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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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Q: Electric charge is distributed over the disk x2+y2=1 so that its charge density is σ(x,y)= 1+x2+y2 (...

A: Electric charge is distributed over the disk x2+y2=1 so that its charge density is σ(x,y)= 1+x2+y2 (...

Q: Using the vector diagram below, and the fact that |c|2 = č · č, prove the cosine law for the triangl...

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Q: Solve the inequality x - 9s 8r.

A: We subtract 8x from both sides and then factor

Q: Evaluate the definite integral. *In 16 2e¬x dx 1- 4e-2x

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Q: Differentiate y = ecos x.

A: We use the chain rule to find the derivative

Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Find the ma...

A: To find the marginal revenue we find dr/dx

Q: Show that the inflection points of the curve y= x sinx lieon the curve y2(x2 +4) =4x2 .

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Q: Locate the absolute extrema of the function on the closed interval. g(x) = x2 – 4x, [0, 5] (х, у) %3...

A: We first find g'(x) using the power rule Then we find the critical points by solving g'(x)=0

Q: Calculus Question

A: Read the graph and try to extract as much information as possible: vertical asymptote at x = -2 and ...

Q: 10.1. 8

A:

Q: . Power Rule for negative integers Use the Derivative Quotient Rule to prove the Power Rule for nega...

A: We write x-m as 1/xm, then we use the quotient rule.

Q: 10.1. 14.2

A: We have given h0 = 15, r = 0.25

Q: find the formula of h(t) if the graph has a maximum point at (60,400) and points of inflection at t=...

A: At t = 50 and 70, h” (t) is equal to 0 as the points are the POI. So, t = 50 and 70 are the roots fo...

Q: Find the derivatives of the functions w = re-r

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Q: Consider the following function. f(x) = x3/2 Find its average rate of change over the interval [1,...

A: Given function

Q: Let a, = 2" cos(n7) for n21. Write out the first 8 terms of the sequence (a, through ag). Determine ...

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Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u, v)...

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Q: 6. Use the scalar triple product to determine if the points A(1,3, 2), B(3, –1,6), C(5, 2,0), and D(...

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Q: 10.1. 13.2.

A: As you have answered the first question correctly, so I will answer part b b) Every term is 0.5 time...

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

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Q: 1. At Tony’s Pizza Parlor in beautiful downtown Pittston, Tony charges$12 for a large pie with 2 top...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Please help with #21. Thanks

A: Given function is Firstly, we will find gradient f at point (4,1,1)

Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the reg...

A: We first sketch the region using a graphing calculator the shaded region is rotating about the x a...

Q: Evaluate the integral ∫dx / x2+10x+26.

A: We first complete the square of the denominator

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x ln x/1 + ln x

A: Let us assume u and v

Q: Find f '(x). f(x) = x2 + 3x + 2/x

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Q: A baseball team plays in a stadium that holds 56000 spectators. With the ticket price at $12 the ave...

A: Let us assume x=ticket price y=audience , y≤ 56000 So the given coordinates are (12, 23000) and (9, ...

Q: Please help with #15. Thank you!

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Q: Compute the integral ∫dx / 5sinx+2cosx+2.

A: Apply t substitution

Q: According to the U.S. Office of Management and Budget, the 2011 budget for defense exceeded the budg...

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Q: 14 - Which of the following is the volume of the object that occurs when the region bound by the y= ...

A: We sketch the region using a graphing calculator The shaded region will rotate around the x axis

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: Evaluate the integral or state that it is divergent.

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Q: Consider a polynomial of the form p(x) = x2(cx4 − 1), where c ̸= 0 is a constant. (a) What is the...

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Q: The height y (in feet) of a ball thrown by a child is y = - 167 + 4z + 3 where z is the horizontal d...

A: The height of ball thrown by a child is where x is the horizontal distance in feet from the point a...

Q: Evaluate the line integral F· dr, where C is given by the vector function r(t). F(x, у, z) sin(x) i ...

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Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of ...

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Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away ...

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Q: Finding Values of an Inverse Function Assume that f is a one-to-one function. 25. (a) If f(2) = 7, f...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: question in screen shot

A: Given: Evaluate the following