Question

求 高人 解答英文的数学题！！急急急急急急急急急！！！！ 正确的话我追加50分！！！！

1. In the diagram below, point M is located on AB. Sketch the locus of points that are 1 unti from AB and the locus of points 2 units from point M. Label with X all points that satisfy both conditions.

2.Determine whether the two lines reoresented by equations y=2x+3 and 2y+x=6 are parallel, perpendicular , or nither. Justify your response.

3.The coordinates of the vertices of △ RST are R(-2,3),s(4,4)and(2,-2).Triangle R'S'T' is the image of △RST after a rotation of 90° about the origin. State the coordinates of the vertices of △R'S'T' .

4.A paint can is in the shape of a right circular cylinder.The volume of the paint can is 600π（派，就是 3.14...）cubic inches and its altitude is 12 inches.
⊙ Find the radius , in inches , of the base of the paint can . Express the answer in simplest radical form.

⊙ Find , to the nearest tenth of a square inch , the lateral area of the paint can .

就4题 求答案啊！！！要完整。

Answer 1

1. Without the diagram, it's impossible to solve it.

2. y = 2x + 3, its slope k1 = 2 (coefficient of x)

2y + x = 6 can be changed to y = -x/2 + 3, its slope is k2= -1/2

k1*k2 = -1, so they are perpendicular.

3. It's not said if the rotation is counterclockwise or clockwise, so I assume it's the former. 

The rotation of the triangle by 90° counterclockwise is equivalent of the coordination system rotating clockwise by 90°, that's -y becomes +x, and +x becomes +y directions, so it's easy to see R'(-3, -2), S'(-4, 4), T'(2, 2).  See diagram.

4. 

(1) V = πr²h, r² = V/(πh) = 600π/(12π) = 50

r = √50 = 5√2 in

(2) V = S*h 

S = V/h = 600π/12 = 50π = 157.0796 ≈ 157.1 in²

追问

1 . the diagram like this.

---A----------------------M--------------B----〉

追答

Use a coordination system like this: AB on the x-axis and M as the origin. Therefore, M(0. 0), and the equation of line AB is y = 0.
(a) the locus of points that are 1 unti from AB would be 2 lines parallel to AB: one above (y = 1) and one below (y = -1).

(b) the locus of points 2 units from point M would be a circle with M as its center and 2 as its radius: x² + y² = 2²

The 2 loci have 4 common points. See figure.

Answer 2

靠

Answer 3

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