How much is 1 + to 100

How much is 1 + to 100

=(1+100)+(2+99)+(3+98)+…… +(50+51)
=101+101+101+…… +101
=101×50
=5050

How to calculate 0.4 * log2 (0.4)?

=0.4*ln0.4/ln2=0.4*(-0.91629073187415506518352721176801)/0.69314718055994530941723212145818=-0.52877123795494493914812777179576

As shown in the figure, △ ABC is an equilateral triangle, points D and E are on AB and AC respectively, and F is the intersection of be and CD. It is known that ∠ BFC = 120 °. Verification: ad = CE

It is proved that: ∵ - BFC = 120 °, ∵ - ECF = ∵ BFC - ∵ CEB = 120 ° - ∵ ABC is equilateral triangle, ∵ - EBC = 180 ° - 60 ° - ∵ CEB = 120 ° - CEB, ∵ - ECF = ∵ EBC, that is, ? - DCA = ∵ EBC, and ∵ ABC is equilateral triangle, ∵ - CAD = ? BCE = 60 °, AC = CB ≌ △ ACD ≌

(1) In the complex set, any quadratic equation with real coefficients has a solution
(1) In the complex set, any quadratic equation with real coefficients has solutions. (2) in the complex set, any quadratic equation with real coefficients has two conjugate complex roots. Are these two propositions correct?

(1) In the complex set, any quadratic equation with real coefficients has a solution
(2) In the complex set, any quadratic equation with real coefficients has two conjugate complex roots. Incorrect, it can be two unequal real roots, but they are not conjugate

F (x), the domain of definition is r, and X is not always 0. F (m) f (n) = MF (n / 2) + NF (M / 2) holds. Find all functions f (x) satisfying the conditions

F (m) f (n) / (MN) = f (n / 2) / N + NF (M / 2) / M is obtained by Mn (m, n are not zero) on both sides of the original formula;
Let g (x) = f (x) / X (x is not zero), then 2g (m) g (n) = g (M / 2) + G (n / 2),
Let m = n, G (M / 2) = [g (m)] ^ 2 > = 0 for any m not zero,
Then we substitute g (M / 2) = [g (m)] ^ 2, G (n / 2) = [g (n)] ^ 2 into 2g (m) g (n) = g (M / 2) + G (n / 2), and get: [g (m) - G (n)] ^ 2 = 0, that is, G (m) = g (n) holds for any m, n is not zero,
That is to say, the function g (x) is a constant function,
Note that G (x) cannot be constant zero (otherwise f (x) will be constant zero) and is nonnegative, that is, G (x) > 0,
If there is x such that G (x) > 1, then G (x / 2) = [g (x)] ^ 2 > G (x), that is, G (x) is not a constant function
Contradiction!
And if there is x such that 0

The circumference of an isosceles trapezoid is 50cm, the waist and height are 10cm and 8cm respectively. What is the area of this trapezoid?

(50-10 × 2) × 8 / 2 = 30 × 8 / 2 = 240 / 2 = 120 (square centimeter) a: the area of this trapezoid is 120 square centimeter

In RL Series AC circuit, if r = 6ohm, inductive reactance XL = 8ohm, the impedance of this circuit is () ohm. Options: A, 14b, 2C, 10ohm

In RL Series AC circuit, if r = 6 Ω and inductive reactance XL = 8 Ω, the impedance of the circuit is (10) Ω
Options: A, 14, 2, C, 10
∵ impedance z = √ R ^ 2 + XL ^ 2 = √ 6 ^ 2 + 8 ^ 2 = √ 100 = 10 Ω
Choose C and 10

Given the set a = {x is greater than negative two, less than or equal to 5}, B = {m + 1 is less than or equal to x, less than or equal to 2m-1}, and a is contained in B, find

A=(-2,5],B=[m+1,2m-1]
2m-1 > = 5 and M + 1 = 3 and M

In the triangle ABC, AC is equal to BC, angle c is equal to 90 degrees, ad is the angle bisector of triangle ABC, De is perpendicular to AB, the perpendicular foot is e, and CD is 4cm

∵ ad is the angular bisector of triangle ABC
DE⊥AB,DC⊥AC
∴DC=DE=4
∵AC=BC
■ ∠ B = 45 degrees
According to trigonometric function, DB = 4 √ 2
AC=CB=4+4√2

If the point corresponding to the complex number 1 + AI in the complex plane is located on the imaginary axis, then a

(1+ai/i
=(1+ai)i/i²
=(i-a)/(-1)
=a-i
On the imaginary axis
So a = 0