find-the-points-at-which-the-line-normal-to-y2-sin-1-05-x-is-parallel-to-the-line-y1-x

Name: find the points at which the line normal to y2 sin 1 05 x is parallel to the line y1 x
Uploaded: 2019-11-27
Duration: 1 min 40 s
Channel: Numerade
Description: Find the point(s) at which the line normal to $y=2 \sin ^{-1} 0.5 x$ is parallel to the line $y=1-x.$

Question

Find the point(s) at which the line normal to $y=2 \sin ^{-1} 0.5 x$ is parallel to the line $y=1-x.$

Clarissa Noh · Accepted Answer

feuds Clear. So when you&#x27;re in here so we have two X plus. Why is equal to one? We&#x27;re gonna find slow. I sleep. Why? Why equals negative two X plus one on our slope is negative too. And then we get why is equal to the square root of X refunding the equation of the tension line of the given curve which is equal to X to the 1/2 power. The derivative is equal to one over two square root of X. Then we&#x27;re gonna find a normal line which is negative to square root of X. This is shown when we use negative one over the derivative. Then we do Negative two squared of X is equal to negative too. We&#x27;re just gonna find for X and Y X equals one. And why is equal to half of one which is equal to one? Then we&#x27;re going to find the equation. This is lye minus one is equal to negative too. X minus one. Why is equal to negative two x plus three

Tom Greenwood · Answer

we&#x27;re given the equation. X y plus two x minus y equals zero, and they want us to find the normal line to this curve that&#x27;s parallel to two X plus y equals zero. Well, the slope of this line iss negative to we just solving get why by itself it&#x27;s in slope intercept form. And so that&#x27;s what we need are soap of our normal line to be the normal has to have a scope of negative, too, and remember that the normal is perpendicular to the tangent high. So if the normal has this hope of negative, too, the tangent line the slope has to be the negative reciprocal of that, and that equals not negative. Positive. 1/2 because it&#x27;s the negative, reciprocal have to change the sign. So the tangent line has a slope, a positive 1/2 and the slope of the tangent mine is the first derivative of your function, so we need to find the derivative of this function and then find out where that derivative equals a value of 1/2. So let&#x27;s start by doing the chain rule first function times the derivative of the second derivative of y respect axes Why Primer D. Y t X plus a second function. Why times the Driven, a first driven of Exit one and then pause two times X. It&#x27;s derivative is too, and then minus derivative. Apply is why Prime again equals zero. So now we want to know where this is going to equal one atthe and so I I wanna solve this for by Prime first. So let&#x27;s do that. Let&#x27;s combine our like prime terms and factor it out so we will have X minus one times y prime how it&#x27;s moved the other terms to the other side of the equation So that all equal negative. Why minus two and then why Prime will equal negative y minus two over the X minus one, and that is supposed equal 1/2. So let&#x27;s set that equal 1/2. And now let&#x27;s do the outward to get why by itself, so many multiply both sides by the X minus one and then by the two. So I get negative. Two y minus four equals X minus one, And then we can solve this for why, at affordable sides not unlike that X plus three, divide by negative, too. So why equals X plus three divided by negative too. Right now, that&#x27;s the Y value. When this thing is going to have a sopa 1/2 we need to find the X values to go on with that. So we need to go back to the original equation. You come back here and we need to substitute this in for why? And then we can solve and find the X coordinates where this is gonna have the slope of 1/2 so we can have X times the X plus three over negative too, plus two times x minus. Why the X plus three over negative too, equals zero. So now if we multiply everything by negative, too, to get rid of her fractions, that will reduce this first traction. And then I distribute the X get X squared plus three x multiplying the two x by the negative to that will become a minus four X and then multiplying the last fraction by negative two and then distributing the subtraction sign in front of it. That becomes minus X minus three, and that all equals zero. So now we have X squared minus two x minus three equals zero not a factor into X equal. Her X minus three and X plus one equals zero. And that means that X equals three and X equals negative one. Are the points where we have hey, Tanja line with a slope of 1/2 or a normal line with a slope of negative too. Are those the X coordinates of our points? The Why coordinates. We can just use hard y equals X plus three over negative to here. So if we plug three in for X three plus three is six six, divided by negative two is negative. Three. So we have the 30.3 negative three and then plug in. Negative one negative. One plus three is too negative. Two divided by negative to this negative one. So we have the point. Negative one negative one. All right. We are almost there. They wanted us to find the equations of those normal lines. What? We know that the slope of the normal line is supposed to be negative too. So if I know the smoke and if I know a point, I can write the equation in point spoke form, or I can find the y intercept. And you slope intercept for So for the 0.3 negative three, we have a soap above negative too. Have to make sure I had my sign. Right. So negative three equals negative, too. Times X, which is three plus the lie intercepted be so negative. Three equals negative six plus B So that means biggest three. So one of our normal lines is going to be Why equals negative two X plus three and then for the point Negative one negative one with the same slope of negative too. We have negative one equals the scope times the X coordinate plus me. And so negative One equals two plus b And here we get B s negative three. So that would be buying clothes. Negative two X minus three

