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In a 15 decimeter long and 12 decimeter wide rectangular water tank, there is 10 decimeter deep water. If you sink into a 60 cm square iron block in the water What is the depth of water in the tank
60 cm = 6 decimeters
Water depth in tank
=（6×6×6）÷（15×12）
=216÷180
=1.2 (decimeter)
In a rectangular water tank 15 decimeters long and 12 decimeters wide, there is water 10 decimeters deep. If one edge is sunk in the water, the length of one edge is 10 decimeters
In a cuboid water tank with a length of 15 decimeters and a width of 12 decimeters, there is water 10 decimeters deep. If a cube iron with a length of 30 cm is submerged in the water, how many decimeters is the water now high?
30 cm = 3 decimeters
Height = 3 × 3 × 3 △ 15 △ 12 + 10 = 10.15 decimeters
Use a 50 cm long and 40 cm wide rectangular iron sheet to make a 10 cm deep uncovered cuboid (the thickness of the iron sheet at the welding joint is not included). What is the volume of this cuboid?
(1) As shown in the figure, volume: 10 × (50-10 × 2) × (40-10 × 2) = 10 × 30 × 20 = 6000 (cm3) answer: the volume of this cuboid is 6000 cubic centimeter. (2) volume: 10 × (50-10 × 2) × (40-10 × 2) = 10 × 30 × 20 = 6000 (cm3) answer: the volume of this cuboid is 6000 cubic centimeter
The quadratic function y = x ^ 2 - (M + 1) x + m ^ 2-m-2 is known
(1) When the function crosses the origin, M =?
(2) When the vertex of the function is on the Y axis, M =?
1. Substituting x = 0, y = 0 into the analytic expression of the function, m ^ 2-m-2 = 0, M = 2, or M = - 1
2. The vertex of the quadratic function is on the y-axis, which means that the symmetry axis is y-axis, so the coefficient of the first term is 0, that is - (M + 1) = 0, and the solution is m = - 1
Given the function f (x) = Log1 / 3 (X & # 178; - 2x), find its monotone interval
First find the definition field: x ^ 2-2x > 0, get: x > 2 or X
Xiaoying weighs 4kg less than Xiaoli, Xiaogang weighs 8kg more than Xiaoying, and Xiaoqiang weighs 3kg more than Xiaoli. Who is the heaviest and who is the lightest? (how to list?)
Given that the range of function f (x) = ln [MX ^ 2 + (m-2) x + (m-1)] is r, then the range of real number m is r
mx^2+(m-2)x+(m-1)>
So m > 0
(m-2) ^ 2-4m (m-1) under root (4 / 3)
It is proved that the function f (x) = 1 / xsin1 / X is unbounded in the interval (0,1), but it is not infinite when x approaches 0 + 0
1) Let xn = 2 / (4N + 1) π, then f (xn) = (4N + 1) π / 2 * sin (4N + 1) π / 2 = (4N + 1) π / 2. When xn tends to 0, f tends to infinity, so it is unbounded
Xiao Ming starts from home at 7:50 every morning and goes to school 1000 meters away from home. His daily walking speed is 80 meters per minute. One day, after Xiao Ming starts from home for 5 minutes, his father chases Xiao Ming at the speed of 180 meters per minute and catches him on the way. (1) how long did it take his father to catch up with Xiao Ming? (2) How far is it from school to catch up with Xiao Ming?
(1) Let's say that when Dad catches up with Xiao Ming, he uses X points. From the meaning of the question, he gets 180X = 80x + 80 × 5, and from item shifting, he gets 100x = 400. From coefficient to 1, he gets x = 4. Answer: it takes dad 4 minutes to catch up with Xiao Ming. (2) 180 × 4 = 720 (meters), х 1000-720 = 280 (meters). Answer: when he catches up with Xiao Ming, he is 280 meters away from school
Let a be a matrix of order n, a is not a 0 matrix, but a ^ 3 = 0
The eigenvalues of a are n zeros, right?
Prove: otherwise, suppose a is similar to diagonal matrix D, that is, there exists invertible matrix t such that
A = t inverse * D * t
So a ^ 3 = t inverse * d ^ 3 * t = 0
D ^ 3 = 0
If D is a diagonal matrix, it is easy to know that d = 0
So a = 0
contradiction
Are you satisfied with the above answers?
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