如图,数轴上点A表示数
,点
表示数
,且
、
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/79928958-238c-49c8-bcda-54592d2acc98.png?resizew=170)
(1)点A表示的数为 ;点
表示的数为 ;
(2)若数轴上有两动点
,
,点
以4个单位
秒从A向右运动,同时点
以2个单位
秒从点
向左运动,问经过几秒
,
相遇?
(3)在(2)的条件下,动点
、
出发经过多少秒,能使
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d4a2b958a04afd5029ebdfbe40d821.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/79928958-238c-49c8-bcda-54592d2acc98.png?resizew=170)
(1)点A表示的数为 ;点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若数轴上有两动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4333bb203d02814c146ed587b69ea69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)在(2)的条件下,动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4b7eb4a69d0faa3ca4efb82cf2c79b.png)
更新时间:2022-11-27 14:10:45
|
相似题推荐
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【推荐1】在数轴上把下列各数表示出来,并用“<”将它们连接起来:
,
,0,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbaf9721c465b3456eccf2b97304a496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66d56ba6d3a43eb6ee597d33387bbf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2384167ae61cf3183559acb3006898a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2de9a7959b4530a35cad7a03b4fc23.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/f9613e77-971d-41db-a0c1-b3ce0f9adb26.png?resizew=304)
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【推荐2】把下列各数在数轴上表示出来,并按从小到大的顺序用“<”连接起来.
-3.5, 0, 2, -2 , 0.5.
-3.5, 0, 2, -2 , 0.5.
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【推荐1】两个有理数在数轴上对应的点之间的距离可以用这两个数的差的绝对值表示,例如,在数轴上,有理数3与1对应的两点之间的距离为
;在数轴上,有理数5与
对应的两点之间的距离为
.在数轴上A, B点对应的有理数分别为a,b,则可将A, B两点之间的距离表示为
或
,记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/e8b4fd89-ef58-4a4b-94da-8bbbb9692aa0.png?resizew=171)
【解决问题】
(1)数轴上有理数
与
对应的两点之间的距离为 .
(2)数轴上有理数x与
对应的两点之间的距离用含x的式子表示为 .
【拓展探究】
(3)如图A,B,P是数轴上的三点,点A表示的数为
,点B表示的数为4,点P在原点处.若点P以每秒2个单位长度的速度从原点出发向右匀速运动,同时点A以每秒3个单位长度的速度向左匀速运动,点B以每秒5个单位长度的速度向右匀速运动,运动时间为t秒.求运动后
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f3a2c1da4845b891e70f59e6f3e3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af626a8f2eff4f8a4f08242eb0bddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13880b9454c5942f164d934b1834783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1103ddae6ffaba2b15808c6df09c0248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68892c2c50f286eed3fe83b26c3f2112.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/e8b4fd89-ef58-4a4b-94da-8bbbb9692aa0.png?resizew=171)
【解决问题】
(1)数轴上有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e22e1223baf7cb3d53e668c2449609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
(2)数轴上有理数x与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01317332a203c898536b1d0459f51d23.png)
【拓展探究】
(3)如图A,B,P是数轴上的三点,点A表示的数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cb9fcb3c10c5b7a667a5a17d965625.png)
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【推荐2】如图,在数轴上点
表示数
,点
表示数
,
表示
点与
点之间的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/114fdc4c-7b29-4cc3-a0f3-af47fb4c1fac.png?resizew=155)
(1)若
,
满足
,求
,
的值.
(2)在(
)的条件下,若
是
的中点,求点
表示的数.
(3)点
从
点以
个单位每秒向右运动,点
同时从
点以
个单位每秒向左运动.若
,求运动时间
的值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/114fdc4c-7b29-4cc3-a0f3-af47fb4c1fac.png?resizew=155)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aacff245312210010cdb5c665d18b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)在(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0670243af8c3f1386071a34c5f19b8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐1】已知数轴上有
、
、
三个点,分别表示有理数
,动点
从
出发,以每秒1个单位的速度向点
移动(到达
点停止运动),设移动时间为
秒.
(1)用含
的代数式表示
到点A和点
的距离(其中
表示点
到点A的距离,
表示点
到点
的距离):
_______;
_______;
(2)当点
运动到
点时,点
从
点出发,以每秒2个单位的速度向
点运动,
点到达
点后
点停止运动.在点
开始运动到
,
都停止.
