Find the exact area, in fractional form, under the curve y = 4x³ over the interval [0, 5].

Q: Which of the following are true about the function f(r) = 24? 1 f(r) is an odd function. II f(x) has…

A: The given function .The aim is to check the function is an odd function, find its vertical…

Q: Rewrite the given scalar equation as a first-order system in normal form. Express the system in the…

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Q: Given the function f'(x) = −x³ – 6x² + 72x, determine all intervals on which f is decreasing.

A: If f'(x)> 0 in an interval I then f(x) is increasing on interval I.If f'(x)<0 in an interval I…

Q: Find all exact solutions on the interval [0, 27). If there is more than one answer, enter them as a…

A: We have given a trigonometric equation .We have to find the solutions on the interval .As we know…

Q: Evaluate the line integral, where C is the given curve. Sext xªy√z dz, C: x = 5, y = t₁ z = t², 0 ≤…

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Q: How about #2?

A: The given differential equation is  ,

Q: Find a basis for the 2-dimensional solution space of the given differential equation: y" - 5y' = 0

A: The given differential equation is

Q: Transform the given system into a single equation of second-order x₁ = −5x₁ + 7x2 x₂ = -7x1 - 5x2.…

A: We have to transform the given system into a single equation of second order.

Q: Graph the polynomial P(x) = x³ + x²-5x + 3 using calculus by showing the given st (e) Sketch the…

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Q: Using matrix algebra techniques, find a general solution to the system. x' = 3x -6y y' = 6x-17y -…

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Q: 4. Solve the following linear systems. 21 + 2x2 2x1 + x1 (a). - 22 x2 x3 3 + 24 = 4 x4 1 + x3 +

A: The system Ax=b is,The augmented matrix is,The reduced system is,The general solution is,

Q: Find a formula for the polynomial p(x) that satisfies all of the following conditions: ● a degree of…

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Q: Recall that if F(x) is an antiderivative of f(x), then so is any function of the form F(x) + C,…

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Q: C. Evaluate d²y dx² at the point (1,2)

A: Consider the curve

Q: Find the limit if it exists. (If an answer does not exist, enter DNE.) x² lim (x, y) → (0, 0) (x² +…

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Q: person is given an injection of 300 milligrams of penicillin at time t = 0. Let f(t) be the amount…

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Q: A circular plate with radius 9 m is submerged vertically in water as shown. Express the hydrostatic…

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Q: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account…

A: The objective of this question is to find the value of Lucy's mutual fund account today, after three…

Q: Use sigma notation to write the sum. X Σ* [[ IM [²(²¹) + ¹] + [²( ² ) + ³] + - + [² (¹) + ¹] [2 [2…

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Q: Find the equation of the tangent line to y = (x³ + 2x + 3) eª at the point where x=0. The equation…

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Q: 0-5-5 x'(t) = -5 0-5 x(t). x( -5 -5 0

A: We have to solve the given initial value problem.

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder a2 + y2 = 25 and…

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Q: 5. L 6. L S S+2 2 S² + 4s +3 S+2 (s² + 4s+6)² 2

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Q: At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can…

A: The objective of the question is to find the estimated number of cars, N, traveling on a 1-mile…

Q: A square-shaped sheet of ice is growing as time passes. If the sheet of ice is always in the shape…

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Q: Function kf(x), f(x) + g(x) xn (n − 1) 1 X exc COS X General Antiderivative Function sin x sec² x…

A: Solution Antiderivatives are the opposite of derivatives means integration.

Q: View Policies Current Attempt in Progress Find the area enclosed by y = 5x and y = x². Round your…

A: This is question of calculusHere we have to find area using integration Further calculation is given…

Q: Evaluate the integral by interpreting it in terms of areas. 3 6.³ |2x - 3| dx

A: Simplify the absolute value of expression under integrand.

Q: Suppose we wish to represent the volume of the solid blob B depicted below with a triple integral. 근…

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Q: The height (feet) of an object moving vertically is given by s= - 16t² + 48t+ 36, where t is in…

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Q: Compute the line integral [xydx+x²dy, where C is the arc of the parabola x = y² that goes from (1,…

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Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

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Q: Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

A: The given function is

Q: needed, enter the values as a simplified fraction. (Examples: 1/2, -14/3) any operation is undefined…

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Q: 10. f(x) = e² 12. h(m): 2 化 Vm

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Q: If the quotient is positive, which of the following must be true? (A) a>0 (B) b>0 (C) ab>0 (D) a-b>0…

A: The objective of the question is to determine which of the given conditions must be true if the…

Q: Suppose f(x,y)= (-y) (25-ay). Answer the following. Each answer should be a list of points (a, b, c)…

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Q: Find an equation for the hyperbola described below. Graph the equation by hand. Vertices at (0, -8)…

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Q: When an object is removed from a furnace and placed in an environment with a constant temperature of…

A: The Newton's cooling law Temperature of the objectProportionality constant Enviornment temperature

Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A: Degree = 5 2 is a zero of multiplicity 3−2 is the only other zeroleading coefficient is 3.

Q: Sketch the graph of the quadratic function. f(x) = x² + 4x + 4 O S No Solution Help -10 9 8 7 6 5 4…

A: To sketch the graph of the following quadratic function.To indicate the coordinates of the vertex,…

Q: Əw Əv y Find when u = 0, v = 0 if w=x² + Əw Əv |u= 0, v = 0 " x=4u-2v + 1, y = 2u + 6v - 1. =…

A: Consider

Q: Let f(a, b) = a/ (b − 1)^2 . a. Describe the domain of f. b. Sketch the level curves of f…

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Q: How many solutions does the equation sin 3x = 1.44−2x^2 ​have? Using Newton's method.  The equation…

A: sin3x=1.44-2x2

Q: If we have to y = C₁e* + c₂xe* is the general solution of the homogeneous differential equation…

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Q: A contractor drew up plans for an addition to a house. The new outside walls will be a total of 80…

A: A contractor drew up plans for an addition to a housse. The new outside walls will be a total of 80…

Q: Sketch the graph of the following, given y = f(x). y = f(x) -4 2 Use the graph to answer this y =…

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Q: 7. Find the parametrized equation for the intersection line of the planes 2x+y-z=1 and 4x - y = 3.

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Q: 6 Evaluate te (t² + 3) (t² + 7) dt using the Fundamental Theorem of Calculus, Part 2. Enter only…

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Q: The graph of f(x) is shown (see figure). 5x² f(x): = x2 (a) Find the following limit. L = lim f(x) =…

A: The given function is