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Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 < 9

Write the equation for the plane.The plane through the point P(-7, 5, -4) and normal to n =

Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 = 16

Find the corresponding position vector. Define the points P = (7, -6) and Q = (4, -3). Find the position vector corresponding to .

Identify the type of surface represented by the given equation. + + = 1

Consider the environmental ethical question of whether or not we ought to protect endangered species. Compare and contrast how someone considering this question from each of the following ethical perspectives/theories would likely analyze/evaluate it:Teleological/Natural Law approachUtilitarian approachDeontological/duty/rights approach*** Remember that copying/pasting from any course materials (other than your own words in the Prep Guide), the internet, or using generative AI like ChatGPT to help “write” or “proofread” or “improve” your answer violates my Academic Integrity policy. Note that generative AI is now incorporated into many popular writing and translating platforms (e.g. Grammarly, Quillbot, Google Translate, DeepL, etc.), so if you’re using those platforms, you’re using generative AI in violation of my policy. USE YOUR OWN WORDS or, if you are unable to do that, properly quote/informally cite them as I discuss in the Academic Integrity section of the Syllabus ***  

What are the main purposes/uses of ethical theories as discussed in our materials for this week?*** Remember that copying/pasting from any course materials (other than your own words in the Prep Guide), the internet, or using generative AI like ChatGPT to help “write” or “proofread” or “improve” your answer violates my Academic Integrity policy. Note that generative AI is now incorporated into many popular writing and translating platforms (e.g. Grammarly, Quillbot, Google Translate, DeepL, etc.), so if you’re using those platforms, you’re using generative AI in violation of my policy. USE YOUR OWN WORDS or, if you are unable to do that, properly quote/informally cite them as I discuss in the Academic Integrity section of the Syllabus ***  

Solve the problem.Let u = 7i + j, v = i + j, and w = i – j. Find scalars a and b such that u = av + bw. a = [aconst] b = [bconst]

Solve the problem. (Give your answer as a terminating decimal.)Find x so that the vectors v = i + xj and w = -3i + 5j are orthogonal.

Solve the problem.For the triangle with vertices located at A(5, 3, 3), B(4, 5, 2), and C(1, 1, 1) , find a vector from vertex C to the midpoint of side AB.