A particle moves in a straight line with the given velocity v(t) = 24 – 6t (in m/s). Find the displacement and distance traveled over the time interval [0, 6]. (Give your answers as whole or exact numbers.) displacement: total distance traveled:

Q: Use the One-to-One Property to solve the equation for x. 5x+1=25 x = 5 x = 1 x = 2 x = 4 x=3

A: given that  5x+1=25 Or 5x+1=52  On comparing  X+1=2  So x=1

Q: 24 ue'sin(s + 2t)

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Q: 4. S (x + 1) √2x − 1 dx

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Q: As shown in the figure below, Isabel is looking at a tree that is leaning at an angle of 87° with…

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A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: An airplane leaves City A and flies 144 km due north to City B. It then turns through an angle of…

A: The solution is given in the next step.

Q: Given the functions: Find: f(x) = 3x - 5 a. f(g(x)) g(x) = x² + 2x - 1 b. (f(h(x)) c. f(g(-1)) h(x)…

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Q: 10. Find the position function s(t) given acceleration a(t)= 2t if v(2) = 0 and s(2)=1.

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Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: Find a, and d for each arithmetic series. See Example 8. 61. S20 1090, 920 = 102 www 63. S16-160, 16…

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Q: Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size…

A: Given query is to find the rate of change.

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Q: 1 I²+1 Estimate the area under the graph of f(x) = = rectangles and right endpoints. Rn = Repeat the…

A: The Right end point approximation formula is: ∫abf(x)dx=∆xf(x1)+f(x2)+f(x3)+...+f(xn) Divide…

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Q: Use Cramer's Rule to solve this system of linear equations for y only: 2x - 4y - 2z = - 4 4x + 3z =…

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Q: 8. Using any work found in Question 7, det 2 3x (x²-5)³ dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the diagram above, and select each statement below that is true. [n n¹] is a 1D projection…

A: The first option is correct.

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Q: A rotating light is located 19 feet from a wall. The light completes one rotation every 2 seconds.…

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

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Q: h. Average value of f on [-4,-1]

A: From graph  f(-4)=5f(-1)=7   formula for average value

Q: Please

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Q: The gradient of f(x, y, z) = xy²z³ at the point (1, 2, 1) is

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Q: A farmer plans to fence in a rectangular pasture adjacent to a river (see figure below). The pasture…

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Q: Find the slope of the tangent line to the curve x² - xy - 2y³ 116 at the point (-2, 4).

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Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

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Q: 6 Find the derivative of: 9/x

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Q: 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x² + 3x using First…

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Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on - (327 3π 5π " 2 2

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Q: Let f(x)= = z+1 x³2x² + x

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Q: The rate of change of the temperature, r(t), in an oven (in degrees Celsius per minute) t minutes…

A: To find out the temperature change using simpson rule.

Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx %3D VI- - x2

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Q: Find the derivative of the function. f(x) = (5x + 7)³ (06² +00) ² f1(x)

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Q: x2 – 4xy – 2y2) dx + (y2 + 4xy − 2x2) dy = 0

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Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: F = 3 x 10-4³-4.4 x 10-³w²+3.93w+0.221

A: Given :

Q: 16. r=8sin ㅇ

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Q: Consider the curve parameterized by x = 2t³ - 33t² + 180t and y = 2t³ + 33t² + 180t. At what points…

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Q: 13 5 3 1 5 Let F= 1 7 -4 and G= -1 2 3 12 3 2 2 5 Find 5F- 4G. 5F - 4G = 00 C

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Q: Find the absolute extrema for the function f(x)=x+ on the interval 0≤x≤ 6.

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: ind the area of the blue region. It is the area under the curve. y y = 3x+1 y=7-x 6 8 4 2 4 00

A: Follow next step

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 1+ X

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Q: Let f (x) = x³ 3x². - Find the absolute minimum value of f(x) on the interval [1, 4].

A: We have to find the function value

Q: √1² +25 -2 I dt

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Q: QUESTION 12 Find d²y/dx². x=1+1²y=t-³

A: Given;  x=1+t2, y=t-t3

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: 구. ( 34 Cxtd) ax An 14 X? (X-1)

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Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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