一个圆形花坛的半径为6米,现要在花坛边缘均匀种植一圈月季花,相邻两株月季花之间的弧长为π米。问一共需要种植多少株月季花?
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正整数是指大于0的整数。选项A是负整数,选项B是0(既不是正数也不是负数),选项C是小数,只有选项D的7是大于0的整数,因此选D。
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[{"id":294,"content":"在平面直角坐标系中,点A的坐标是(3, -2),点B的坐标是(-1, 4)。若点C是线段AB的中点,则点C的坐标是","type":"选择题","subject":"数学","grade":"初一","stage":"小学","difficulty":"简单","answer":"A","explanation":"根据平面直角坐标系中两点间中点坐标公式:若点A的坐标为(x₁, y₁),点B的坐标为(x₂, y₂),则中点C的坐标为((x₁ + x₂)\/2, (y₁ + y₂)\/2)。将点A(3, -2)和点B(-1, 4)代入公式,得:横坐标为(3 + (-1))\/2 = 2\/2 = 1,纵坐标为(-2 + 4)\/2 = 2\/2 = 1。因此,点C的坐标为(1, 1)。选项A正确。","options":[{"id":"A","content":"(1, 1)"},{"id":"B","content":"(2, 2)"},{"id":"C","content":"(1, 2)"},{"id":"D","content":"(2, 1)"}]},{"id":1908,"content":"某学生在整理班级同学的课外阅读情况时,收集了以下数据:喜欢小说的有18人,喜欢科普书的有12人,既喜欢小说又喜欢科普书的有5人。那么,只喜欢小说或只喜欢科普书的学生共有多少人?","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"A","explanation":"本题考查数据的收集与整理,涉及集合的简单运算。已知喜欢小说的有18人,其中包括只喜欢小说和既喜欢小说又喜欢科普书的学生;喜欢科普书的有12人,也包括只喜欢科普书和两者都喜欢的学生。两者都喜欢的人数为5人,因此只喜欢小说的人数为18 - 5 = 13人,只喜欢科普书的人数为12 - 5 = 7人。所以,只喜欢小说或只喜欢科普书的学生总人数为13 + 7 = 20人。正确答案为A。","options":[{"id":"A","content":"20"},{"id":"B","content":"25"},{"id":"C","content":"30"},{"id":"D","content":"35"}]},{"id":1821,"content":"如图,在平行四边形ABCD中,对角线AC与BD相交于点O。已知∠AOB = 90°,AC = 10,BD = 24,则该平行四边形的面积是( )","type":"选择题","subject":"数学","grade":"八年级","stage":"初中","difficulty":"中等","answer":"B","explanation":"在平行四边形中,对角线互相平分,因此AO = AC ÷ 2 = 5,BO = BD ÷ 2 = 12。由于∠AOB = 90°,所以三角形AOB是直角三角形,其面积为 (1\/2) × AO × BO = (1\/2) × 5 × 12 = 30。平行四边形被对角线分成四个面积相等的三角形,因此总面积为 4 × 30 = 120。故选B。","options":[{"id":"A","content":"60"},{"id":"B","content":"120"},{"id":"C","content":"240"},{"id":"D","content":"480"}]},{"id":2541,"content":"一个圆形花坛的半径为6米,现计划在花坛中心安装一个自动旋转喷水器,喷水范围形成一个扇形,其圆心角为θ(0° < θ < 360°)。已知喷水覆盖区域的面积S(平方米)与圆心角θ(度)之间的关系为 S = (θ\/360) × π × 6²。若要求喷水覆盖面积恰好为花坛总面积的1\/3,则θ的值应为多少?","type":"选择题","subject":"数学","grade":"九年级","stage":"初中","difficulty":"中等","answer":"B","explanation":"首先计算整个花坛的面积:π × 6² = 36π 平方米。题目要求喷水覆盖面积为总面积的1\/3,即 (1\/3) × 36π = 12π 平方米。根据题中给出的公式 S = (θ\/360) × 36π,代入 S = 12π 得:12π = (θ\/360) × 36π。两边同时除以π,得到 12 = (θ\/360) × 36。两边同除以12,得 1 = (θ\/360) × 3,即 θ\/360 = 1\/3,解得 θ = 120°。因此正确答案为B。","options":[{"id":"A","content":"90°"},{"id":"B","content":"120°"},{"id":"C","content":"150°"},{"id":"D","content":"180°"}]},{"id":2160,"content":"某学生在数轴上标出三个有理数 a、b、c,其中 a 与 b 关于原点对称,c 是 a 与 b 之间距离的一半,且 a > 0。