15 of a number is 60 more than 16. Find the number

15 of a number is 60 more than 16. Find the number

60 △ 15-16 = 60 △ 130, = 1800. A: this number is 1800

X + 3 / 3 x = 36

x+x/3=36
3x+x=36×3
4x=36×3
x=27

The formula for calculating the circumference of a circle is______ &Nbsp; or______ ．

The formula C = π D or C = 2 π R can be used to calculate the circumference of a circle

It is proved that when x > 1, the x power of E is greater than Xe

Certification:
Let f (x) = e ^ x-xe
be
f'(x)=e^x-e>0 (x>1)
So f (x) Yan gezeng
Therefore, f (x) ≥ f (0) = 1 > 0
thus
e^x>ex

Please give the calculation process
The first line is x 7 10
The second line is 1 a B
The third line is C D E
If the sum of the three numbers in each horizontal line, each vertical line and diagonal line is equal, what is the value of X?

The value of X is 22

It is known that E and F are the points on edge Aa1 and edge CC1 of cube abcd-a1b1c1d, and AE = C1F. It is proved that the quadrilateral ebfd1 is a parallelogram

Take DM = AE = C1F on dd1, connect cm, EM, ∵ CF = d1m = cc1-c1f, CF ∥ d1m, ∥ quadrilateral cmd1f is parallelogram, ∥ cm ∥ FD1, CM = FD1. Similarly, it can be proved that quadrilateral ADME is parallelogram, ∥ EM ∥ BC, EM = BC, ∥ BCME is parallelogram, ∥ be ∥ cm, CM = be, ∥ be ∥ FD1, be = FD1, ∥ quadrilateral ebfd1 is parallelogram

a. B is a real number. If a ^ 2 + B ^ 2 = 5, then the maximum value of a + B is?

Because a ^ 2 + B ^ 2 > = 2Ab, so (a + b) ^ 2 = a ^ 2 + B ^ 2 + 2Ab

Y = Xe ^ y for dy / DX

Comprehensive application of plane vector
x. Y is any real number, prove with vector method: X * x + y * y > = 2XY
Please provide the solution process, thank you

It is proved that: let x = AI + BJ, y = CI + DJ. A, B, C, D ∈ R.I, J be the unit vectors on X and Y axes respectively, and
I ^ 2 = I &; I = 1 * 1 * cos0 ° = 1; J ^ 2 = J &; J = 1 * 1 * cos0 ° = 1, I &; J = 1 * 1 * cos90 ° = 0
x^2+y^2-2xy=(ai+bj)^2+(ci+dj)^2-2(ai+bj)(ci+dj)
=(ai)^2+(bj)^2+2ab(i•j)+(ci)^2+(dj)^2+2cd(i•j)-2[aci^2+bdj^2
+(ac+bd)(i•j)
=a^2+b^2+c^2+d^2-2(ac+bd)=(a-c)^2+(b-d)^2≥0.
That is, x ^ 2 + y ^ 2 ≥ 2XY

Find the range of function FX = LG (4 ^ X-2 ^ x + 1 + 11)

Let t = 2 ^ x > 0
Then the true number G (T) = T ^ 2-2t + 11 = (t-1) ^ 2 + 10
When t = 1, G (1) = 10 is the minimum
So g (T) > = 10
So f (x) > = LG10 = 1
That is, the range of F (x) is f (x) > = 1