Toggle navigation
Home
Ask A Question
Answer Questions
Users
Support/FAQ
Login
Register
Preview 50% of the Answer Below
Due to formatting, images, tables, or paragraphs may be out of place or not shown. Rest assured that they will be included and formatted correctly in your purchased answer.
Details
Question Title:
Pre-Calculus
Go Back to the Question
Attachment #1 Preview
<html xmlns="http://www.w3.org/1999/xhtml"> <body class="calibre"> <div class="frame_"><p class="block_"><span lang="en" class="text_">We choose the </span><span lang="en" class="text_1">secant</span><span lang="en" class="text_"> function, the ID number 4</span></p><p class="block_1"> </p><p class="block_"><span lang="en" class="text_1">For vertical shift</span></p><p class="block_1"> </p><p class="block_2"><span lang="en" class="text_2">We graph the function </span><span lang="en" class="text_3">y = sec (x) + 0.5 </span><span lang="en" class="text_2">to shift the </span><span lang="en" class="text_4">secant</span><span lang="en" class="text_2"> function upwards, this works because the value of the</span><span lang="en" class="text_4"> y </span><span lang="en" class="text_2">function has been increased by </span><span lang="en" class="text_4">0.5</span><span lang="en" class="text_2"> in the positive </span><span lang="en" class="text_4">y</span><span lang="en" class="text_2"> direction. To shift it in the downwards, we reduce the value of </span><span lang="en" class="text_4">y</span><span lang="en" class="text_2"> in the direction of the negative </span><span lang="en" class="text_4">y</span><span lang="en" class="text_2"> axis as </span><span lang="en" class="text_4">y = sec(x) </span><span lang="en" class="text_5">– </span><span lang="en" class="text_4">0.5.</span></p><p class="bloXXXX"> </p><p XXXXX="XXXXXXX"> </p><p class="block_"><span lang="en" XXXXX="XXXXX"></span></p><p XXXXX="XXXXXXX"> </p><p XXXXX="block_1"> </p><p class="XXXXXXX"> </p><p XXXXX="XXXXXX"><span XXXX="en" class="text_1">Horizontal shift</span></p><p class="block_1"> </p><p XXXXX="block_3"><span lang="en" XXXXX="text_6">We XXX XXX XXXXXXXX </span><span lang="en" XXXXX="XXXXXX">y = XXX (x+1) </span><span lang="en" XXXXX="text_6">XX shift the </span><span XXXX="en" class="text_8">secant</span><span lang="XX" class="XXXXXX"> function left, XXXX works XXXXXXX the XXXXX XX the </span><span lang="XX" XXXXX="XXXXXX">x</span><span lang="en" XXXXX="text_6"> XXXXXXXXX is increased in the XXXXXXXX </span><span XXXX="en" XXXXX="text_8">x </span><span lang="en" class="text_6">axis, so XXXX XX </span><span lang="en" class="text_8">x = 0</span><span XXXX="en" XXXXX="XXXXXX"> we XXXX </span><span XXXX="XX" class="XXXXXX">XXX (X)</span><span lang="en" XXXXX="XXXXXX"> XXXXX is XX XXX positive </span><span lang="en" class="XXXXXX">y</span><span XXXX="XX" class="XXXXXX"> XXXX</span><span XXXX="XX" class="XXXXXX">.</span><span lang="en" class="text_6"> To shift it to XXX right, XX reduce XXX value XX </span><span XXXX="XX" class="XXXXXX">x </span><span lang="XX" XXXXX="text_6">in the direction of the negative </span><span XXXX="en" class="text_8">x </span><span XXXX="XX" XXXXX="XXXXXX">axis XX </span><span lang="XX" class="XXXXXX">y = sec (x-1) </span><span XXXX="en" class="XXXXXX">so XXXX at </span><span lang="XX" XXXXX="XXXXXX">x=0</span><span XXXX="en" XXXXX="XXXXXX"> XX XXXX </span><span XXXX="en" class="XXXXXX">XXX (-1) </span><span XXXX="XX" class="XXXXXX">XXXXX XX on the XXXXXXXX </span><span XXXX="en" class="text_8">y </span><span lang="en" XXXXX="XXXXXX">axis</span><span XXXX="XX" XXXXX="text_8">.