The maximum of y = 2Sin x minus SiNx + 1

The maximum of y = 2Sin x minus SiNx + 1

Y = 2Sin square x-sinx + 1
=2 (sinx-1 / 4) square + 7 / 8
Because the value range of SiNx is - 1 to 1, take - 1
So the maximum value of the original formula is 4

(TaNx SiNx) / x ^ 2Sin ^ 2x limit x --- > 0

Because TaNx SiNx = SiNx / cosx - SiNx, so (TaNx SiNx) / x ^ 2Sin ^ 2x = (SiNx / cosx - SiNx) / x ^ 2sinxcosx = (1-cosx) / x ^ 2sinxcosx molecular equivalent infinitesimal is: x ^ 2 / 2, denominator sinxcosx = sin (2x) / 2, denominator is equivalent to x ^ 3, so the result is to find 1 / 2x in X -- > 0

Solve equation. Simplify. Calculate problem. Recommend more

7(2x-1)-3(4x-1)=4(3x+2)-1;
(5y+1)+ (1-y)= (9y+1)+ (1-3y);
[ ( )-4 ]=x+2;
20%+(1-20%)(320-x)=320×40%
2(x-2)+2=x+1
2(x-2)-3(4x-1)=9(1-x)
11x+64-2x=100-9x
15-(8-5x)=7x+(4-3x)
3(x-7)-2[9-4(2-x)]=22
3/2[2/3(1/4x-1)-2]-x=2
1 2x-10.3x=15
2 0.52x-(1-0.52)x=80
3 x/2+3x/2=7
4 3x+7=32-2x
5 3x+5(138-x)=540
6 3x-7(x-1)=3-2(x+3)
7 18x+3x-3=18-2(2x-1)
8 3(20-y)=6y-4(y-11)
9 -(x/4-1)=5
10 3[4(5y-1)-8]=6
10/3 (x/5+3/7)=9x/2
5/3（x+0.5)+2=3x-6
5x+2(2x/3+2)=2/3(x-6)+2
(2x-7)/2-(6x-5)/3=2x+3
(3x+2)/5-(x-6)=x/3
6x-(x/3+2)=2(x/5+5/2)-3
3(x/11-2)-5=2+3x/3
10/3(2x-6)=3/5
x/2-(x/3-2)=3
2/3(x+3)-3=5x/3
5/3(2x-5/3)=2x/5-8/9
25(x/3-x/2+2/5)-2=3/5(x-2/7)+4/9

The original price of a TV set was 1800 yuan. First, the price was increased by 10%. After the price was reduced by 10%, how much is the current price

1782

When (M + n) ^ 2 + 595 is the minimum, simplify m ^ 2 + 2n ^ 2-2 / M / + 2 / N / = (expressed by the formula containing m)
/M / means the absolute value of M

Since the square of a number is greater than or equal to 0, when (M + n) ^ 2 + 595 takes the minimum value, that is, M + n = 0
That is n = - M
So the original formula = m ^ 2 + 2n ^ 2-2 / M + 2 / n
=m^2+2m^2-2/m-2/m
=3m^2-4/m

It is known that a, B and C are the three sides of triangle ABC, a ^ 2 + B ^ 2 + C ^ 2 + 338 = 10A + 24B + 26c

a^2+b^2+c^2+338=10a+24b+26c
a^2-10a+b^2-24b+c^2-26c+338=0
a^2-10a+b^2-24b+c^2-26c+(25+144+169)=0
a^2-10a+25+b^2-24b+144+c^2-26c+169=0
(a-5)^2+(b-12)^2+(c-13)^2=0
(a-5)^2≥0,(b-12)^2≥0,(c-13)^2≥0
a-5=0,b-12=0,c-13=0
a=5,b=12,c=13
5^2+12^2=13^2
So the triangle is a right triangle with ∠ C = 90 °

If a commodity is sold at 80% of the price, it will get a profit of 960 yuan. If it is sold at 80% of the price, it will lose 832 yuan. What is the purchase price of this commodity?

Let the price be x and the purchase price be y
x-y=960
0.8x-y=-832
y=8000

Use the nine numbers from 1 to 9 once each to form three three digit numbers of a, B and C. among them, a can be divided by 7, B by 9, C by 11, and the requirements are as follows
The sum of these three numbers should be as large as possible. What are the three numbers of a, B and C?

Guo Dunyong replied:
The three three digits of a, B and C are: 714963825
714/7=102,963/9=107,825/11=75.
714 + 963 + 825 = 2502 is the maximum

Mathematical judgment
There are two truest fractions smaller than one-half and larger than one-fifth
Give reasons

There are two minimalist true fractions smaller than (1 / 2) and larger than (1 / 5). (×)
After enlarging their denominator or numerator by the same multiple at the same time, we will find that there are many fractions in them, such as:
1/4 3/10 7/20 2/5…………

In the parallelogram ABCD, BC = 6 and BC is 3 ′ 8 of the perimeter of the parallelogram ABCD, then AB =?

Is BC 3 / 8 of parallelogram ABCD?
Then: BC / L (perimeter) = 3 / 8
∴l=8BC/3=8*6/3=16
∵2AB+2BC=16
∴AB=2