Problem 55500. Easy Sequences 71: A Nonlinear Function with Quadratic Domain

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Consider the function:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>y = ax^2+bx+c</w:t></w:r></w:customXml><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The outputs of this function are fed as domain to another function:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>z=\\sin\\left( \\pi\\ \\cdot\\ \\frac{\\Gamma(y)+1}y{} \\right)</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\Gamma(y)</w:t></w:r></w:customXml><w:r><w:t>, is the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Gamma_function\"><w:r><w:t>Gamma Function</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given the values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>c</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, and a limit </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>,</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> find the all values of</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x\\in\\mathrm{Z}</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, so that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>z=0</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>y \\le n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>. </w:t></w:r><w:r><w:t>For example if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[a, b, c]= [1,1,1]</w:t></w:r></w:customXml><w:r><w:t>, and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=50</w:t></w:r></w:customXml><w:r><w:t>, the only integer values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t> that will satisfy the above criteria are:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                    </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>xs=[-7, -6, -4, -3, -2, -1, 0, 1, 2, 3, 5, 6]</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Please present the final output as a unique row vector sorted ascending. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>-----------------</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>NOTE:</w:t></w:r><w:r><w:t> Some MATLAB's built-in math functions may only give approximate values. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 347.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 173.75px; transform-origin: 343px 173.75px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Consider the function:</span></span></div><div style="block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.75px; text-align: left; transform-origin: 320px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">                    </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="104" height="19.5" style="width: 104px; height: 