Find the average value of the function over the given interval. f(x) = x³ +4 over [-2, 0]

Q: Find the minimum distance from the point (-2, -2, 0) to the surface z = √√9-2x-2y. (Hint: To…

A: To find the minimum distance from the point .

Q: 8. The base of a solid is bounded by the graph of x² + y² = a², where a > 0. Find the volume of the…

A: The base of the solid is bounded by the graph

Q: Suppose you need to know an equation of the tangent plane at a surface S at the point P(3, 1, 4).…

A: Answer is given below:  Explanation:Question 1:Answer:   Now 50 %D -S> Univen It) - 24+ 21 , 1 -…

Q: In this problem, use properties of definite integrals. 5 (4x-x2) dx= If [² (4x – (4x-x2) dx= -11 and…

A: Answer is -3Explanation:

Q: Calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables…

A: fxx= -98 sin(7x) cos(2y) fyy = - 8 sin(7x) cos(2y) fxy = - 28 cos(7x) sin(2y) fyx = - 28 cos(7x)…

Q: A retailer anticipates selling 5,200 units of its product at a uniform rate over the next year. Each…

A: We need to find a minimum inventory cost and number of units.

Q: Differential equations have been used extensively in the study of drug dissolution for patients…

A: Answer is given below:  Explanation:Question 1:Answer:

Q: Solve 5 sin(2x) = 4 for the two smallest positive solutions A and B, with A <B

A:

Q: Are these lines parallel, -2_2-1 -2 2-1 and -1+3 Explain. -2 10

A: Yes, the given lines are parallel.Explanation:Step 1: Given,…

Q: and Y. If Zxy = -5y, what Assume z is a smooth function of x can you say about each of the…

A: Answers: (a) −5y(b) 0(c) −5Explanation:Step 1:

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.05t³ +…

A: Answers :: Part -&gt; (A)S′(t)=0.15t2+1.6t+3 Part -&gt; (B)S(6)=66.6S′(6)=18Explanation:Sol)

Q: Calculate the derivative of the function. Then find the value of the derivative as specified.…

A:

Q: 1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while the height, h, is…

A: Note: According to Bartleby guidelines we can solve only one question.  If you want more questions…

Q: Do the following with the given information. 21 cos(x²) dx (a) Find the approximations Tg and Mg for…

A: The integral is given by:Formulas for the trapezoid rule and midpoint rule:Trapezoid rule:Midpoint…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 - x^2 and…

A: Given the region is bounded by the curve and line

Q: ii) siny+x= y.

A:

Q: Compute the characteristic polynomial det (xI - A) of A. Show that landa = 5 is an eigenvalue of A.

A: 1)The characteristics polynomial  is x3−3x2−9x−52) λ=5is an eigen value of matrix AExplanation:

Q: a homeowner wishes to insulate  his 1200 square foot house's attic. The total cost C (r) for r…

A: The homeowner should place 9 inches of insulation in the attic to minimize the total…

Q: Carry out the indicated division and then evaluate the following integral (exact answer): +2 + 6x +…

A:

Q: Consider the functional S[31, 32] = [ dx [7y² + 24y,y2+21y2² +4y² + 12y1y2+9y3] · - Y₁ = azı 322, y2…

A: Functional separability lets you break down a complex functional (think fancy function) into simpler…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Question 1: The answer is option a. ((10,−6,−3)+s(1,2,−2)​)Question 2:The correct answer is option…

Q: Consider the following. y y=x³-2x -4 -2 + 2 2 y=2x 2 (a) Find the points of intersection of the…

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: The concentration of a drug in an organ t seconds after it has been administered is given by x(t) =…

A: The objective of the question is to understand the concentration of a drug in an organ at any given…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: 9)The correct answer is: "False". A normal vector to a line is perpendicular to that line, not…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: 5)Option A is correct answer  6) Option D is correct answer Explanation:

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Let S be the part of the sphere x^2 + y^2 + z^2 = 1 that lies above the conez = sqrt(x^2 + y^2).…

A: The objective of this question is to evaluate the surface integral of the function sqrt(x^2 + y^2)…

Q: Find a and b such that [-1, a, 6] and [b, 8,12] are collinear

A:

Q: Determine the angle that vector a = (12,-3, 4) makes with the y-axis.

A: The angle between the vector a=(12,−3,4) and the y-axis is approximately 103.34…

Q: Find the EXACT value of the area of the surface obtained by rotating y = x³, for 0≤ x ≤ 2 about the…

A:

Q: Find the distance between the points using the following methods. (1,5), (6,9) (a) the Distance…

A: a)Distanceformula:         Distance(d)=41​units b)Integration:          Distance(d)=41​units…

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A: The arc length = 8.352 unitExplanation:

Q: Calculus I May I please have the solutions for the following? Thank you

A: Answers are given belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: Calculate the asymptotes of the following functions provided in the image

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Suppose z = = f(x, y) = (x² + 5) sin(y) + xy². By setting one variable equal to a constant (either x…

A:

Q: Let f(x) = ex-x. (a) Find the critical values of f. Classify each of these values as a relative…

A: (a) Critical point x=0At, x=0 , f(x) has relative minimum value 1.(b) y=(e-1)x(c) a=0…

Q: Using the Laplace theorem, find the determinant of the following matrix : D = [2 1 3}/ [4 5 6]/ [7 8…

A: The objective of this question is to find the determinant of a 3x3 matrix using the Laplace theorem.…

Q: Please answer these three question using differential equation thank you

A: Please find the attached file for details....Thank you...Explanation:

Q: (a) Let vt) be a differentiable vector valued function of t. If v. (dy/dt) = 0 for all t, can we say…

A: The |v| is constant. Explanation:Step 1:

Q: Evaluate | cos5 (9x) sin(9x) da

A: we use the method of substitution to evaluate the given integral.

Q: Let -3x3 + 3y³ - 4z³ – 3xyz - - Use partial derivatives to calculate the point (-6, 1, −2). 647 = 0.…

A:

Q: By setting one variable constant, find a plane that intersects the graph of z = 2y2 - 6x² + 1 in a:…

A:

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: 364π​  cubic units Explanation:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Givne that the region is bounded by a curve  and line

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The point (1, 2, 3) is in the plane r=(−3,4,0)+t(6,4,−2)+s(1,−4,4).Explanation:Steps and…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: 3)Option C is correct answer  4)Option A is correct answer  Explanation:

Q: b. How would you rewrite each expression if it was an integrand for a trig. integral? Just the first…

A: We have to rewrite each integrand1.    Sin3xcos4x2.     Sin2x3.      Cosec3xcot3x

Q: Find the curvature x(t) of the curve r(t) = (-3 sint) i + (-3 sint) j + (-5 cost) k

A: The given curve equation The curvature

Q: What are the Test Statistic and P-Value?

A: a. The null and alternative hypotheses are, H0: μD​ ≥ 0 Ha: μD​ &lt; 0 where D = AFTER - BEFORE b.…