Find the reference angle, θ′ for the angle θ  = -135°

Q: Find the projection of u onto v and the vector component of u orthogonal to v for u = 3i − 5j + 2k a...

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Q: Explain the error inthe equation Then rewrite the right side of the equation to correct the error th...

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Q: Use the inverse of the coefficient matrix to solve the systems in Problems 4x + 3y - 2z = 0 5x + 6y ...

A: Given: The system of equations, 4 x + 3 y - 2 z = 0, 5 x + 6 y + 3 z = 10, 3 x + 5 y + 2 z = 2

Q: Solve each inequality for x b)     1-2lnx<3

A: Given: The equation given is 1-2 ln x<3

Q: Derivatives Find and simplify the derivative of the followingfunctions

A: We need to find the derivative and simplify  the given function.  

Q: A bag contains two red marbles, three green ones, one lavender one, three yellows, and four orange m...

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Q: Find two positive numbers whose sum is 100 and the sum of whosesquares is a minimum.

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Q: ider the point (3, Trectangular coordinates. What IS radius in polar coordinates: (2 decimal places)

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Q: Find the limit limx→π/2tanxtan3x.

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Q: What value of a makes ƒ(x) = x2 + (a/x)have a point of inflection at x = 1?

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Q: There are twelve times as many football players on a football team as there are coaches. Write a for...

A: Let c represent the number of coaches and p represent the number of players. Given there are 12 time...

Q: Clarify the differences between a sequence and a series?

A: Sequence is an array of numbers arranged according to a certain rule. For example,

Q: Equations of planes Find an equation of the following planes. The plane passing through the points (...

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

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Q: First make a substitute and then use integration by parts to evaluate the integral.

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Q: In the function given. Evaluate the integrals.

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Q: Comparing growth rates Determine which of the two functions grows faster, or state that they have co...

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Q: Select all of the following tables which represent y as a function of x. -2 -4 -2 -5 -5 -1 -2 -3 3 1...

A: A relation given in the table represents y as a function of x when each value of x has unique y valu...

Q: Evaluate the geometric series or state that it diverges.

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Q: Graph y = 4 - x. Select integers for x, starting with -3 and ending with 3.

A: Given: The Graph of the function is y = 4 - x. The integers are selected for the value of x, startin...

Q: Solve each inequality for x a)     1<e^(3x-1)<2

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Q: The shaded region R in the figure is bounded above by the curve y =sin(2x) and below by the line u=-...

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Q: a. If r(t) = (at,bt,ct) with (a,b.c) (0,0,0), show that the angle between r and r' is constant for a...

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Q: Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numb...

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Q: Consider the following velocity functions. In each case, complete the sentence: The same distance co...

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Q: A​ full-time employee who works 40 hours per week earns ​$ 18.50 per hour. Estimate that​ person's a...

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Q: Areas of regions Find the area of the following region.

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Q: Convert the rectangular equation 3x - y = 6  to a polar equation that expresses r in terms of θ.

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Q: Evaluate the integral. inegral  0 to 1    [ (x-4) / ( x2  - 5 x +6 )] dx

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫4x3/(x4 + 1)2 dx, u = x4 + 1

A: Now put

Q: Let R be a region bounded by x-axis, the curve y= cos.x between x= - 2 and x=-lines. If the region R...

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Q: The position vector of a moving particle is given as Rct)- (1+3t + sピ")i + ( 4ヒ+Hビ)j-6costk ヒ=o Find...

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Q: Find the area under the curve y=1/x3 from x=1 to x=tand evaluate it for t=0 ,100 , and 1000. Then fi...

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Q: Describe and sketch the surface given by the function.                                             g...

A: Given Data The equation of the surface is g(x,y)=x.   The equation g(x,y)=x is a simple equation of ...

Q: A solid ball is bounded by the sphere ρ= a.Find the moment of inertia about the z-axis if the densit...

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Q: Evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits th...

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Q: Give a geometric description of the following sets of points. x2 + y2 - 14y + z2 ≤ -13

A: Consider the given equation: Here the objective is to give the geometric description of the given e...

Q: If A=ai+j and B=4i+3j find a so that i) A and B parallel ii) The angle between A and B is (pi/6)

A: Angle between two vectors (say ‘a’ and ‘b’) is given by

Q: The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Profes...

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Q: Use the graph of f. Where applicable, use interval notation.Explain why f represents the graph of a ...

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Q: Evaluate w at x =y=Z=l if w= (os(uv) u= Xy Z and V = %3D %3D

A: Consider the given function:

Q: First make a substitution and then use integration by parts to evaluate the integral.

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Q: Trigonometric limits Use Theorem 3.10 to evaluate the following limits.

A: Given limit is

Q: Let f be a function which is continuous, differentiable , and holds -1s f(x)<1 over the interval 0, ...

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.