19.5px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The outputs of this function are fed as domain to another function:</span></span></div><div style="block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">                    </span></span><span style="vertical-align:-15px"><img src="data:image/png;base64,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" width="153.5" height="35" style="width: 153.5px; height: 35px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">where </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="31" height="18" style="width: 31px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">, is the </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Gamma_function"><span style=""><span style="">Gamma Function</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">.</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 31.5px; text-align: left; transform-origin: 320px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">Given the values of </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">, </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">, </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">c</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">, and a limit </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">,</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; "> find the all values of</span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="38" height="18" style="width: 38px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">, so that </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="35" height="18" style="width: 35px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; "> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="37" height="18" style="width: 37px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">For example if </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="112" height="18" style="width: 112px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">, and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">, the only integer values of </span></span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">x</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> that will satisfy the above criteria are:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">                    </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhQAAAAkCAYAAADRn6NhAAAAAXNSR0IArs4c6QAAE8RJREFUeF7t3QXQ9c5VBvCnuLtbi0txd0oLFHcoUtzd3VukeHF3aSlWXAoM7u7u7i5F5zfdnYY0uUlukntz/90z8873zSR3s3t2s/uc50julCZNA00DTQNNA00DTQNNAys1cKeVv28/bxpoGmgaaBpoGmgaaBpIAxRtETQNNA00DTQNNA00DazWQAMUwyp86SQ/NKLd50jyG6s13xpoGmgaaBpoGmgaOK4GXiLJj450765JfrV/rQGKcUDxOUlef+Dy7yf5j+OugdazpoGmgaaBpoGmgdUaeNwkTzfQys8meZEGKObrF0Nx/yQvPP8n7c6mgaaBpoGmgaaBO7wG/qUBimVz3ADFMn21u5sGmgaaBpoGHjk00ADFwnlugGKhwmbe/vRJXjKJOJTHSfJlQ7TZzLaucdt7JfmUJE+S5O+u0YH2zJvVwF3Kmn8Ev/PNjujhHb8jj+2a0/PoSV4tybcneehOHXmUJM+V5MWSPGtx59vj/uHE8xqgWDgZ1wIUT5jkd5I86cz+PmMSMR1HFnE6r5zkA8uC/dgk31MCW//3yB3v9e15kvxkkse6EUABvL1DoSb13UH2w0nEBv3FDej9hZK8YZIXSPKcSX6m/H3+jfS/qvhpk7xLEmD07ZN8xU66N99vnuTFk/xPksdP8v1JvjjJH+/0zEuMzf7xWkleobig7Y0/UYLmGST/vvHYHi/J2yR52fK8Pyvr7vOS/OLGz9Kc5/1KkmcYafvTk7zHDs997LJe3jvJ3ybxHOvFeKekAYopDfWuXwtQvGmSr5zZ159K8qIz773WbU+V5AuSvHqSByd59yR/dK3OrHjuYyZ5SJKXKW0cnaF4nSRfUqwaGUmAp82f/FWSl0ryWyv0sedPHSAfkOTjRh5iw3uLMh979mNt209ZAJ2xYOOIA38PQHHP0u43JHm/JP+U5ImTfGo5iN+ogMm1Y6q/v9TYnijJZyS590jHAQt7JiNsC2Gpf12SOyf5hWLYPVun4ddN8o1bPKjThjUBGI2JPd5ev6UIqPzSwkx4zz4mCZAwVxqgmKupct81AIWN9AeS/G7ZHKBGlkZfWJs2pfcp9PvCoV3sdvTZ1yfR3w9Lcr8k/3Wxp2/7oPcvln7N+jkyoLBZsEpZHt9b1pC19fJJvjqJw+BbkrzmtirarLV7lf5jsn6sULAA0dsVq9GDgArj/JPNnrptQ0+Q5G6F0cIY1ENoD0CBwcE8YSoFkf9bZyis358ujBowvEW6+yXH9mmF8rd3/HqSxyhs1fsm4WYh35XkNZL858opfLIk353ks5M8oHPAPnth9bw/f5PkWZL8/cpn1Z9zaWDeGJFDc8PtgDXYUl4lydcUphXz8x1nNN4AxUKlXQNQ2CDfOsm7JvnvE/11uH18Oah/eeG4LnX70yT5wSTPnORBSd5kYkyX6tc5z7Fh8ynSO5cHOSqgAByABn0dYoKsry8qmy8LdolVco7ulv4Gnf3zSd4gyY/3fmzz/aTCcrn04Unuu/QBV7gfS1dp5D0AhQP1lYo7BRvYF24WdD1Q83pJtnQz7jk2AOhzk9x9wMVl7X5bEnUSiPFjENfIB5c1930DjTxvYSxcwu6N1WZY+nyg/kNLXNkljK2X6wCU90wCsJ0jDVAs1No1AAWLBs12KtjPgSEHmLzgxpvDQhWN3s49wL0hbgIV6QW8BZ/90ID4GVktfODYol8qNx0VUKBngbkxqwY4qutHvM4/bjXpG7XjwEM3A3BD4iD5tcKyfFOS197ouXs2w/LlZiJbA4rn7qxJ4B272RcWdXVvbU2f7zk24NE+gn0ZEvtKvSY+RZr/uQKsvmVxzw618WglSJHryj6NSV4r9nLgRUwQRmRvEaPxI6WuBNcYJvBcENMAxcLZugagmNPFipT5ZT9hzg+ucE/XJyi4Cf1+q8JqUcTsk5N0N++jAoopPdcKsF9bAh6n7r/0dYcIf+4pUG0zFCOCysfqHV32PHTvU9yJGBAxMkPsgyj+Py0g7KPL/VvpbK+x6bN9wyE/JsA+lwAwYM2w9PcSBZ7+ubjYxFlsAcQrW/CvBVhg5BgC4kLOPehPjR9w4TYkz7cywLQBioUr7aiAoro7sBM/t3BMl7jdS46yroFMUDHqHRqvL+Ul+rHFM/ijP7EwLUDFHQFQfGSSty1W1m9voaSN27BOpih54E58CNeOgLyjy16HrnHL3JEBww/+qicUIWZGYLQDSyzAVrLn2OasBXEVYhzesbh1thpXvx1sKx2LOfjmjR4C1A9VYhZL8UGFnZl6F+Z2pbt3OTdkUGkbGHvUMzJlzgIUKFEo6hWLrwqVLZoY2iUOCBHFXurP7PljLAb0JQtVp6E7v5VyJ6qU5TdHINUtZCi48VS7RwQUdGoxCEyyQJaOaQs9TrVxj5IS6j6502hIMSH8oehqYAPtxhI9croralNqq42qpordOqCwGcqyeeeNgvOm1sJe1wGJNy7W66no+L2ev7TdvQ5d+0D9BICgvjc70TGxCFKIBRU++QzQNneMe41tzvO5IVj3zhfvptTLPQQj8YVJPqoEgG7xDOcaMCFAmtEFDHpOV+yRDMgtQIXzFotDPiTJnxfDolaCticL4BZTIUNoSs4CFJAfgWC+KsnzJ3m3Ah6ACxQKETUKtbF8qqCqpK1RCCuP1GhkG9rcjUC7InjXiOBAwGiJHBFQoKkcyDImUJdHFEFylXpEw/KBfmeJPFfM6q3KOrCxcY0AHUcUAX9AcNeXf6uAAmvk3ZRnLkZHxDzr6FTg7xHnRJ8cImIogFMsmEyoo8teh65YmZrlMlWrQMYMq5ds6a7ba2xz5tT5hKGYYmfmtDV0DwOOESy9EgBwjjnzThV8WvMsrLPzVUp0FUyc1N+1wp2icBXBTDqbZZcAY84VGYPV4BNb8ZsTDzwLUHTbFBFqYCKF5eI60OTrOuBsWJBy12IWLCNoRhRuN1obSnKIQERzpAGKh2tJ3ITDYOvAqjnzMPcecwtgEoGMUrC6YgMCTkVl2wyB1L+e2/iF7vPi0TOas/sRuFsDFBhEBXFkdgjY6wr/tOj/WwMVig0JiGOwzDVKLrRsRh+z16HbzTwA5IHgMfmIJNxdhCUMlG0he41tTt+w484TVvbWBacYO94PZ1hXnGUCgfcMMsckYuGwpBgYwHlNerQCZzXmQ2otY7lmq9WxWUuyZnwIzJlrjKeYkdWAQi61nHDojBsDegMoxsSnv3W8y1C41wHCp85CPbIcjaGo7g6HBJ/pHkE7W8yHLAgHr+p1itIMfZW1Hgqeh35jPR1F5O2LvGbR9zepWwMU1oxNCeCXOQHocXmgvIliR/LRb0XqnsNw0fdbAUN7HbqAQaX5BWcCDWMCTNTr6sJslW6+19im1qTnKvaEmdnCgu8/zzuDhX/qAiq8N/RGptigqb7PuS6dVBYT8WzFvc4VLpU/KD8+FYwNoNVAf1VJuUDGZDWgsNGiF1EkLAPU9SkEo/AIiggA8e2GW6tfPxdQqAehgNO5AnmiuaYEEBM/MWWJTLXTvy7+RazLGnH4VuoZWIRyAUrAYUi40KwHyHtt6t/W/adfGQZDaYt7AIqt+z81j2hiFgjdb5ElwY3JBbdG7BOMlSlRhhtT6tsGW31H5RL93+vQ5X/nCydilaROjolDl+6I2hFbWdh7jW1qLRgv95fD9hKxZOIJuT5qmrKMmhpLONXXc6/bGwELexGXxLniXa9Fs4BK4HNInGPV1TGVhrsaUOhApbMVKZrKmzUB3B51ExasV3Oxz1XMJX83F1Dw36HGzxUbKcA1JdXd4d45m+9Ue/V6zRqZe//Qfd0NqhbZQQ3WojNDv6kvi28M+AbBubJl/+lWwDB3zBCzsgeg2LL/c3XoYK7MBDpUrMi50i2Uc24bAtKmqvWxxhky3K1blm6/RP/3OnRZ0PU7FnRzKsXSdTQ+Ecy5tqpkneu9xnZqLfHxC2gUhLr1dzxOPbdbz0OQ+Vh9jHPfg/7vGO1ck1MBt1PPcxbXyp6nDFJsZi10x1XNZT0mmwAKUaeQkn/RI1NC6QIiieA8i+BWaMq5gMJh6AU9V7zYfzjxY1SvYDoLw6LeajPwWBuCdtcIOq26YD6rZBEAj09xolEL9p02iDrfsv/igrhgloo5OfdbAlv2f26/zUu1UAX2zfkY0FjbXHAA5RrRl1OgRh8fWNxQU8FiS/txif7veehiLbGXU6XUa9ooV0el7pfqauj+Pcc29DxnSs0snJONsMUYu23U2EApuGIO9hTZlYrqTbFPc/rAcMOqyPax744J1oWbRzXdbpJF//7VgAI1+OWFcUBXs9bmpLNItanBQsrpnoq7GBpkC8p8WHaM6oYCBWuk9pxFdI17oFopxISbbKy0cwUeGI01DM+WY7ROa+GXoXa5+9DMxCFcwTHXzu9t2ZGd20IVA6VAn/HMeY937tJo80px23cwdFv5/S89lj0P3cpwWX8Cb4fmkkGigqZvX2xdrnzPsfXnCXBC18uC2MrltXQtALYYkrtewI3PFe28XFMiu44PI4mZnAKeFXhMFU5cBSgE1/EfiYuoJVyHPpst+IM10c3qENzCn66QhkEJploiDVA87LPfqHj0bGV8lujwkvd2A4BO9be6PBQpsq5uQfZweVxj3Fg1rJgPzFUa/Br9mHom5gyYcIhIcRsS8TjcNlt9rGmqT+dc3/PQ7a5J8zr0mXIBubXmi2j+Wj7+nLH0f7Pn2LrP4vKyV3BzjGWF+WiZD6NtyeD2xytQu6Ysdz/CtoUu+23UQNot5kzshwxNWSOYiqH3pevy4E3wYccxORtQQLcszvoteBQMKgbaETFK+J59LMUBIs2mH7VfUTS3h5K5tyBzXR57j0X+c/2MLhA35Nvv9oH1KfCOG2KNb3zNuMTXAI5jrjE0M4tKtkH/ZTlC/8fGPgdQHLn/dVyKQklLGyu/KzjLhnPNmCfsFr+/gLRTKeYYJXtPt6jREfrfXUNLD12UM0Ns6Lsc/bVpf2Zk2K/GvhNSawINBUqvXa97jq2OlUsRoymmYCwQErAU3IvBrXvk2rH1dV2DG8c+J7Bk3qb2V3sj4MetwvXQZ56Wjs2eyy2LkcR8KF/fF2XspZMK4EQAnPpw4CJA4eD6y9KgPHYbiw2IVGu5WjdyZgmL00ZlQnWse/DVbzv4rayIW5CjAIrq7phjyQvSwg6hBi0Kfr5rlFd28NrkxVX4kE4//RL6BUb76VdH6f+5gOII/RcfIfLdxiuYq//NAQwiP7AN2prqi0p5fs8/DRReo/CYwxQjau2OBWuyEhkyigEpPlTlCP3v65RFWJkDdD3WZUzo3HXuNRYql/GU1IMAi8Og6+69dCmIm4XvmlTLKlus173HhvF0qDJOxuKUZJXJhmB41fNl6dgYbuID6QuQrWmWVVcqPJsXbk4ArW/YLZ034EefGdn+32VdPEuaKLcKZsFZ3JWlY6u/vXdhJZ0RAqH7biPgXXbHnHTy2YCiRrJ6mLQyC7AbqOYlrhYDtsI99XplIoAKEwtVsTRQJ9AbBuNavq+pl7J//SiAgi4xPlN5wfpfK2nWsUgVU2ntGiJTwoEmbRibJXiMFUGv1oOgTEVpui/mkfo/pLMphuII/a9+V/3HAonqrl8edfjaNG1WQ1larB6bl8OaAKWqm15SagXeua4Y/uwHlQ4eof9DuurWFLAvMqzGpJuN4Z5nmhmf4xnmVDCdMsvYSXuvugIOEn/9b1BssV73HBvw+62lsu6cNYiZqgbU0rGJL6lxUNwC5kn8gv0L4+u9Yb2LYxtiiZfMG1ZJPFAttc39WD+dLg5GHJp0YHv/UCXYpWOruvNc7mVrAgGgYjXDA4gCdI1NMa/6Pp3S+WxAoXFIjBIpCeLvFlGC5BxwDgn1zXWuXucaqakmUDHLVJlXyFF06dGLWXUVeARAUd0dwBj/6JTPzobK8rTJ8j/XqqZzXsY97tFnrJWCSii3h5YXXqXMhww88Gj973dxClAcof