Find the length of the indicated portion of the curve.. r(t) = (7 cost) + (7 sin t) + (√51) k. Ostst The length of the curve is ☐ (Type an exact answer, using as needed.)

Q: Find the directional derivative, Dчf, of the function at the given point in the direction of vector…

A: Therefore, the required answer is Du​f(2,3)=0Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Evaluate the following integrals using partial fraction decomposition, when applicable. 16. dx…

A: 16). I=51​ln∣x+1x−4​∣+C 17).  I=2−3​ln∣2x+1∣+2ln∣x+2∣+CExplanation:Step 1: Step 2: Step 3: Step 4:

Q: When a bowl of hot soup is left in a room, the soup eventually cools down to room temperature. The…

A: 201.6°F113.75°FThe soup cool off more quickly over the next 20 minutes.Explanation:Step 1: Average…

Q: (c) [6 pts] In(x + 1) In(1 - x) = 2. I (d) [7 pts] 2.31-2x = 7.64+x

A: Question cx = 0 and 3 Question dx=−3ln(3)+ln(2)3ln(2)+3ln(3)+ln(7)​≈−1.835Another way of expressing…

Q: Page

A: The mean value of the probability density function 0  ≤ x ≤ 60 is simply the centroid's…

Q: If f'(x)=0 for all *, then a) f(x)=(x) for every x₁ x₂ c) f(x)>(x) for every x₁>x₂ d) f(x)>(x) for…

A: If  then which option is correct .

Q: f(x, y, z) = xe²yz, P(1, 0, 1), u = (a) Find the gradient of f. Vf(x, y, z) = < (b) Evaluate the…

A: Therefore, the required answers are a) "&gt;▽f(x,y,z)=&lt;e2yz,2xze2yz,2xye2yz&gt;b)…

Q: Verify that the following functions are inverses of each other. Clearly show the proofs! f(x)=2e1x+4…

A: f(x) and g(x) are inverse of each other Explanation:

Q: Evaluate the integral. 1/2 7 cos²(6) de

A:

Q: The daily cost C (in dollars) for a manufacturer to produce a electronic video components is given…

A: An increase of $ 5600/191Explanation:

Q: Simplify. CSCX CSCX CO Use algebra and the fun mental trigonometric identities. Your answer should…

A:

Q: An offshore oil well is 2 kilometers off the coast. The refinery is 5 kilometers down the coast.…

A:

Q: u × v = (1, 1, 0), ux w = (0, 3, 1), V X W = (2, −1, 1)

A:

Q: Use the linear approximation of f(x, y) = 3x+2y at (0,0) to estimat f(-0.02, 0.03)≈

A:

Q: Given the series: 1 1 k k+3 k=6 does this series converge or diverge? diverges converges ×

A:

Q: Calculate the mean, median, and mode from the following data set: 1,2,3,4,5

A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: Find the directional derivative of the function f(x, y, z) = √xyz at the point (3,2, 6) in the…

A:

Q: Calculate the expected value of X, E(X), for the given probability distribution. -6 -3025 10 E(X) =…

A: E(X) = 1.2Explanation:The expected value of a random variable X, denoted as E(X), for a given…

Q: Find an equation of the tangent plane at the given point: F(r,s) (32 +21), = - - (2,1) z = Submit…

A:

Q: Find equations of the following. x² - 2y²+ x² + y = 5, (5,3,-2) (a) the tangent plane (b) the normal…

A: Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1: Step 2:

Q: can you solve this question for me please

A: The objective of this question is to determine whether each of the given integrals is proper,…

Q: Find the slope of the tangent line to the parametric curve x= t³ + 4t at the | y = t² + 3t point t =…

A: m= -253/52Explanation:Step 1: Step 2: Step 3: Step 4:

Q: The function f(x) - 244 is concave down on which interval?

A: Given: To Find: To determine the interval on which the above function is concave down.

Q: Find the second partial derivatives of the function f(x, y) = x³ ³ + 2x²y. дх² = If 2. 3. 4. дудх…

A:

Q: Use the Table of Integrals in the back of your textbook to evaluate the integral: sec sec³ (9x) dx

A: Given Indefinite integral as follows

Q: 2 sin x+3sx=3 Write your answer in radians in terms of π. If there is more than he solution,…

A: c

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: The required answer is 24Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"…

A: given IVP

Q: Find the interval(s) where f"(x) > 0. (Enter your answer using interval notation.) Find the…

A:

Q: Answer the following questions for the function defined on the interval [-15, 17]. 3 f(x) x = x² -…

A: a) Vertical Asymptotes   -4, 4 b) Concave Up  (−4,0)∪(4,17) c) Inflection point x-coordinate…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The two people will be closest after 55 minutes and 23 seconds. And since they both start at noon,…

Q: Solve the given system of differential equations by systematic elimination. (D+ 1)x+(D1)y = 8 9x+…

A:

Q: Find a general formula for f("). f(x) = (x+4)-1 (Use symbolic notation and fractions where needed.)

A: Given that the function

Q: On what interval(s) is the function f(x) = x9= 9x8 + 17 both increasing and concave up? (Enter your…

A: Given the function

Q: Use the Linear Approximation to estimate Af = f(4.7)- f(5) for f(x)=x -3x². (Use decimal notation.…

A: The given function is

Q: Question 2 The graphs of a function f and its derivative f' are shown. Identify each curve and…

A: We have graphs of f and f'We have to identify curve of f and f'

Q: Find the slope of the tangent line to the curve below at the point (7,7 4x+3y+ √3xy =…

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Q: A. Find the equations of the intersection line between the planes 3xyz2 and x-y+2z = 3

A:

Q: If z = sin () and x = ln(u) and y = v4, find the following partial derivatives using the chain rule.…

A: Given that

Q: On what interval(s) is the function g(x) = e notation.) (0.7) -8x7 both decreasing and concave down?…

A: We need to find an interval where the function is decreasing and concave down.

Q: 4) A company wishes to manufacture a box with volume 36 ft, has an open top, and is twice as long as…

A: Question No. (4): A company wishes to manufacture  a box with volume 36 ft3, has an open top, and is…

Q: Solve the following initial value problem: with y(1) = 9. y = dy +8y = 1t

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Q: Find the value of the constant C for which the integral converges. Evaluate the integral for this…

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Q: An equilateral triangular plate with sides 4 m is submerged vertically in water so that the base is…

A: An equilateral triangular plate with sides   4 m is submerged vertically in water so that the base…

Q: Can you give me an example question or problem that meets the following criteria: 1. How to…

A: The objective of this question is to understand the process of determining the parametric equation…

Q: The equation r(t)=(12 sin t) i+ (4 cos t) j +(8t) k is the position of a particle in space at time…

A: The equation  is the position in space in time . To find the particle's velocity and acceleration…

Q: 4 3 2 -5-4-3-2-1 1 2 3 4 5 3 The function graphed above is: Increasing on the interval(s) Decreasing…

A:

Q: Write the equation in spherical coordinates. (a) 5226x2 + 6y2 (b) x² + 5z² = 2 × ×

A: The given equations

Q: 8) Write the expression -3sinx + 4cosx in the form ksin(x + a) for 0 < a < 2. Round a to three…

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Q: Sketch a graph of x = = 2t+ 3, y = t + 3. S 3 1 2 3 4 5 -1 -5-4-3-2-1 2 1 -2 -3 45 -4 Clear All…

A: The graph is provided below. The blue line is for y = t + 3 and the red line is for x = 2t + 3 Just…