若 a = 6,则 c 的值是多少?","type":"选择题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"中等","answer":"D","explanation":"因为 a = 6 且 a 与 b 关于原点对称,所以 b = -6。a 与 b 之间的距离为 |6 - (-6)| = 12。c 是该距离的一半,即 12 ÷ 2 = 6 个单位长度。但题目中 c 是位于 a 与 b 之间距离的一半位置,即从 a 向左移动 6 个单位或从 b 向右移动 6 个单位,最终都到达原点 0。因此 c = 0。","options":[{"id":"A","content":"3"},{"id":"B","content":"-3"},{"id":"C","content":"6"},{"id":"D","content":"0"}]},{"id":640,"content":"某班级组织了一次环保活动,收集废纸和塑料瓶。已知每千克废纸可兑换0.8元,每千克塑料瓶可兑换1.2元。一名学生共收集了15千克废品,兑换后获得16元。若设该学生收集的废纸为x千克,则根据题意可列出一元一次方程为:","type":"选择题","subject":"数学","grade":"初一","stage":"初中","difficulty":"简单","answer":"A","explanation":"设收集的废纸为x千克,则塑料瓶为(15 - x)千克。废纸每千克兑换0.8元,总价值为0.8x元;塑料瓶每千克兑换1.2元,总价值为1.2(15 - x)元。两者之和等于16元,因此方程为0.8x + 1.2(15 - x) = 16。选项A正确。选项B错误地将两种废品都设为x千克;选项C颠倒了废纸和塑料瓶的对应关系;选项D使用了减法,不符合实际兑换逻辑。","options":[{"id":"A","content":"0.8x + 1.2(15 - x) = 16"},{"id":"B","content":"0.8x + 1.2x = 16"},{"id":"C","content":"0.8(15 - x) + 1.2x = 16"},{"id":"D","content":"0.8x - 1.2(15 - x) = 16"}]},{"id":2516,"content":"某学生设计了一个圆形花坛,其周长为6π米。现计划在花坛外侧修建一条宽度为1米的环形步道,则这条步道的面积是多少平方米?","type":"选择题","subject":"数学","grade":"九年级","stage":"初中","difficulty":"简单","answer":"A","explanation":"首先根据圆的周长公式C = 2πr,由已知周长6π米可得:2πr = 6π,解得半径r = 3米。这是花坛的内半径。步道宽1米,因此包含步道后的外圆半径为3 + 1 = 4米。步道的面积等于外圆面积减去内圆面积:π×(4²) - π×(3²) = 16π - 9π = 7π(平方米)。因此正确答案是A。","options":[{"id":"A","content":"7π"},{"id":"B","content":"8π"},{"id":"C","content":"9π"},{"id":"D","content":"10π"}]},{"id":2220,"content":"某学生在记录一周内每天气温变化时,发现某天的气温比前一天上升了3℃,记作+3℃;那么如果某天的气温比前一天下降了2℃,应记作____℃。","type":"填空题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"-2","explanation":"根据正数和负数表示相反意义的量的概念,气温上升用正数表示,气温下降则用负数表示。因此,下降2℃应记作-2℃。这符合七年级数学中正负数在实际生活中的应用要求。","options":[]},{"id":2227,"content":"某学生记录了一周内每天气温的变化情况,规定气温上升记为正,下降记为负。已知周一气温变化为 -3℃,周二为 +5℃,周三为 -2℃,则这三天中气温变化总和为 ___ ℃。","type":"填空题","subject":"数学","grade":"七年级","stage":"初中","difficulty":"简单","answer":"0","explanation":"根据题意,气温变化总和为 -3 + (+5) + (-2)。先计算 -3 + 5 = 2,再计算 2 + (-2) = 0。因此,三天气温变化总和为 0℃,表示整体上没有变化。","options":[]},{"id":2373,"content":"某公园计划修建一个矩形花坛,其一边靠墙(墙足够长),其余三边用总长为20米的防腐木围栏围成。设垂直于墙的一边长度为x米,花坛的面积为y平方米。若要使花坛面积最大,则x应取何值?","type":"选择题","subject":"数学","grade":"八年级","stage":"初中","difficulty":"中等","answer":"B","explanation":"设垂直于墙的一边长度为x米,则平行于墙的一边长度为(20 - 2x)米(因为三边总长为20米,包含两个x和一个长边)。花坛面积y = x(20 - 2x) = -2x² + 20x。这是一个开口向下的二次函数,其最大值出现在顶点处。顶点横坐标为x = -b\/(2a) = -20\/(2×(-2)) = 5。因此,当x = 5时,面积最大。故正确答案为B。","options":[{"id":"A","content":"4"},{"id":"B","content":"5"},{"id":"C","content":"6"},{"id":"D","content":"10"}]}]