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Who knows the formula for calculating the center of an object by calculus
I know the formula for the center of gravity
Suppose the axis of the center of gravity is x, and f (x, y, z) is the density of the object at any point
∫∫∫xf(x,y,z)dv
x=-----------------
∫∫∫f(x,y,z)dv
The integral region is the entire object
And then the coordinates of the center of gravity are (x, 0,0)
The problem of vector product
Let the two sides of the parallelogram ABCD be ab = a-2b, ad = a-3b, ι a ι 5, ι B ι 3, and the angle between a and B be π / 6. The area of the parallelogram (AB, ad, a, B are vectors)
AB * ad = (a-2b) * (a-3b) = A & sup2; - 5A * B + 6B & sup2; = 25-5 * 5 * 3 * cos π / 6 + 6 * 9 = 79 - (75 radical 3) / 2|ab| & sup2; = A & sup2; - 4AB + 4B & sup2; = 25-30 radical 3 + 4 * 9 = 61-30 radical 3|ad| & sup2; = A & sup2; - 6ab + 9b & sup2; = 25-45 radical 3 + 9 * 9 = 106-45 radical 3 parallel four
Can the dot product of two vectors be negative?
Yes!
As long as the angle between two vectors is obtuse
How to calculate 1.25 times 0.88 in a simple way
1.25x0.88
=1.25x8x0.11
=10x0.11
=1.1
Simplify (2 / A-1 minus 1) by a2-6a + 9 / A-1
The original formula = (3-A) / (A-1) × (A-1) / (A-3) &;
=1/（3-a)
What is the sum of two negative numbers
Or negative number. Negative sign unchanged, the number can be added!
To solve the ternary linear equation 3x-y + 2Z = 3 2x + y-3z = 11 x + y + Z = 12, I suddenly forgot the method of solving the ternary linear equations!
3x-y + 2Z = 3 (1) 2x + y-3z = 11 (2) x + y + Z = 12 (3) (1) + (2) get 5x-z = 14 (4) (1) + (3) get 4x + 3Z = 15 (5) (4) × 3 + (5) get 9x = 57 x = 3 substitute x = 3 into (4) get 15-z = 14 z = 1 substitute x = 3Z = 1 into (3) get y = 8, that is: x = 3Y = 8Z = 1
3 / 8 * [(1 and 1 / 2 + 2 and 2 / 3) divided by 5 / 6-2 and 1 / 3] simple algorithm
Our teacher said to use the multiplication allocation rate, but I think it's relatively simple to calculate it directly. In the end, there are only 3 / 8 titles left, and 8 / 3 scores will be 1. I don't know what to do
How to express the difference between the sum of squares of a and B minus half of the sum of squares of a and B
3(x^2+y^2)-(x+y^2)/2
One out of 50 minus one multiplied by one out of 49 minus one multiplied by one out of 48 minus one One out of four minus one multiplied by one out of three minus one multiplied by one out of two minus one
（1/50 -1)(1/49 -1)(1/48 -1).(1/3 -1)(1/2 -1)
(-1)^48(1*2*3*4*5*6*7.*48*49)
=---------------------------------
2*3*4*.*49*50
=1/50
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