7£®Èçͼ£¬Ôڰ뾶Ϊ$10\sqrt{3}£¨m£©$µÄ°ëÔ²ÐΣ¨ÆäÖÐOΪԲÐÄ£©ÂÁƤÉϽØÈ¡Ò»¿é¾ØÐβÄÁÏABCD£¬ÆäÖеãC¡¢DÔÚÔ²»¡ÉÏ£¬µãA¡¢BÔÚ°ëÔ²µÄÖ±¾¶ÉÏ£¬ÏÖ½«´Ë¾ØÐÎÂÁƤABCD¾í³ÉÒ»¸öÒÔBCΪĸÏßµÄÔ²ÖùÐιÞ×ӵIJàÃæ£¨×¢£º²»¼Æ¼ô²ÃºÍÆ´½ÓËðºÄ£©£¬Éè¾ØÐεı߳¤BC=x£¨m£©£¬Ô²ÖùµÄ²àÃæ»ýΪS£¨m2£©¡¢Ìå»ýΪV£¨m3£©£¬
£¨1£©·Ö±ðд³öÔ²ÖùµÄ²àÃæ»ýSºÍÌå»ýV¹ØÓÚxµÄº¯Êý¹ØÏµÊ½£»
£¨2£©µ±xΪºÎֵʱ£¬²ÅÄÜʹµÃÔ²ÖùµÄ²àÃæ»ýS×î´ó£¿
£¨3£©µ±xΪºÎֵʱ£¬²ÅÄÜʹԲÖùµÄÌå»ýV×î´ó£¿²¢Çó³ö×î´óÖµ£®

·ÖÎö £¨1£©Á¬½áOC£¬ÓÉBC£¬OC£¬¿ÉµÃOB£¬ÉèÔ²Öùµ×Ãæ°ë¾¶Îªr£¬ÓÉABΪµ×ÃæÔ²µÄÖܳ¤£¬¿ÉµÃ°ë¾¶r£¬ÔËÓÃÔ²ÖùµÄ²àÃæ»ý¹«Ê½ºÍÌå»ý¹«Ê½£¬¼´¿ÉµÃµ½ËùÇó½âÎöʽ£»
£¨2£©ÔËÓÃÅä·½ºÍ¶þ´Îº¯ÊýµÄ×îÖµÇ󷨣¬¿ÉµÃ²àÃæ»ýSµÄ×î´óÖµ¼°xµÄÖµ£»
£¨3£©Çó³öÌå»ýº¯ÊýµÄµ¼Êý£¬¿ÉµÃµ¥µ÷Çø¼äºÍ¼«Öµ£¬ÇÒΪ×îÖµ£¬¼°xµÄÖµ£®

½â´ð ½â£º£¨1£©Á¬½áOC£¬ÒòΪBC=x£¬$OC=10\sqrt{3}$£®
ËùÒÔ$OB=\sqrt{{{£¨10\sqrt{3}£©}^2}-{x^2}}$£¬¡­£¨1·Ö£©
ÉèÔ²Öùµ×Ãæ°ë¾¶Îªr£¬Ôò$AB=2\sqrt{300-{x^2}}=2¦Ðr$£¬
¼´$r=\frac{{\sqrt{300-{x^2}}}}{¦Ð}$£¬¡­£¨2·Ö£©
Ôò$S=2x\sqrt{300-{x^2}}£¨0£¼x£¼10\sqrt{3}£©$¡­£¨4·Ö£©
$V=¦Ð{r^2}x=\frac{{300x-{x^3}}}{¦Ð}£¨0£¼x£¼10\sqrt{3}£©$¡­£¨6·Ö£©
£¨2£©$S=2x\sqrt{300-{x^2}}=2\sqrt{300{x^2}-{x^4}}=2\sqrt{-{{£¨{x^2}-150£©}^2}+22500}£¨0£¼x£¼10\sqrt{3}£©$£¬
ËùÒÔµ±x2=150ʱ£¬¼´$x=5\sqrt{6}£¨m£©$ʱ£¬Ô²ÖùµÄ²àÃæ»ýΪSΪ×î´ó¡­£¨10·Ö£©
£¨3£©¡ß$V=¦Ð{r^2}x=\frac{{300x-{x^3}}}{¦Ð}£¨0£¼x£¼10\sqrt{3}£©$
¡à$V'=\frac{{300-3{x^2}}}{¦Ð}$£¬ÓÉV'=0½âµÃx=10£¬¡­£¨13·Ö£©
ÓÖÔÚx¡Ê£¨0£¬10£©ÉÏV'£¾0£¬ÔÚ$x¡Ê£¨10£¬10\sqrt{3}£©$ÉÏV'£¼0£¬
ËùÒÔ$V=\frac{{300x-{x^3}}}{¦Ð}$ÔÚ£¨0£¬10£©ÉÏÊÇÔöº¯Êý£¬ÔÚ$£¨10£¬10\sqrt{3}£©$ÉÏÊǼõº¯Êý£¬
ËùÒÔµ±x=10£¨m£©Ê±£¬Ô²ÖùµÄÌå»ýVµÄ×î´óֵΪ$\frac{2000}{¦Ð}£¨{m^3}£©$¡­£¨16·Ö£©£®

