Question

На координатной плоскости найдите координаты вершины B квадрата АВСD, ЕСЛИ ИЗВЕСТНЫ ТРИ ЕГО ВЕРШИНЫ А(4,1), С(2,1) И D(2,-1)СКОЛЬКО ЦЕЛЫХ РЕШЕНИЙ ИМЕЕТ НЕРАВЕНСТВО 2<|x| <10?вычислите площадь круга, если его радиус равен 5,8Какое утверждение неверно?сечение шара плоскостью есть кругсечение сферы плоскостью есть окружность пересечение двух шаров есть окружность плоскость, проходящая через центр сферы, есть окружность с наибольшим радиусом

Answer 1

В (4; -1)

|Х| = |-3|,|3|,|-4|,|4|,|-5|,|5|,|-6|,|6|,|-7|,|7|,|-8|,|8|,|-9|,|9|.

S = 3,14 * 33,64 = 105, 6296 cм.2

Answer 2

Finding the coordinates of vertex B of square ABCD on the coordinate plane

To find the coordinates of vertex B of square ABCD, we can use the information given about the other three vertices: A(4,1), C(2,1), and D(2,-1).

Since ABCD is a square, we know that the opposite sides are parallel and equal in length. Therefore, the distance between A and B is equal to the distance between C and D.

To find the coordinates of B, we can use the midpoint formula. The midpoint of AC is the same as the midpoint of BD.

The midpoint formula is given by: Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Using the coordinates of A(4,1) and C(2,1), we can find the midpoint of AC: Midpoint of AC = ((4 + 2)/2, (1 + 1)/2) = (3, 1)

Since the midpoint of AC is the same as the midpoint of BD, the coordinates of B are (3, 1).

Number of integer solutions for the inequality 2 < |x| < 10

To find the number of integer solutions for the inequality 2 < |x| < 10, we need to consider the possible values of x that satisfy the inequality.

The inequality can be broken down into two separate inequalities: 1. 2 < x < 10 2. -10 < x < -2

For the first inequality, the integer solutions are 3, 4, 5, 6, 7, 8, and 9. These are 7 integer solutions.

For the second inequality, the integer solutions are -3, -4, -5, -6, -7, -8, and -9. These are 7 integer solutions.

Therefore, the total number of integer solutions for the inequality 2 < |x| < 10 is 7 + 7 = 14.

Calculating the area of a circle with a radius of 5.8

The formula to calculate the area of a circle is given by: Area = π * r^2

Given that the radius of the circle is 5.8, we can substitute this value into the formula: Area = π * (5.8)^2

Using the value of π as approximately 3.14159, we can calculate the area: Area ≈ 3.14159 * (5.8)^2 ≈ 105.6716

Therefore, the area of the circle with a radius of 5.8 is approximately 105.6716 square units.

Identifying the incorrect statement

The incorrect statement among the following options is: The intersection of two spheres is a circle.

The intersection of two spheres is not always a circle. It can be a circle, a point, or even an empty set, depending on the relative positions and sizes of the spheres.

The correct statements are: - The intersection of a sphere and a plane is a circle. - The intersection of a sphere and a plane can be an ellipse or a point, depending on the relative positions and orientations of the sphere and the plane. - The intersection of two spheres can be a circle, a point, or an empty set, depending on the relative positions and sizes of the spheres. - A plane passing through the center of a sphere forms the largest possible circle on the sphere.

Therefore, the incorrect statement is that the intersection of two spheres is always a circle.