、
两点之间的距离能否为2个单位?如果能,请求出此时点
表示的数;如果不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f524766e6e489d20bc90a8e2e445e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/19/194730a3-9e30-464d-af0f-c54f8db8b18c.png?resizew=179)
(1)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5745e2dc1d5308872c68ae932cd13ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e7d551cca653e2d638c8cab4c2fda8.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】如图,在数轴上点A表示的数是a,点B表示的数是b,且
,
(1)填空:
,
;
(2)在线段
上有一点C,满足
,求点C表示的数;
(3)动点P从点A出发,以每秒6个单位长度的速度沿数轴向左匀速运动;动点Q从点B出发,以每秒4个单位长度的速度沿数轴向左匀速移动;动点M从点A出发,以每秒3个单位长度的速度沿数轴向左匀速移动,设运动时间为t秒,当
时,
的值是否发生变化?若不变求出其值;若变化,写出范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497786c7b8111351be78584cc86f73fd.png)
(1)填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002471e69d992c4d10c8255ba152e7a.png)
(3)动点P从点A出发,以每秒6个单位长度的速度沿数轴向左匀速运动;动点Q从点B出发,以每秒4个单位长度的速度沿数轴向左匀速移动;动点M从点A出发,以每秒3个单位长度的速度沿数轴向左匀速移动,设运动时间为t秒,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8bb21444e1cfad8b7ab49bbb594be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cd2c554e76a65ba4e9e9dadc2552f7.png)
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【推荐1】阅读理解:如图①,若线段
在数轴上,A、B两点表示的数分别为a和
,则线段
的长(点A到点B的距离)可表示为
.
请用上面材料中的知识解答下面的问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/5a2c28b7-29dc-4b47-bd66-1a2ea8861a2c.png?resizew=304)
如图②,一个点从数轴的原点开始,先向左移动
到达P点,再向右移动
到达Q点,用1个单位长度表示
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/b138cf2f-ca04-4927-930b-5c728c249ffe.png?resizew=725)
(1)请你在图②的数轴上表示出P,Q两点的位置,并求出此时线段
的长;
(2)若将图②中的点P向左移动
,点Q向右移动
,求此时线段
的长(用含x的代数式表示),并求出当线段
的长为
时的x值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff367dc5225a95a231f83433034a1ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7819f6e7447bbe91baac7eb439940d72.png)
请用上面材料中的知识解答下面的问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/5a2c28b7-29dc-4b47-bd66-1a2ea8861a2c.png?resizew=304)
如图②,一个点从数轴的原点开始,先向左移动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1b7aa6e3693af226ef7324c37534c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/b138cf2f-ca04-4927-930b-5c728c249ffe.png?resizew=725)
(1)请你在图②的数轴上表示出P,Q两点的位置,并求出此时线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)若将图②中的点P向左移动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc64ac2446a970ba62639c28a26d6adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7a47db1a819143213f848f80cdf687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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【推荐2】如图,点O为数轴原点,
,长方形
的宽
为6单位长度,长
为8单位长度.点P从点O出发,沿射线
方向运动,速度为每秒2个单位长度,设运动时间为t秒,回答下列问题.
(2)t秒后点P对应的数为 (用含t的式子表示).
(3)当
时,求t的值.
(4)如图,在点P运动过程中,在数轴上取点E,点E在点P右侧,线段
,以
为直角边,E为直角顶点,向上作等腰直角三角形
,当
与
面积和为12时,直接写出t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3dfcd8aff269dd5aba398816490c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
(2)t秒后点P对应的数为 (用含t的式子表示).
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbb2dce15f3d0fe839688575d2a8ff8.png)
(4)如图,在点P运动过程中,在数轴上取点E,点E在点P右侧,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de853a263e59781532f89fdab2a0acb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd28db93364ac2a6f0e75ed245dbbfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
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【推荐3】如图,点A、B和线段CD都在数轴上,点A、C、D、B起始位置所表示的数分别为-2、0、3、12;线段CD沿数轴的正方向以每秒1个单位的速度移动,移动时间为t秒.
(1)用含有t的代数式表示AC的长为多少,当t=2秒时,AC的长为多少.
(2)当0<t<9时AC+BD等于多少,当t>9时AC+BD等于多少.
(3)若点A与线段CD同时出发沿数轴的正方向移动,点A的速度为每秒2个单位,在移动过程中,是否存在某一时刻使得AC=2BD,若存在,请
直接写出t的值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2018/12/24/2103542025510912/2166811754807296/STEM/6ba6404631dc431bac34ce7aaf13c6e7.png?resizew=406)
(1)用含有t的代数式表示AC的长为多少,当t=2秒时,AC的长为多少.
(2)当0<t<9时AC+BD等于多少,当t>9时AC+BD等于多少.
(3)若点A与线段CD同时出发沿数轴的正方向移动,点A的速度为每秒2个单位,在移动过程中,是否存在某一时刻使得AC=2BD,若存在,请
![](https://img.xkw.com/dksih/QBM/2018/12/24/2103542025510912/2166811754807296/STEM/7865cf76fc6d4dfc81b9b9b080bff185.png?resizew=24)
![](https://img.xkw.com/dksih/QBM/2018/12/24/2103542025510912/2166811754807296/STEM/6ba6404631dc431bac34ce7aaf13c6e7.png?resizew=406)
![](https://img.xkw.com/dksih/QBM/2018/12/24/2103542025510912/2166811754807296/STEM/d4988bcc9deb49f69dc46c29f675ac0d.png?resizew=399)
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