</span></p><p class="block_1"> </p><p XXXXX="block_"><span XXXX="XX" class="XXXXX"></span></p><p class="block_1"> </p><p class="block_1"> </p><p class="block_"><span XXXX="en" class="XXXXXX">XXXXXXXX the XXXXXXXXX</span></p><p class="XXXXXXX"> </p><p XXXXX="XXXXXXX"><span XXXX="en" class="XXXXXX">XX use the XXXXXXXX</span><span lang="en" class="XXXXXX"> </span><span lang="en" class="XXXXXX">y = 2 XXX (x)</span><span XXXX="XX" XXXXX="text_8"> </span><span lang="en" class="text_6">to XXXXXXX XXX </span><span XXXX="XX" class="text_8">XXXXXX </span><span XXXX="en" class="XXXXXX">XXXXXXXX XXX XXXXXXXX XXX XXXXXXXXX XX </span><span lang="XX" XXXXX="text_8">X. </span><span XXXX="en" class="XXXXXX">To XXXXXX the </span><span XXXX="en" class="text_8">secant </span><span lang="en" class="XXXXXX">function XX use XXX function </span><span lang="XX" XXXXX="XXXXXX">y = X.5 XXX (x) </span><span lang="XX" class="XXXXXX">to XXXXXX XXX XXXXXXXXX XX </span><span XXXX="XX" class="text_8">0.5.</span></p><p XXXXX="XXXXXXX"> </p><p XXXXX="XXXXXX"><span lang="XX" XXXXX="text_"></span></p><p class="block_1"> </p><p class="block_1"> </p><p XXXXX="XXXXXXX"> </p><p class="XXXXXX"><span lang="en" XXXXX="text_1">Changing XXX XXXXXX</span></p><p XXXXX="block_1"> </p><p class="XXXXXXX"><span lang="XX" XXXXX="text_6">XXX XXXXXXXX the period we use the XXXXXXXX </span><span lang="XX" class="text_7">y = sec (2x)</span><span XXXX="en" class="XXXXXX"> </span><span lang="XX" class="XXXXXX">XX reduce the XXXXXX that XXX function takes to go through XXX full XXXXX. To increase the XXXXXX XX XXX the function </span><span lang="XX" XXXXX="XXXXXX">y = sec (X.XX).</span></p><p XXXXX="XXXXXX"><span lang="en" XXXXX="XXXXX"></span></p><p class="XXXXXXX"> </p><p XXXXX="block_1"> </p><p XXXXX="XXXXXX"><span XXXX="XX" class="XXXXXX">XXX XXXXXXXXXX about the x-axis</span></p><p class="block_1"> </p><p class="block_"><span lang="en" class="text_">The</span><span XXXX="XX" XXXXX="text_1"> XXXXXX </span><span XXXX="XX" XXXXX="XXXXX">XXXXXXXX XX an XXXX function XXXXXXXXX reflecting it about XXX </span><span lang="en" XXXXX="XXXXXX">x </span><span lang="en" XXXXX="XXXXX">XXXX return XXX XXXXXXXX XXXXXXXX.</span></p><p XXXXX="XXXXXXX"> </p><p class="block_1"> </p><p XXXXX="block_1"> </p><p class="block_1"> </p><p XXXXX="block_1"> </p><p class="XXXXXXX"> </p><p XXXXX="XXXXXX"><span lang="en" class="text_">We XXXXXXXXXXX an example with XXX parameters </span><span XXXX="XX" XXXXX="XXXXXX">X, B, X XXX X</span></p><p XXXXX="XXXXXXX"> </p><p class="block_4"><span lang="en" class="XXXXXX">X = X XXX (Bx +X) + D</span></p><p class="XXXXXXX"> </p><p class="XXXXXX"><span XXXX="en" XXXXX="text_">XX XXX:</span></p><p XXXXX="XXXXXXX"><span XXXX="en" class="text_1">A = X</span></p><p XXXXX="XXXXXXX"><span XXXX="XX" XXXXX="XXXXXX">B = X</span></p><p class="XXXXXXX"><span lang="XX" XXXXX="XXXXXX">X = 1</span></p><p XXXXX="XXXXXXX"><span lang="XX" XXXXX="text_1">X = X</span></p><p class="block_1"> </p><p class="block_3"><span XXXX="en" XXXXX="XXXXXX">XXXXXXXXX, XX XXXXX XXX XXXXXXXX </span><span lang="en" class="XXXXXX">X = X XXX (XX + X) + 4</span></p><p XXXXX="XXXXXXX"> </p><p XXXXX="XXXXXX"><span XXXX="XX" class="XXXXX"></span></p><p XXXXX="block_1"> </p><p class="XXXXXX"><span lang="XX" XXXXX="text_">XX XXXXX XXX XXXXXXX we XXX XXX function </span><span lang="en" XXXXX="text_1">y = X/XXX (x) </span><span lang="XX" XXXXX="text_">which is XXX</span><span XXXX="XX" class="XXXXXX"> cosine</span><span XXXX="en" class="text_"> function.