Home / Mathematics / Calculus /PROBLEM 3 Suppose g(x, y) = 8 In(y) - 2. 53.1 Find g(x,y) 53.2 Find g(x, y). 53.3 Find 9 x(x,y). 53.4 Find yr (x, y) 53.5 Find 9yy(x, y).

Question PROBLEM 3 Suppose g(x, y) = 8 In(y) - 2. 53.1 Find g(x,y) 53.2 Find g(x, y). 53.3 Find 9 x(x,y). 53.4 Find yr (x, y) 53.5 Find 9yy(x, y).

0A76F7 The Asker · Calculus

Transcribed Image Text: PROBLEM 3 Suppose g(x, y) = 8 In(y) - 2. 53.1 Find g(x,y) 53.2 Find g(x, y). 53.3 Find 9 x(x,y). 53.4 Find yr (x, y) 53.5 Find 9yy(x, y).

More

Transcribed Image Text: PROBLEM 3 Suppose g(x, y) = 8 In(y) - 2. 53.1 Find g(x,y) 53.2 Find g(x, y). 53.3 Find 9 x(x,y). 53.4 Find yr (x, y) 53.5 Find 9yy(x, y).

Community Answer

Honor Code

Solved 1 Answer

See More Answers for FREE

Enhance your learning with StudyX

Receive support from our dedicated community users and experts

See up to 20 answers per week for free

Experience reliable customer service

Get Started

5.14:- g(x, y)=8 \ln (y)-x(1) \sqrt{g_{a}^{\prime}(x, y)}=-1(2) g_{y}(x, y)=\frac{8}{y}(3) \operatorname{l}_{x x}(x, y)=\frac{\partial}{\partial x}(-1)g_{x x}(x, y)=0(4) \operatorname{gy}_{x}(x, y)=\frac{\partial}{\partial x}\left(\frac{8}{y}\right)g_{y x}(x, y)=0(5)\begin{array}{l}g_{y y}(x, y)=\frac{\partial}{\partial y}\left(\frac{8}{y}\right) \\g_{y y}(x, y)=\frac{-8}{y^{2}}\end{array} ...

Related Questions

A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 7 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts (a) and (b) below. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? If she walks at 3 mi/hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)

Use the relation $ \lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 $ to determine the limit of the given function. \[ f(\theta)=\frac{7 \sin \sqrt{10} \theta}{\sqrt{10} \theta} \] \[ \lim _{\theta \rightarrow 0} \frac{7 \sin \sqrt{10} \theta}{\sqrt{10} \theta}= \] (Type an integer or a simplified fraction.)

Using $ \lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 $, find the limit. \[ \lim _{t \rightarrow 0} \frac{7 \sin (\sin 4 t)}{9 \sin 4 t} \] $ \lim _{t \rightarrow 0} \frac{7 \sin (\sin 4 t)}{9 \sin 4 t}=\quad $ (Simplify your answer.) Using θ→0limθsinθ=1, find the limit. t→0lim9sin4t7sin(sin4t) t→0lim9sin4t7sin(sin4t)= (Simplify your answer.)

I'm trying to solve this and am getting a very different answer from the book. Can someone please help. I know that $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$ . So I have to take $\tan(\theta) = \frac{x}{7}$ and find values for sin and cos in terms of $x$ . So here goes: $\frac{\sin(\theta)}{\cos(\theta)} = \frac{x}{7}$ Then $\cos(\theta) = \frac{7\sin(\theta)}{x}$ and $\sin(\theta) = \frac{x\cos(\theta)}{7}$ Now to find cos and sin in terms of $x$ I plug in values into $\sin^2(\theta) + \cos^2(\theta) = 1$ $\left(\frac{x\cos(\theta)}{7}\right)^2 + \cos^2(\theta) = 1$ then $\cos^2(\theta) = \frac{49}{x^2+49}$ $\sin^2(\theta) + \left(\frac{7\sin(\theta)}{x}\right)^2 = 1$ then $\sin^2(\theta) = \frac{x^2}{x^2+49}$ Now plug these values into $2\sin(\theta)\cos(\theta)$ and I get $2\left(\frac{x}{\sqrt{x^2+49}}\right)\left(\frac{7}{\sqrt{x^2+49}}\right)$ This is very different than the answer in the book and the graphs are different too. Can someone please tell me what I'm doing wrong? The book answer is $1-\frac{x^2}{x}$

A $ 5.8 \mathrm{~mol} $ acetone-ethanol solution containing $ 70 \% $ acetone is allowed to reach equilibrium at $ 60^{\circ} \mathrm{C} $ and $ 1 \mathrm{~atm} $. Use the following binary phase diagram for acetone and ethanol based on experimental data to answer the following questions. a) Determine the bubble point temperature and the dew point A 5.8 mol acetone-ethanol solution containing 70% acetone is allowed to reach equilibrium at 60∘C and 1 atm. Use the following binary phase diagram for acetone and ethanol based on experimental data to answer the following questions. a) Determine the bubble point temperature and the dew point temperature of the acetoneethanol solution from the Txy diagram provided. b) Determine the bubble point temperature and the dew point temperature of the acetoneethanol solution without using the phase diagram provided. c) Discuss whether it is more likely that the values calculated in part a and part b are different due to non-idealities or experimental error.

Vapor—liquid equilibrium data for mixtures of acetone (A) and ethanol at 1 atm are given in the following table:(a) Use the given data to construct a Txy diagram for this system.(b) A thermocouple inserted into a two-phase mixture of acetone and ethanol at equilibrium reads 62.1°C. The system pressure is 1 atm. Use the Txy diagram to estimate the mole fractions of acetone in the liquid and vapor phases.(c) An Equimolar mixture of acetone and ethanol is fed to an evacuated vessel and allowed to come to equilibrium at 65°C and 1.00 atm absolute. Estimate (i) the molar compositions of each phase. (ii) The percentage of the total moles in the vessel that are in the vapor phase. and (iii) the percentage of the vessel volume occupied by the vapor phase.(d) A liquid mixture containing 40.0 mole% acetone and 60.0 mole% ethanol is fed to a continuous flash evaporator. Vapor and product streams leave the unit in equilibrium at 1.00 atm. The molar flow rate of the vapor product stream is 20% of the molar flow rate of the feed stream. Estimate the operating temperature of the evaporator and the compositions of the liquid and vapor product streams(e) Use Raoult’s law to estimate the bubble-point temperature and vapor composition in equilibrium with an Equimolar liquid mixture of acetone and ethanol. Calculate the percentage errors in the estimated values of Tb and y. Propose a reason why Raoult’s law produces poor estimates for this system. (Suggestion: Consider the molecular structure of the twocomponents.)