µãÆÀ ±¾Ì⿼²éÔ²ÖùµÄ²àÃæ»ýºÍÌå»ýµÄ×îÖµµÄÇ󷨣¬×¢ÒâÔËÓöþ´Îº¯ÊýµÄ×îÖµÇ󷨺ÍÓɵ¼ÊýÇóµ¥µ÷Çø¼ä¡¢¼«ÖµºÍ×îÖµ£¬¿¼²é»¯¼òÕûÀíµÄÔËËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®ÒÑÖªP£¨x£¬y£©ÊǺ¯Êýy=1+lnxͼÏóÉÏÒ»µã£¬OÊÇ×ø±êÔ­µã£¬Ö±ÏßOPµÄбÂÊΪf£¨x£©£®
£¨¢ñ£©Çóº¯Êýf£¨x£©µÄ¼«Öµ£»
£¨¢ò£©Éèg£¨x£©=$\frac{x}{a£¨1-x£©}$[xf£¨x£©-1]£¬Èô¶ÔÈÎÒâµÄx¡Ê£¨0£¬1£©ºãÓÐg£¨x£©£¾-1£¬ÇóʵÊýaµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®º¯Êýy=2cos2£¨$\frac{x}{2}$-$\frac{¦Ð}{4}$£©£¬£¨x¡ÊR£©µÄµÝ¼õÇø¼äÊÇ[2k¦Ð+$\frac{¦Ð}{2}$£¬2k¦Ð+$\frac{3¦Ð}{2}$]£¬k¡ÊZ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÈçͼËùʾ£¬ÔÚÈýÀâÖùABC-A1B1C1ÖУ¬¾ØÐÎABB1A1µÄ¶Ô½ÇÏßÏཻÓÚµãG£¬ÇÒ²àÃæABB1A1¡ÍÆ½ÃæABC£¬AC=CB=BB1=2£¬FΪCB1Éϵĵ㣬ÇÒBF¡ÍÆ½ÃæAB1C£®
£¨1£©ÇóÖ¤£ºAC¡ÍÆ½ÃæBB1C1C£»
£¨2£©Çó¶þÃæ½ÇA1-B1C-BµÄÓàÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

2£®ÉèÏßÐÔ·½³Ì×éµÄÔö¹ã¾ØÕóΪ$£¨\begin{array}{l}{2}&{3}&{{t}_{1}}\\{0}&{1}&{{t}_{2}}\end{array}£©$£¬½âΪ$\left\{\begin{array}{l}{x=3}\\{y=5}\end{array}\right.$£¬ÔòÈý½×ÐÐÁÐʽ$[\begin{array}{l}{1}&{-1}&{{t}_{1}}\\{0}&{1}&{-1}\\{-1}&{{t}_{2}}&{-6}\end{array}]$µÄֵΪ19£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÒÑÖªf£¨x£©=$\frac{x+1}{{e}^{x}}$£¨eÊÇ×ÔÈ»¶ÔÊýµÄµ×Êý£©£®
£¨¢ñ£©Çóº¯Êýf£¨x£©µÄ¼«´óÖµ£»
£¨¢ò£©Áîh£¨x£©=a+2f¡ä£¨x£©£¨a¡ÊR£©£¬Èôh£¨x£©ÓÐÁ½¸öÁãµã£¬x1£¬x2£¨x1£¼x2£©£¬ÇóaµÄȡֵ·¶Î§£»
£¨¢ó£©ÉèF£¨x£©=aex-x2£¬ÔÚ£¨¢ò£©µÄÌõ¼þÏ£¬ÊÔÖ¤Ã÷0£¼F£¨x1£©£¼1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÒÑÖªÕý·½ÌåABCD-A1B1C1D1µÄÀⳤΪ3£¬EΪCDµÄÖе㣬ÔòµãD1µ½Æ½ÃæAEC1µÄ¾àÀëΪ£¨¡¡¡¡£©
A£®$\sqrt{6}$B£®$\sqrt{3}$C£®$\sqrt{2}$D£®1

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®ÉèÔÚÖ±ÈýÀâ×¶ABC-A1B1C1ÖУ¬AB=AC=AA1=2£¬¡ÏBAC=90¡ã£¬E£¬FÒÀ´ÎΪCC1£¬BCµÄÖе㣮
£¨1£©ÇóÒìÃæÖ±ÏßA1BÓëEFËù³É½Ç¦ÈµÄ´óС£»
£¨2£©ÇóÖ±ÏßEFÓëÆ½ÃæABCËù³É½Ç´óС£»
£¨3£©ÇóµãCµ½Æ½ÃæAEFµÄ¾àÀ룮

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

17£®Èçͼ£¬ÒÑÖªAB£¬ACÊÇÔ²µÄÁ½ÌõÏÒ£¬¹ýB×÷Ô²µÄÇÐÏßÓëACµÄÑÓ³¤ÏßÏཻÓÚD£®¹ýµãC×÷BDµÄƽÐÐÏßÓëABÏཻÓÚµãE£¬AE=3£¬BE=1£¬ÔòBCµÄ³¤Îª£¨¡¡¡¡£©
A£®$\sqrt{2}$B£®$\sqrt{3}$C£®2D£®$\frac{3}{2}$

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