(d) Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer.

Q: 15 4 12 x

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Q: 1. Evaluate the following integrals: 5/2 d. S3 1 1/2 2 2x -x -dx

A: The integral is  ∫1/25/2 12x3-x2dx

Q: 11. If g(x) = 4x In x, find g'(x) A. 1+ lnx* C. 4+ lnx¹ B. +4 lnx D.

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Q: Determine the type of conic section that each general equation will produce. a.)x²+y²+8-4y-2=0…

A: To determine the type of conic section.

Q: Suppose wexy + yz² while x(s, t) = s+t, y(s, t) = cos(s), and z(s, t) = est. Determine Əw Əw and Əs…

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Q: Solve the logarithmic equation for x, as in Example 7. (Enter your answers as a comma-separated…

A: Note: Since the student has posted multiple questions and does not mention any specific question, so…

Q: 2. The position of a rider on a Ferris wheel is an example of periodic motion. Find three other…

A: 1 )A Rocking Chair

Q: If 0 satisfies the inequalities sin (0) > 0, sin(0) cos(0) > 0, in which quadrant must lie? 1.…

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Q: Evaluate the following integral in spherical coordinates. 2 /4 4 csco 2 SS S p² sin o dp do de Ο π/6…

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Q: Water is leaking out of an inverted conical tank at a rate of 8000 cubic centimeters per min at the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 8. Find an equation of the parabola with vertex at (-1,4) and y=5 as the line of directrix. Draw the…

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Q: 9. lim 818 4x + 3 5x − 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2) Solve the given Variable separable DE 1) x cos² y dx + tany dy =0

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Q: Evaluate the integral 9 3 12 SS S 00 4y 9 3 12 SSS 0 0 4y (Type an exact answer.) 3 cos (x²) 4√2 3…

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Q: eah expressi 36 Si=1/3180° < 0 <3·10° 0 ter 0 312=80 Simplify 3

A: Given that:sinϕ=-13 ;           180°&lt;ϕ&lt;270°

Q: Problem 2 Consider the function f(x) = x³ 4x² +10. Find the x- coordinates of the local extrema.…

A: We have given function  fx=x3-4x2+10 Derivative of the function is given as  f'x=ddxfx…

Q: 5/136 A cable weighing 25 newtons per meter of length is suspended from point A and passes over the…

A:

Q: Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table. t…

A: Given data as: and  Length of time interval∆t=10 sec.

Q: (a) Prove that F(x, y, z) = (y² cos r+z³)i+(2y sin r-4)j+(3r2+2)k is a conservative vector field.…

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Q: 21-22 Find y' and y". 21. y = x² ln(2x)

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Q: The function f(x) = 2x³ - 45x² + 300x + 9 has one local minimum and one local maximum. Use a graph…

A: Topic - Local extrema's of a function We are given an equation, f(x)=2x3-45x2+300x+9And it's known…

Q: The equation N (t) 550 models the number of people in a town who have heard a rumor 1+49e-0.7t after…

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Q: Given f(x, y, z) = 4x²y + 2xz² − 3yz + 4, find the direction of maximal increase from (1,2,1) and…

A: Direction of maximum increase of f(x,y,z) is grad(f(x,y,z)) and max value of increase=…

Q: 23. y = 2 x² + 1 x² - 1 3

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Q: The table below shows the six basic solutions to the following e-system. 2x₁ + 3x₂ +5₁ = 18 4x₁+3x2…

A: Solution : From the given table it is clear that the pairs of (x1, x2) are

Q: Assume that marginal revenue is given by: dI(x) / dx = 2,500 - x - 2x2 a) Determine the revenue…

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Q: Given the vectors u=-i-3j and w=-7i+5j, find -4u and u-w. Write your answers in the form ai+bj.

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Q: Perform the subtraction. E4816-C8416 E4816-C841616 (Simplify your answer.)

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative of the expression.

Q: 2) Evaluate the definite integral cos a dx. Round your answer to 4 decimal places.

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Q: Worldwide annual sales of smartphones in over a 5 year period were projected to be approximately q =…

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Q: Prove: If U AUB and An B = Ø, then A = U\ B

A: we can prove the  given statement .

Q: Describe (don't sketch) the "level curve" defined by sin(√x² + y²) = 1.

A: Given:      sinx2+y2=1⇒x2+y2=sin-1(1)⇒x2+y2=π2+2πn⇒x2+y2=π24+2π2n+4π2n2

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: The given region is:x=33y ,      x=0    and     y=2

Q: Determine the solution for the following higher-order nonhomogeneous differential equation. Also,…

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: New question: 37 please as well

A: The given function is; y=xx.

Q: dz Given z = xy + sin(xy2), with x(t) = 2t + 1 and y(t) = -t², find dt t=1

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Q: Consider the following. e¹ - 4x = 3 (a) Find the exact solution of the exponential equation in terms…

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Q: Problem 5. they all start at n = 1. List the first six terms of the sequence given by the formula.…

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Q: Solve: dy/dx = −(y − 27) ^2/3 , with y(0) = 91. Express your answer as y=f(x).

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Q: Initially an 800 gallon tank contains 400 gallons of water in which is dissolved 50 lbs of salt.…

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Q: How do you evaluate the following integral: Integral of (-sin2(x)) dx I'm tempted to use the basic…

A: As we know the trigonometric identity: cos2x=1-2sin2x And use the common integral:…

Q: (b) Let rzi+yj + zk, and let r= ||r||. If f is a differentiable function of one variable, show that…

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Q: Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find…

A: WE can determine if each of the following vector field is the gradient of a function f(x,y) .

Q: 7. Determine the standard equation of the parabola in the figure given only its focus and vertex.…

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Q: "roblem 9. True or False. Explain your choice carefully. is convergent. nv2, n = 1, 2, 3, ... is…

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Q: Use a double integral to find the area of the region bounded by all leaves of the rose r = 5 sin 50.…

A: The given curve is: r=5 sin5θ

Q: + on 0 = -1/3 cohere 10404190 Find Sin 2 0

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Q: 5. Find the equation of a parabola with vertex at the origin whose properties are given below. a.…

A: