Chapter 2.1, Problem 16ES

Steel Production Planning: Let S  represent the amount of steel produced (in tons). Steel Production is related to the amount of labor used(L) and the amount of capital used ( C ) by the following function:S = 20L⁰˙³⁰C⁰˙⁷⁰In this formula L represents the units of Labor input and C the units of Capital input. Each unit of Labor costs $50, and each unit of Capital costs $100. a:Formulate an optimization problem that will determine how much labor and capital are needed to produce 50,000 tons of steel  at minimum cost.                                                                                                                                                                                             Q#3B: Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L>0 and C>0.)…

Use the accompanying Grade Point Averages data to find 80%,85​%, and 99%confidence intervals for the mean GPA.   view the Grade Point Averages data. Gender    College    GPAFemale    Arts and Sciences    3.21Male    Engineering    3.87Female    Health Science    3.85Male    Engineering    3.20Female    Nursing    3.40Male    Engineering    3.01Female    Nursing    3.48Female    Nursing    3.26Female    Arts and Sciences    3.50Male    Engineering    3.00Female    Arts and Sciences    3.13Female    Nursing    3.34Female    Nursing    3.67Female    Education    3.45Female    Engineering    3.17Female    Health Science    3.28Female    Nursing    3.25Male    Engineering    3.72Female    Arts and Sciences    2.68Female    Nursing    3.40Female    Health Science    3.76Female    Arts and Sciences    3.72Female    Education    3.44Female    Arts and Sciences    3.61Female    Education    3.29Female    Nursing    3.20Female    Education    3.80Female    Business    3.26Male…

(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}. (a) (2 points) Calculate the divergence V. F. (b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that the triple integral √ (V · F) dV = √ 2²(1. = x²(1 − x² - y²) dA. E

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(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy). (a) (2 points) Calculate V. F. (b) (6 points) Given a vector field is everywhere defined with V G₁(x, y, z) = * G2(x, y, z) = − G3(x, y, z) = 0. 0 0 F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that F = 0, let G = (G1, G2, G3) where F₂(x, y, y, t) dt - √ F³(x, t, 0) dt, * F1(x, y, t) dt, t) dt - √ F Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).

5) Solve the triangle. 2 95° 4 B с A) c=3.63, A=59.5°, B = 25.5° C) c = 4.63, A = 59.5°, B = 25.5° A B) c 4.63, A 25.5°, B = 59.5° = = D) c 5.63, A = 25.5°, B = 59.5°

Find zw. Leave your answer in polar form. = လ 3π 2 z = 6 cos 6 cos 37 3π + i sin 2 57 W = 12 cos + i sin 6 6 ༠།ལྦ་

10 Write the expression (1 – i) i)in the standard form a + bi.

11) The letters r and 0 represent polar coordinates. Write the equation r sine = 10 using rectangular coordinates (x, y). A) x = 10y B) y = 10 C) x = 10 D) y = 10x