A * b = 3a-2b (1) 6 * 5=___________ (2) Given a * 9 = 6, find a

A * b = 3a-2b (1) 6 * 5=___________ (2) Given a * 9 = 6, find a

A * b = 3a-2b
(1)6*5=3×6-2×5
=18-10
=8
(2) Given a * 9 = 6, find a
3×a-2×9=6
3a-18=6
3a=24
a=8

The module of Z = 1, Z is not equal to positive and negative I, it is proved that Z / (1 + Z ^ 2) belongs to R

|If Z | = 1 and Z ≠ ± I, then z = cos θ + isin θ
z/(1+z²)
=(cosθ+isinθ)/[1+(cosθ+isinθ)²]
=(cosθ+isinθ)/(1+cos²θ+2isinθcosθ-sin²θ)
=(cosθ+isinθ)/(2cos²θ+2isinθcosθ)
=(cosθ+isinθ)/2(cosθ+isinθ)cosθ
=1/2cosθ
So Z / (1 + Z & sup2;) is a real number
When (COS θ + isin θ) & sup2;, we don't need to use demover's theorem Cos2 θ + isin 2 θ to extract the common factor directly

Among the fruits sold by fruit shops, apples are 25 kg more than pears, and apples are 1 / 4 more than bananas. How many kg are bananas and apples sold?

25 / (1 / 4) = 100 (kg). This is pear. Apple is 100 + 25 = 125 (kg). Because 25 accounts for 1 / 4, the total amount is 25 / (1 / 4)

The square of inequality (X-2) multiplied by (x-3)

（x-2）²（x-3）＜0
Because (X-2) & sup2; ≥ 0, x-3 < 0 and (X-2) & sup2; ≠ 0
That is, X ≠ 2
The solution is x < 3, X ≠ 2

If the direction vector of line L is a = (1,1,1), then the sine value of the angle between line L and plane xoy is

Normal vector n = (0,0,1) of plane xoy
Sine value of the angle between the line L and the plane xoy = icosi
=(vector a · vector n) / (I vector aii vector I)
=[(1,1,1) · (0,0,1)] / [(radical 3) * 1]
=1 / (radical 3)
=(radical 3) / 3

There are 48 people in the class going for an outing in the wild. A total of 7 cars are rented, and each car is full. The jeep is limited to 4 people, and the van is limited to 8 people
How many jeeps and vans do you rent?

Rent 2 jeeps: 2 * 4 = 8, 5 minibuses: 5 * 8 = 40 / 40 + 8 = 48, so rent 2 jeeps and 8 minibuses respectively

If the eigenvalues of the third order invertible matrix A are 2,3,4, then the eigenvalues of a ^ - 1 are

The eigenvalues of a ^ - 1 are 1 / 2, 1 / 3 and 1 / 4, respectively

The problem of dot product of two vectors
If vector a is perpendicular to vector B, then vector B is equivalent to zero
So why is vector a parallel to vector B, not equivalent to the product of the module of vector a and the module of vector B? I think the included angle is zero, cos0 = 0
Please give me some advice
thank you

First, cos0 = 1
Secondly, vector a is parallel to vector B, which means that the cross product of vector a and vector B is 0?

Two teachers of a school plan to take some students to travel and contact two travel companies with the same price
After negotiation, the preferential condition of company a is that one teacher charges in full, and the rest is 7.50% off. The preferential condition of company B is 20% off for all teachers and students
(1) When the number of students is equal to how many, a and B charge the same price?

Your question is different from what I said in my private letter. I've been hungry for two hours, and I've finally worked it out for you
Suppose there are X students and the price of each company is y yuan
((x+2)*0.8*y-((x+1)*0.75*y+y))/(x+2)*0.8*y=1/32
If y is eliminated, the following results are obtained:
((x+2)*0.8-((x+1)*0.75+1))/(x+2)*0.8=1/32
The results are as follows
32*(0.8x+1.6-0.75x-1.75)=0.8x+1.6
After finishing the above formula, we can get the following results
1.6x-4.8=0.8x+1.6
The solution is as follows
0.8x=6.4
x=8
Another question:
(x+2)*0.8*y=((x+1)*0.75*y+y)
Namely:
0.8x+1.6=0.75x+1.75
The solution is: x = 3

Lim x tends to 0 (√ (1 + x) - √ (1 + x ^ 2)) / (√ (1 + x) - 1)

Rational denominator
Denominator = x
Molecule = 1 + X + √ (1 + x) - √ (1 + x ^ 2) (1 + x) - √ (1 + x ^ 2)
When X - > 0, molecule = X
Numerator / denominator = 1