A particle travels along the x-axis such that its velocity is given by 1,2 v(t) == cos(t²-4) What is the distance traveled by the particle over the interval 0 < t < 3? You may use a calculator and round your answer to the nearest thousandth. hift

Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Could you do part b please

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. h(2) = re* (a) Determine the domain (b) Determine if the graph has any asymptotes, or any kind(s)…

A:

Q: I Find the following indefinite integrals. dx = cos(t) (5 sin(t) +12)² dt = +C +C

A:

Q: 4. 2

A:

Q: -t An object moves in a straight light according to the position function s(t) = 2te where s is in…

A: Step 1: An object moves in a straight line   with position as a function s(t)=2te−t , where s is in…

Q: Question 7 Find the equilibrium point for a product D (x) = 25 - 0.009x² and S (x) = 0.007x². Round…

A: We know that The equilibrium point occurs when the demand function (D(x)) equals the supply function…

Q: Whole of question 2 ans for part c us 1.5D

A:

Q: Find the smallest number n of terms needed to obtain an approximation of the series > 30ke - 0.27k²…

A:

Q: Find a constant a such that for any region D in the xy plane, the surface area of the graph above D…

A: Hope you got your answer , if any query then raise it.Kindly do rate this helpful....Thank You

Q: Evaluate the line integral Ly² da + 2xy³dy C where C is a positively oriented ellipse x² + 2y² = 2.

A:

Q: The temperature of the earth is rising, as a result of the "greenhouse effect," in which carbon…

A:

Q: 00 n=1 (-1) "200 n0.7 For the series below calculate find the number of terms n that must be added…

A:

Q: step by step calculations please

A:

Q: d = ☐ A buoy floating in the ocean is bobbing in simple harmonic motion with period 8 seconds and…

A:

Q: 9

A:

Q: 2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at…

A: Sure, let's break down each part:(a) Transition Matrix \( P \):The transition matrix represents the…

Q: The demand for a particular item is given by the function D (x) = 1,450 - 3x². Find the consumer's…

A: If you have any questions let me know in comment box thankyou for your question.

Q: Consider the function y = f(x) shown in the graph below. At points x = 1 and x = 3 determine whether…

A: Step 1: Step 2: Step 3: Step 4:

Q: Use the Fundamental Theorem of Calculus to find 8 cos() da

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Communication True or False: 11. A normal vector to a line is perpendicular to that line. 12. Lines…

A: True. A normal vector to a line is indeed perpendicular to that line. It defines what's "up" or…

Q: 2. Sketch the region R whose area is given by the iterated integral 2 0 - 4-y2 dxdy.

A: Thanks for your patience!Kindly comment if you need any further clarifications.

Q: j √(6y 7 + 9z 7 + 6xk) · d7 where C is the boundary of the triangle with vertices (3, 0, 0), (0, 5,…

A: First parametrize the boundaries of the triangle. (3,0,0) to…

Q: Help

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Verify that F Vy and evaluate the line integral of F over the given path: F= (xy², x²y), 4(x, y) = ½…

A: Step 1: Step 2: Step 3: Step 4:

Q: MAT441 CALCULUS II – PROJECT #5 Evaluate S cos (3x) dx. √√4 - sin² (3x) Answer. Step 1: Exercise 1

A:

Q: Find the derivative of the given function. 7 y= x²e-9x y' = (Type an exact answer.)

A: Step 1: Step 2: Step 3: Step 4:

Q: 1 k 3 Let A and B are 3x3 matrices where A = 261 04 k (i) Find the value(s) of k if A is a…

A: The objective of the question is two-fold. First, we need to find the value of 'k' for which the…

Q: For the following fields, calculate curl F: 1. F(x,y,z) = 〈x2 -y, 4z, x2〉 2. F(x,y,z) - 〈-3y,3x〉

A: Step 1:(1) The given field is:F(x,y,z)=⟨x2−y,4z,x2⟩To compute the curl of a vector field, we can use…

Q: Differentiate the following:

A: Step 1:Step 2:Step 3:Step 4:

Q: Let f be defined from f(x) = from image. Find the limit for lim(x-&gt;1) f(x) / ln x

A: Step 1: **Use the rule of L'Hopital:**  The expression…

Q: Use this method to find the power series centered at 0for the following functions. Give the interval…

A: Step 1:Given that, ex=∑k=0∞​k!xk​ which interval of convergence is −∞&lt;x&lt;∞.  Step 2:Now,…

Q: Determine whether the vector field is conservative and, if so, find the general potential function.…

A:

Q: A 20ft by 28ft swimming pool is filled with water. The depth is measured at regular intervals,…

A: Since m=n=2; h=10 and k=14; A=10*14=140then we get the depth of water along the points designated…

Q: Find the absolute maximum and minimum of f(x, y) = 4x + y within the domain x² + y² <4. 1. Absolute…

A: Step 1: State the given multivariable function and its domain: f(x,y)=4x+ydomain: x2+y2≤4 Step 2:…

Q: What is the weekly fixed cost of producing sleeping bags?  Round to the nearest integer. $______…

A: Referenceshttps://en.wikipedia.org/wiki/Linear_regression

Q: Suppose a thin plate is bounded by y=0 , x=0, x=1, and y=e^-x and has areal density of p(x,y)= xy.…

A: To find the center of mass of the thin plate, we need to calculate the moments with respect to the…

Q: Find the open intervals where f (z) is concave up and where it is concave down. Enter your answer in…

A: Step 1: Step 2: Step 3: Step 4:

Q: why did i get this question wrong please help steps

A:

Q: H.W: replace the following polar equations by equivalent Cartesian equation, then describe or…

A:

Q: 2. Consider the following. S S Y 14. dA, D = {(x, y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ √√x} x2 +1 (a) Rewrite the…

A:

Q: The demand function for a television is given by p = D(x) = 49284 -0.03x2 dollars. Find the level of…

A: To find the level of production for which the revenue is maximized, we need to find the point where…

Q: • Surface Area of a parametric curve revolved around the y-axis: S=2T b 2 2 dz dy x(t). dt dt dt

A: The formula you provided represents the surface area of a parametric curve revolved around the…

Q: (a) Evaluate the integral 2 32 -dx. x² +4 Your answer should be in the form kл, where k is an…

A:

Q: (iii) Figure 5.1 shows the mathematical model of a cable which is supported at two points (A and B)…

A: Q.(iii)Solution:The relationship of the x- and y- co-ordinates of a point s(x,y) on the cable is…

Q: Rewrite the following integral as a Type 2 integral. Draw a clear, detailed diagram of the domain of…

A: Step 1:  Step 2:

Q: Determine the work done along the path C, over the vector field F(x,y) =〈9x2,4y〉for each of these…

A: The answers are attached in the form of images:

Q: The sum of the areas of the rectangles approximates the area under the curve, though not very well.…

A: Notice that there are four rectangles in the figure. Let us name them A1, A2, A3, and A4, starting…

Q: K The population density of a city is given by P(x,y) = -20x² - 20y² + 200x +480y+ 190, where x and…

A: To find the maximum population density, we need to find the critical points of the function and then…

Q: Maximum Profit Yaster Gadgets manufactures and sells x smartphones per week. The weekly price-demand…

A: Revenue function: R(x) = 487x - 0.47x^2Marginal revenue: R'(x) = 487 - 0.94xCost function: C(x) =…