17£®ÔÚƽÐÐËıßÐÎABCDÖУ¬AB=4$\sqrt{7}$£¬BC=4£¬µãPÔÚCDÉÏ£¬AC½»BPÓÚµãQ£¬Èô$\overrightarrow{CP}$=3$\overrightarrow{PD}$£¬$\overrightarrow{AP}•\overrightarrow{BP}$=-12£®Ôò$\overrightarrow{AB}•\overrightarrow{AQ}$=£¨¡¡¡¡£©
A£®66B£®68C£®72D£®76

·ÖÎö ÈçͼËùʾ£¬A£¨0£¬0£©£¬B£¨$4\sqrt{7}$£¬0£©£®ÉèC£¨x£¬y£©£¬$\overrightarrow{BC}$=$£¨x-4\sqrt{7}£¬y£©$£¬ÀûÓÃ|$\overrightarrow{BC}$|=4=$\sqrt{£¨x-4\sqrt{7}£©^{2}+{y}^{2}}$£¬¿ÉµÃ${y}^{2}=16-£¨x-4\sqrt{7}£©^{2}$£®ÓÉÓÚ$\overrightarrow{CP}$=3$\overrightarrow{PD}$£¬$\overrightarrow{CD}=\overrightarrow{AB}$=$£¨-4\sqrt{7}£¬0£©$£®¿ÉµÃ$\overrightarrow{AP}$=$\overrightarrow{AC}+\overrightarrow{CP}$£¬$\overrightarrow{BP}$=$\overrightarrow{AP}-\overrightarrow{AB}$£®¿ÉµÃ$\overrightarrow{AP}•\overrightarrow{BP}$=-12=$£¨x-3\sqrt{7}£©£¨x-7\sqrt{7}£©$+y2£®ÓÚÊÇÁªÁ¢¿ÉµÃx£®½ø¶øµÃ³ö£®

½â´ð ½â£ºÈçͼËùʾ£¬
A£¨0£¬0£©£¬B£¨$4\sqrt{7}$£¬0£©£®
ÉèC£¨x£¬y£©£¬$\overrightarrow{BC}$=$£¨x-4\sqrt{7}£¬y£©$£¬
¡à|$\overrightarrow{BC}$|=4=$\sqrt{£¨x-4\sqrt{7}£©^{2}+{y}^{2}}$£¬»¯Îª${y}^{2}=16-£¨x-4\sqrt{7}£©^{2}$£®
¡ß$\overrightarrow{CP}$=3$\overrightarrow{PD}$£¬$\overrightarrow{CD}=\overrightarrow{AB}$=$£¨-4\sqrt{7}£¬0£©$£®
¡à$\overrightarrow{CP}$=$\frac{3}{4}\overrightarrow{AB}$=$£¨-3\sqrt{7}£¬0£©$£®
¡à$\overrightarrow{AP}$=$\overrightarrow{AC}+\overrightarrow{CP}$=$£¨x-3\sqrt{7}£¬y£©$£®
$\overrightarrow{BP}$=$\overrightarrow{AP}-\overrightarrow{AB}$=$£¨x-7\sqrt{7}£¬y£©$£®
¡à$\overrightarrow{AP}•\overrightarrow{BP}$=-12=$£¨x-3\sqrt{7}£©£¨x-7\sqrt{7}£©$+y2£®£¨*£©
°Ñ${y}^{2}=16-£¨x-4\sqrt{7}£©^{2}$´úÈëÉÏʽ»¯¼ò¿ÉµÃ£º
x=$\frac{9\sqrt{7}}{2}$£®
¡ßCD¡ÎAB£¬
¡à$\frac{AQ}{QC}=\frac{AB}{PC}=\frac{4}{3}$£®
¡à$\overrightarrow{AQ}$=$\frac{4}{7}\overrightarrow{AC}$=$\frac{4}{7}$£¨x£¬y£©£®
¡à$\overrightarrow{AB}•\overrightarrow{AQ}$=$\frac{16\sqrt{7}}{7}$x=$\frac{16\sqrt{7}}{7}¡Á\frac{9\sqrt{7}}{2}$=72£®
¹ÊÑ¡£ºC£®

µãÆÀ ±¾Ì⿼²éÁËƽÐÐËıßÐεÄÐÔÖÊ¡¢ÏòÁ¿¹²Ï߶¨Àí¡¢ÊýÁ¿»ýÔËËãÐÔÖÊ¡¢·½³ÌµÄ½â·¨¡¢ÏòÁ¿Èý½ÇÐη¨Ôò£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

7£®ÐźűøÓÃ3ÖÖ²»Í¬ÑÕÉ«µÄÆì×Ó¸÷Ò»Ã棬´ò³ö3Ãæʱ×î¶àÄÜ´ò³ö²»Í¬µÄÐźÅÓжàÉÙ¸ö£¿

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

8£®Èôº¯Êýf£¨x£©=$\root{3}{x}$£¨x¡Ý0£©µÄ·´º¯ÊýÊÇf-1£¨x£©£¬Ôò²»µÈʽf-1£¨x£©£¾f£¨x£©µÄ½â¼¯Îª{x|x£¾1}£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

5£®ÉèÆ溯Êýf£¨x£©Âú×ãf£¨x£©=$\left\{\begin{array}{l}{-1£¨x¡Ý1£©}\\{1£¨0£¼x£¼1£©}\end{array}\right.$£¬Ôòf[f£¨sin6£©]=£¨¡¡¡¡£©
A£®-1B£®0C£®1D£®2

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®±È½Ïlogsin1cos1£¬logsin1tan1£¬logcos1sin1£¬logcos1tan1µÄ´óС£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

2£®ÔÚ1Óë9Ö®¼ä²åÈën-1¸öÊýb1£¬b2£¬¡­bn-1ʹÕân+1¸öÊý³ÉµÈ²îÊýÁУ¬¼ÇΪAn+1ÔòÊýÁÐ{An+1}ͨÏʽΪAn=9-$\frac{8}{n}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

9£®ÓëƽÃæÏòÁ¿$\overrightarrow{a}$=£¨-$\frac{1}{3}$£¬-$\frac{2}{3}$£©´¹Ö±µÄµ¥Î»ÏòÁ¿µÄ×ø±êΪ£¨¡¡¡¡£©
A£®£¨$\frac{2\sqrt{5}}{5}$£¬-$\frac{\sqrt{5}}{5}$£©B£®£¨-$\frac{2\sqrt{5}}{5}$£¬$\frac{\sqrt{5}}{5}$£©
C£®£¨$\frac{\sqrt{5}}{5}$£¬-$\frac{2\sqrt{5}}{5}$£©»ò£¨-$\frac{\sqrt{5}}{5}$£¬$\frac{2\sqrt{5}}{5}$£©D£®£¨$\frac{2\sqrt{5}}{5}$£¬-$\frac{\sqrt{5}}{5}$£©»ò£¨-$\frac{2\sqrt{5}}{5}$£¬$\frac{\sqrt{5}}{5}$£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÔڵȱÈÊýÁÐ{an}£¨n¡ÊN*£©ÖУ¬a1£¾1£¬¹«±Èq£¾0£¬Éèbn=log2an£®ÇÒb1+b2+b3=6£¬b1b3b5=0£®
£¨1£©Çó{an}µÄͨÏîan£®
£¨2£©Èôcn=$\frac{1}{n£¨{b}_{n}-6£©}$£¬Çó{cn}µÄÇ°nÏîºÍSn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

7£®ÒÑÖªÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$ÓëË«ÇúÏß$\frac{{x}^{2}}{{m}^{2}}-\frac{{y}^{2}}{{n}^{2}}=1$Óн»µãP£¬ÇÒÓй«¹²µÄ½¹µãF1£¬F2£¬ÇÒ¡ÏF1PF2=2¦Á£®ÇóÖ¤£ºtan¦Á=$\frac{n}{b}$£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