/eX3VNuBa9w5gGaZYMA8yEMuinqEzvr80TS0n4VafW3ZZrp1svYapd+4l+dqP9r93/bp+BIoDM92AqSHNd+WZB1g7LfgVEH+4SL1XLJPcrDZ/SCWOQWwBD6VAEKLAWle3p/3bNet17bNaxAnMKKs4RFH63ns45Y7NvYh9kwcjcc9A7+LmUvDen6k4snTcAxoHOUPR/DJYy4iqYMsRqrOLQ2M8ZW7cdrDeAiRxwdmuPO0w57rkVVGcDijmT98hwzxEAxRo9A3ziE/b8pO+a/k39tvV/SkP7XmcpsXiVeb9FufX+2+SBDu6cNWm9c+fuku9bG9vcWZm+75Lz1u1NAxTTc/P/7rh1QIHW5laYizgXqmf321v/d1fxyQfwo9r4WUu3KLfef+yS+DVW7CXkku9bG9t2M3rJeWuAYsW8ARRooCFBY9ZSpisesctP+ckULlGOlpvp1qT1//ozhgpFaXOd7JmCt9dIb73/Yge4fgTHblUie0zXl37f2ti2WfWXmjcuNwH2QzJYi0PHmjyiBvj8xS4MCZ/0VPrmtXTKh8y3rADLLUrr/3VnTZEufzJALhk7sdWob73/0vp8b0HV1r2/FUHnl3zf2ti2WuWXmzcxVEDg7HOwAYrtJvkILQnkvMTHcvYaa+v/Xpqd127T/zw97XVX3Y8vVb30kvPdxrbdqrnkvC3qdQMUi9TVbm4aaBpoGmgaaBpoGhjSQAMUbV00DTQNNA00DTQNNA2s1kADFKtV2BpoGmgaaBpoGmgaaBr4PyFdoWG/6y9IAAAAAElFTkSuQmCC" width="266" height="18" style="width: 266px; height: 18px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Please present the final output as a unique row vector sorted ascending. </span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">-----------------</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="font-weight: 700; ">NOTE:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> Some MATLAB's built-in math functions may only give approximate values. </span></span></div></div></div>

Solve

Solution Stats

3 Solutions
2 Solvers

Last Solution submitted on Sep 11, 2022

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

William on 7 Sep 2022

What is "n"? ... and what are we supposed to calculate?

Ramon Villamangca on 7 Sep 2022

Hi William,
`n` is the upper limit of `y`. We are to calculate all integer values of `x` that will make `z = 0`.

William on 7 Sep 2022

Oh, I see. On my screen, the statement of the problem is not displaying properly, so that half of it is missing until the cursor is placed on a visible line and scrolled down.

Ramon Villamangca on 8 Sep 2022

Is this Cody glitch, because all the problems I'm viewing are showing only a few lines of display?

Dyuman Joshi on 8 Sep 2022

@William, @Ramon

Cody UI has been facing some problems since last few days, where you have to manually scroll down to see the rest of the content (problem statement, test case etc).
I have already reported this to the Cody Team and they are working on a fix. I will update the community accordingly.

Solution Comments

Show comments

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 55500. Easy Sequences 71: A Nonlinear Function with Quadratic Domain

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author116

Problem Tags

Community Treasure Hunt

Problem 55500. Easy Sequences 71: A Nonlinear Function with Quadratic Domain

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author116

Problem Tags

Community Treasure Hunt

Players

WeChat