高中数学-高考试题(上海交通大学 1931年多边形)

问答题（1931年上海交通大学）

Homologous sides of two similar polygons have the ratio of 5 to 9 , the sum of the areas is 212 sq. ft. Find the area of each figure.

答案解析

暂无答案

讨论

高中数学

If two circles tangent at C and a common exterior tangent touches the circles in A and B, the angle ACB is a right angle.

Find the sum of the geometical series -2,,-1/3 to 6 terms.

Find the sum of the arithmetical series 49,44,39,… to 17 terms.

A motion picture film 120 feet long contains a certain number of individual pictures.If each picture were 0.1 of an inch shorter, the same film would contain 720 more pictures, how long is each picture?

Factor the following:4(a-b)²-12(a-b)(e+9e²)

Factor the following:4a-16b+4a+1.

Find the equation of the ruled surface whose generators are the system of the lines x-2y =4kx,k(x-2y)=4 and discuss the surface.

Find the equation of the sphere which passes through (1,5,-3),(-3,0,0) which center on the 3x+y+z=0,x+2y +1 = 0.

Find the equation of the plane passing through the line (x-x1)/a1 =(y-y1)/b1 =(z-z1)/c1 which is parallel to the (x-x2)/a2 =(y-y2)/b2 =(z-z2)/c2 .

Find the equation of the projection of the linex=z+2,y=2z-4 upon the plane x+y- z = 0.

多边形

以 n 角形之顶点为顶点，而不是 n 角形之边为边之三角形共有若干？

n 多边形诸角之和=______.

Find the sum of n terms of the series whose nth term is 3(4n+4n²)-5n³.

Find the general term and the sum ofn terms of the series -3,-1,11,39,89,167.

Six persons throw for a stake, which is to be won by the one who first throws head with a coin: if they throw in succession, find the chance of the fourth person.

Find the maximum value of (7-x)4 (2+x)6 when x lies between 7 and 2.

Find the maximum value of (5+x)(2+x)/(1-x).

Find all the positive angles less than 380° which satisfy the equation sinx+sin2xsin3x = 0.

A man borrows $5000 at 4 percent compound interest, if the principal and interest are to be repaid by 10 equal instalments, find the amount of each instalment; having given 1g 1.04 =0.0170333 and lg675565=5.829667.

Chords of the circle p=29cosθ which pass through the pole are extended a distance 2b. Find the locus of their extremities.

平面几何

圆内各等弦中点之轨迹为一同心圆周，试证之.

设已知三角形之底边、面积及其顶角，求作此形.

设由圆外一点作一切线一割线，证明此切线为割线及其圆外线分的比例中率.

设一圆之半径为 25 尺，其外切四边形之圆界为 400 尺，试求此四边形之面积。

知一边一邻角及其余二边之和，求作三角形。

设一三角形之底边为 600 尺，其二底角一为 30°，一为 120°，试求其他二边及其高为若干尺。

有 Rt△ABC(C为直角)，以A为圆心，斜边之长为直径作圆，割 AC 于点 D及 AB 于点 O，自 D 引与 AO 正交之弦 DE，证 △ADE 与 △OCB 全等.

三角形二边之和大于其他一边.

作通过二定点，中心在一定直线上之圆.

试证三角形之三中线相会于一点.