Tanishq Gupta · Answer

the question. We have to find all the points so face it&#x27;s a square and it&#x27;s good act. Which did? Normal. Like beat, right? Yeah. One mosquito minus moving. What&#x27;s the solution that you know? Yeah, but And that makes school, right? Yes. Extra. What? The spy spread. That&#x27;s right. Tell after external life, it&#x27;s a closely okay, seven. So we can go to fly by Mhm Excite off the raw fish tanks activist thing. But yeah, aspect it&#x27;s e must said the question like beat him and hold government people. What next? Finance? Yes, yes. Yeah. A normal life on the sole basis is better. Cool that Yes, a s that context Quiet. Yeah. Make that explain. I think the big question next life but like this history speaker is the best point. Was that therefore point in time? Bye bye on, find that Bye. I guess it would be. And this goes

Amrita Bhasin · Answer

this question gives us why is sign of Ax Plus three. And they asked us to look at the derivative in order to find equations of the lines that are tin gin and normal. So what we know here is that we know the derivative of Sinus co sign, and the derivative of Constant is simply zero. So we know we have thus and we know our m you consider the street a slope is negative one. Therefore we have why is sign of pie Plus three, which is simply zero plus three, which is obviously just three now substituting into the tangent and that stops shooting into the normal. We have our two lines in the

Peter Winans · Answer

we are looking for the equation of the line. It&#x27;s normal to the function. Worry equals two over X, and we want to find the normal line at the co ordinate 12 So to find the equation of the line, we need point that&#x27;s on the line and we need the slope of the line. We have the coordinate already. That&#x27;s according it 12 that were given. So no, we have to find the slope. And when we&#x27;re talking about slope, of course we now we&#x27;re talking about definition of the derivative, which is of prime of X equals. The limit is each is approaching zero of f of X plus age minus F of X, all the vibe age. So in this case, this will be the limit. His each is approaching zero of two over X plus age minus F of X is to over acts all divided by age. And we can see here that we&#x27;ve created this complex direction. Now we also have each in our denominator down here. And if we were to evaluate our limit right now, we&#x27;ll discover there we&#x27;re make this undefined because we&#x27;ll be dividing by zero, which we can do. So we have to simplify this expression before we can evaluate this limit. So I&#x27;m going to find a common denominator so that I can add those two fractions in the numerator of the complex fraction together. So I&#x27;m gonna multiply the first fraction by acts and I will get two x over x times X plus age minus And here I&#x27;m going to get two times x plus age over x times X plus age. All of this is over age, you know when this will be equal to the limit, his age is approaching zero two x over x times X plus a h venous two x plus two h over X times X plus age Oh, that is still over H Now I can combine those fractions. I can subtract them two x minus two x zero. So I will be left with the limit is each is approaching zero of negative to age over x times X plus age all over age. Now we&#x27;ve done all this work still going to be undefined when h zero. So the next thing we have to dio is he used the rules for dividing fractions. So we will have the limit. His age is approaching zero. And if I divide negative to age over X times X plus age by age, it&#x27;s the same as multiplying by one over age. And once again I can reduce those ages. And we will now have the limit as each is approaching zero of negative, too over X Times X plus age. In this. Now we can safely evaluate. We can plug zero in for the H and we will be left with negative two over X Times X, which is going to be X squared. So that right there is our f prime of acts. It&#x27;s not oh that we want them. Remember, we&#x27;re still trying to find the equation of the line normal to this curve. The normal line is going to be perpendicular to the tangent line. So what we really need is the equation of the tangent line so that I can find the slope of the normal line. And that&#x27;s where this derivative comes in because this derivative represents the slope of the tangent line. So the scope of our tangent line it will be f prime of acts. And remember, we&#x27;re working with a coordinate 12 So f prime of one of prime of one is going to be negative to over one squared. It&#x27;s gonna be negative too. That&#x27;s the slope of our tangent line. Stop of the normal line is going to be perpendicular to the slope of the tangent plane. And it means the slope is gonna be the negative reciprocal of this slope. So the if I need gate the reciprocal of negative, too. I&#x27;m gonna have a slope of 1/2 and now I finally can write the equation of my life formula for the equation line. Why? Minus y one equals m times X minus X one. So where you will have y minus two equals 1/2 times X minus one. Why minus two equals 1/2 X man It&#x27;s 1/2 and now the last thing we have to do is add to double sides and we get why equals 1/2 X and to would be equivalent to four halves for have splits negative 1/2 will be three halves and that right there is the equation of our normal line

Clarissa Noh · Answer

uh, so equation off the normal I&#x27;ll to the curve and that is parallel to the lie. So So here we have slope because negative active to off this line and we want We want the normal light to be parallel to this. So So this normal lie should have slope equals negative two and therefore tension lie which perpendicular to it. Ah, Therefore the product over there slope should be negative one. So this one slope should have one over two. And we come here The white hex. We got one over two, two square root of X. And so we want one over two square root of X equals one over two and that gives us access host one. So the equation of the normal life the first we&#x27;ll figure out the cause a point down the line. The point on the lines actually host one. Why close one slope of the normalized Negative, too. So here the equation off the normal I should be. Why? Minus one equals inactive to x minus one

Problem

Use a calculator to display the graphs of $y=\sin…

Problem 42 Easy Difficulty

Find the point(s) at which the line normal to $y=2 \sin ^{-1} 0.5 x$ is parallel to the line $y=1-x.$

Answer

More Answers

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Kayleah T.

Caleb E.

Michael J.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 27

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Kayleah T.

Caleb E.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Kayleah T.

Caleb E.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Kayleah T.

Caleb E.

Michael J.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus