = h(x). Unfortunately, they…

A: Find the graph of y=fx and y=f'x.

Q: Q15 Find all non-zero derivatives of the following function: f(x) = 5x³ - 7x² + 9x - 1

A: Here we differentiate f(x) with respect to x until it becomes a constant

Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 4 sin…

A: By using the double integration to find the area of the plane region  enclosed by the curves. y=sin…

Q: Evaluate the integral. cos y dy 2 sin y + 3 siny-4 S

A: To evaluate∫cosysin2y+3siny-28dy

Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: Find the arc length of y = 4x + 1 on 0 ≤ x ≤ 2.

A: Recall the formula: ddxconstant=0ddxx=1∫dx=x+C

Q: Suppose that f (x, y) = x³y². The directional derivative of f (x, y) in the directional (-3, 3) and…

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Q: Suppose the demand for a certain brand of a product is given by ​D(p)=−p^2 / 416+450​, where p is…

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Q: Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist,…

A: We find the first and second derivatives using the power rule F(t)=3t5-20t3+20F'(t)=ddt3t5-20t3+20…