45 = () x () x () prime in brackets

45 = () x () x () prime in brackets

45=（3）X（3）X（5）

36 = () + () = () + () = ()+（
It's four () + ()=

36=5+31=7+29=13+23=17+19

Fill in the brackets with the appropriate prime number 84 = () + () = () + ()

84=(41)+(43)=(11)+(73)

48 = () + () = () + () = () + () = () + () = () () + ()

5+43
7+41
11+37
17+31
19+29

Let Sn be the sum of the first n terms of the arithmetic sequence {an}, if S5 = A8 + 5, S6 = A7 + a9-5, then the tolerance D is equal to______ ．

∵ SN is the sum of the first n terms of the arithmetic sequence {an}, S5 = A8 + 5, S6 = A7 + a9-5, ∵ 5A1 + 5 × 4D2 = a1 + 7d + 56a1 + 6 × 5D2 = a1 + 6D + A1 + 8D − 5, the solution is A1 = - 52, d = 5

Z = f (x / y, XY), find DZ

Let u = x / y, v = XY, then
(where D in the proportional form of DS / DT is the sign of partial derivative; D in the single form such as DZ is the sign of derivative, i.e. d)
dz/dx=(dz/du)(du/dx)+(dzdv)(dv/dx)
=(1/y)(dz/du)+y(dz/dv)
dz/dy=(dz/du)(du/dy)+(dz/dv)(dv/dy)
=(-x/y²)(dz/du)+x(dz/dv)
therefore
dz=(dz/dx)dx+(dz/dy)dy
=[(1/y)(dz/du)+y(dz/dv)]dx+(-x/y²)(dz/du)+x(dz/dv)dy

A car needs 3000 grams of gasoline to drive 6 kilometers. According to this calculation, how many kilometers can one kilogram of fuel run, and how many kilograms of fuel can one kilometer run

1kg = 6 △ 3 / 5 = 10km
1km = 3 / 5 △ 6 = 1 / 10kg

The concept of adjacent complementary angle: two angles have a common edge, the other edge is mutual (what), such two angles are adjacent complementary angles

Two straight lines in opposite directions

Is u = x / (x ^ 2 + y ^ 2) a harmonic function? To find its corresponding analytic function, we need to solve the problem concretely

If u (x, y) satisfies Laplace equation, u x = (y ^ 2-x ^ 2) / (x ^ 2 + y ^ 2) ^ 2U x = (2x ^ 3-6xy ^ 2) / (x ^ 2 + y ^ 2) ^ 3U y = - 2XY / (x ^ 2 + y ^ 2) ^ 2uyy = (- 2x ^ 3 + 6xy ^ 2) / (x ^ 2 + y ^ 2) ^ 3U y = - 2XY / (x ^ 2 + y ^ 2) ^ 2U y = (- 2x ^ 3 + 6xy ^ 2) / (x ^ 2 + y ^ 2) ^ 3, u x x + uyy = 0 satisfies Laplace equation

When the temperature of an object is constant, the state of the object may change, and the molecule will change_____ Possible changes, such as____ During endothermic melting, the internal energy increases while the temperature remains unchanged

In the process of crystal endothermic melting, the internal energy increases while the temperature remains unchanged. The reason is that the internal energy increases through heat transfer, and heat transfer can absorb heat. However, when melting, the absorbed heat is not used to raise the temperature, but to reduce the binding between molecules, that is, to increase the potential energy of macromolecules, When the volume or state of the object (or the number of molecules contained in the object) changes, the distance between molecules changes, and the force between molecules changes, resulting in the change of molecular potential energy. Therefore, the internal energy of the object also changes
Potential energy, crystal