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(See attached file for full problem description) Could someone please help me with the problem and show me ALL the steps.

L'Hospital's Rule, Asymptotes, Global Extrema, Inflection Points

F(x) = x^2 e^(17x) 1. Find an equation for each horizontal asymptote to the graph of f. 2. Find an equation for each vertical asymptote to the graph of f. 3. Determine all critical numbers. 4. Determine the global maximum of the function. 5. Determine the global minimum of the function. 6. Find inflection points. 7. Fin

Real and Non-Real Affine Intersection Points and Their Multiplicities

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let

Solving a Word Problem Subject to Constraints

Joe has to take a test which consists of short-answer questions worth 9 points each and essay questions worth 25 points each. He must do at least 9 short-answer questions, but won't have time to do more than 10. He has to answer at least 3 essay questions, but can't spend time to do more than 10. If no more than 19 questions can

Hyperbolas and Completing the Square : Vertices, Foci and Asymptotes

Completing the square problems: HYPERBOLAS- Find the center, vertices, foci, and asymptotes of the hyperbola. Please give the equation in standard form, i.e. (x-h)^2/a^2 - (y-k)^2/b^2=1 or other way around. 15) ? 9x^2-y^2-36x-6y+18=0 Answer: Center (2,-3) Vertices (3,-3), (1,-3) Foci: (2+ or √10, -3)

Splitting Fields : Find the splitting fields over Q for x^3+3x^2+3x-4.

Find the splitting fields over Q for x^3+3x^2+3x-4. Recall a splitting field is as follows: Let K be a field and let f(x)=a_0+a_1*x+...+a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements r_1,r_2,...,r_n elements of F such that (i) f(x

Rectangular Kitchen Measured Cost

1st one: A family has a rectangular kitchen which measures 12 by 18 feet. They want to put diagonal heating coils in the floor of the room. How much will it cost them to put in the coils if they cost $25 foot? 12 x18 =216= Area 216x25= 5400 but since they want to put diagonals would I take half of this? 2nd one: A wi

Vertical Pole Supports and Anchors

1st one- One leg of an isosceles right triangle measures 12 meters long. Find the length of the hypotenuse of the triangle.? Would it be 12 over the sq rt of 2 2nd one A wire is needed to support a vertical pole 18ft tall. A cable will be anchored to a stake and it forms a 30 degree with the ground. nearest tenth... How fa

Reducing Speed Limit Requirements

The 42 kilometer drive from Oakdale to Ridgemont usually takes 28 minutes. Because highway construction requires reduced speed limit, the trip now takes 14 minutes longer. Find the reduced speed limit in km/hr.

Square roots in a system of equations.

An explanation of the steps to use in a problem involving square roots in a system of equations using the sample problem given. Thank You. Please see attached.

Modern Algebra Question

Modern Algebra Question If G is a group in which (a.b)^i =a^i.b^i for three consecutive integers i for all a,b belongs to G, show that G is abelian. The fully formatted problem is in the attached file.

Inflection points calculations

What are the inflection points? (a) f(x) = 12x^5 +15x^4 -240x^3+19 (One of the inflections is 0. Find the rest. Results cannot be -2.82 and 2.07) (b) f(x) = (x^2 - 8x + 32)(x-4)

A Fence Three Sides of a Rectangular Yard

Justin wants a fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. Justin has 80 feet of fencing available. (recall: area of a rectangle =length *width). One side is x and another is 80-2x - Write an equation to represent the area of the exercise yard

Revenue Equation and Maximum Revenue Determination

A company that manufactures typewriter ribbons knows that the number of ribbons, x, it can sell each week is related to the price, p, of each ribbon by the equation x=1200-100p. the amount of revenue earned each week would be R(X)= 1200P-100P^2. - Graph the revenue equation and label the x- and y-intercepts. - Find the max

Application Word Problem : Distance, Time and Speed - Object thrown Upward

An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/second. It's distance, s(t) in feet above the ground after t seconds is given by the equation: s(t)=-16^2+144t+100 - find the maximum height, s(t), of the object above the ground. - find the height of the building, th



Fields Extensions/Algebraic

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K. Let S be the subspace of F. Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

Factorizing Functions Solved

Need help learn all the steps to solve these problems. Solve 3x^2 GE - 4x - 1 X^2-3x-3 +2 = 0 find all solutions