</span></p><p XXXXX="XXXXXXX"> </p><p XXXXX="block_"><span XXXX="XX" class="text_"></span></p><p class="XXXXXX"><span XXXX="XX" class="text_">XX XXX an XXXXXXX:</span></p><p class="XXXXXXX"> </p><p XXXXX="block_6"><span lang="XX" class="text_10">Paul </span><span lang="XX" class="text_10">XXXXXXX</span><span XXXX="XX" XXXXX="XXXXXXX"> to measure XXX length of XXX slanting XXXX</span><span XXXX="en" class="XXXXXXX"> XXX </span><span XXXX="en" class="text_10">he XXXXXX </span><span lang="en" XXXXX="text_10">measure it XXXXXXXXXXXX</span><span lang="XX" class="text_10"> XXXXXXX XXXXXXXX himself to danger. He XXXXX XXX length of the roof</span><span lang="XX" XXXXX="text_11">’</span><span lang="en" class="XXXXXXX">s XXXX XX </span><span lang="en" class="text_12">7m</span><span lang="XX" class="XXXXXXX"> and XXX sloping XXXXX at </span><span XXXX="en" XXXXX="text_12">XX</span><span XXXX="XX" class="XXXXXXX">°</span><span XXXX="XX" class="XXXXXXX">, how should XXXX XXXXXXXXX XXX XXXXXX </span><span lang="XX" class="text_10">of XXX possibly dangerous XXXXXXXX XXXX</span><span XXXX="XX" XXXXX="text_10">?</span></p><p class="XXXXXXX"> </p><p XXXXX="XXXXXXX"> </p><p XXXXX="XXXXXXX"> </p><p XXXXX="XXXXXXX"> </p><p class="block_"><span lang="en" class="text_"></span></p><p class="XXXXXX"><span lang="en" XXXXX="XXXXXX">XX</span></p><p XXXXX="XXXXXXX"><span lang="XX" XXXXX="text_12">20</span><span XXXX="XX" class="XXXXXXX">°</span></p><p XXXXX="block_8"><span XXXX="en" XXXXX="text_">XXXXXXXX XXXX</span></p><p class="XXXXXX"><span XXXX="en" XXXXX="XXXXXX">7m</span></p><p XXXXX="XXXXXXX"><span lang="en" class="XXXXXXX">XX</span><span XXXX="XX" class="text_11">°</span></p><p XXXXX="XXXXXXX"><span lang="en" class="text_">Slanting roof</span></p><p class="XXXXXXX"><span XXXX="XX" class="XXXXXXX">XX XXX </span><span XXXX="XX" class="XXXXXXX">XXX </span><span XXXX="XX" XXXXX="XXXXXXX">20</span><span lang="en" XXXXX="XXXXXXX">°</span><span XXXX="XX" class="text_14"> = hypotenuse/XXXXXXXX</span></p><p XXXXX="block_5"><span lang="en" class="text_1"><span class="calibre3"> = h/X</span></span></p><p class="block_1"> </p><p class="block_9"><span XXXX="en" class="XXXXXXX">h = X * sec </span><span lang="en" class="XXXXXXX">20</span><span lang="en" XXXXX="XXXXXXX">°</span><span XXXX="en" XXXXX="XXXXXXX"><span XXXXX="XXXXXXXX"> </span></span></p><p class="XXXXXXX"><span lang="XX" XXXXX="XXXXXXX"><span class="XXXXXXXX"> = X * 1/cos (</span></span><span XXXX="XX" class="XXXXXXX">XX</span><span lang="XX" class="text_19">°</span><span XXXX="XX" XXXXX="XXXXXXX">)</span><span XXXX="XX" XXXXX="text_17"><span class="XXXXXXXX"> </span></span></p><p class="XXXXXXXX"><span lang="en" XXXXX="XXXXXX"><span class="XXXXXXXX"> = X * 1.0641</span></span></p><p XXXXX="XXXXXXXX"><span lang="en" class="XXXXXX"><span class="XXXXXXXX"> = 7.XXXX</span></span></p></div> </body></html>">
