Evaluate the line integral

C |

F · dr,

where *C* is given by the vector function
**r**(*t*).

F(x, y, z) = sin(x) i + cos(y) j + xz k

r(t) = t^{5} i − t^{4} j + t k, 0 ≤ t ≤ 1

In: Math

find the general solution to the second order linear
non-homogeneous differential equation

(y"/2)-y' +y = cos x

In: Math

Given: f(x) = x 2−36 x 2−7x+6 Find the following

a. V.A.

b. Domain

c. H.A.

d. X-intercept

e. Y-intercept

f. Graph

In: Math

Find the tangential and normal components of the acceleration vector. ? (?) = ? ? ?̂+ √2 ? ?̂+ ? −??̂

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-Let O (0,0,0) be the origin and A(a+1,b,c) where a,b and c are the last three digits of your student ID. Find, describe and sketch the set of points P such that OP is perpendicular to AP

- Let u=<a , b+1 , c+1> find and describe all vectors v such that |u x v|=|u|

a=1 , b=1 , c=9

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For f(x)=x^2+x-2/x^2-4, determine the equation for any vertical asymptotes, the equation for any horizontal asymptotes, and the x-coordinates of any holes

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csc beta = 2/3. What is the beta to the nearest degree?

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Determine an example of a vector field that would yield a positive value for a line integral around a circle that is traversed once clockwise for any nonzero radius and explain how you know your vector field is correct.

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Express the following systems of equations in matrix form as A x = b. What is the rank of A in each case (hint: You can find the rank of a matrix A by using rank = qr(A)$rank in R. For each problem, find the solution set for x using R.

a. X1+5X2+2X3=5

4X1-X2+3X3=-8

6X1-2X2+X3=0

b. 3X1-5X2+6X3+X4=7

4X1+2X3-3X4=5

X2-3X3+7X4=0

X2+3X4=5

In: Math

. Let Π be a finite incidence geometry. Prove that, if every line in Π has exactly n points and every point in Π lies on exactly n + 1 lines, then Π is an affine plane. Come up with a similar criterion for finite geometries satisfying (EP) (those geometries are called projective planes).

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Explain how to solve the following problems step by step, and reason it should be solved that way:

1) Find domain for each problem and explain in brief in each case. How do you find the domain of these problems without using a graph (don't state the problem only)? Explain this: why is there a difference between in the domain of an even and an odd indexed radical? Why the domain of a function with a square root in the denominator IS different than the domain of a function with square root NOT in the denominator?

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Find the domain of the function g(x) = square root of 3x+3

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why are the domain and range of square root function restricted to [0,∞) ?

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Which option below provides the best description of the relationship between a quadratic parent function and a square root parent function?

A. The square root function is the quadratic function reflected across the y-axis.

B. The quadratic function and square root functions have no inverse.

C. The square root function is the quadratic function reflected across the line y = x, with a limited domain.

D. The square root function is the quadratic function reflected across the x-axis

In: Math

Graph the square root of the following function. State the domain and range of the square root of the function.

y = -2x + 4

In: Math