The application of quadratic equation of one variable in the second grade mathematics of junior high school The same 8m long aluminum alloy window frame material is made into a rectangular window frame. What is the maximum lighting area of the window frame? What is the side length of the window frame when the daylighting area of the window frame is the largest

The application of quadratic equation of one variable in the second grade mathematics of junior high school The same 8m long aluminum alloy window frame material is made into a rectangular window frame. What is the maximum lighting area of the window frame? What is the side length of the window frame when the daylighting area of the window frame is the largest

The maximum daylighting area is actually the maximum value of the area. If one side length is XM, the other side length is (4-x) M,
The area is s = x (4-x) = - x ^ 2 + 4x = - (X-2) ^ 2 + 4
So when the length of a side is 2m, that is, when the figure is square, it is the largest area, and the largest area is 4 square meters

There are 120 guest rooms in a hotel. The daily rent of each guest room is 50 yuan, which is full every day. After the hotel is decorated, the rent should be raised. According to the investigation, if the daily rent of each guest room is increased by 5 yuan, the daily rent of each guest room will be reduced by 6 rooms (regardless of other factors). If the daily rent of each guest room is increased by 5 yuan, the total income of the daily rent of the guest room can reach 6750 yuan

If the rent of each guest room is increased by 5x yuan, the number of guest rooms will be reduced by 5x ／ 5 × 6, that is, 6x rooms. According to the equation (120-6x) (50 + 5x) = 6750, we can get x2-10x + 25 = 0, х X1 = x2 = 5. The rent will be increased by 5x = 5 × 5 = 25 yuan. Answer: the rent of each room will be increased by 25 yuan

Square difference formula of mathematics in grade two
(1) The solution of equation (x + 6) (x - 6) - x (x - 9) = 0 is______ .
(2) 1998 ^ 2 - 1997 x1999
(3) 3x (2 ^ 2 + 1) (2 ^ 4 + 1) ·· (2 ^ 32 + 1) + 1

1、4
2、1998^2 -（1998-1）（1998+1）=1998^2 -1998^2 +1=1
3、 3=2^2-1
So the original formula = (2 ^ 2-1) (2 ^ 2 + 1) (2 ^ 4 + 1) (2^32+1)+1
=(2^4-1)(2^4+1)…… (2^32+1)+1
Using the square difference repeatedly
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64

PA, Pb and PC are three rays starting from point P. the angle between each two rays is 60 degrees. Then the cosine of the angle between PC and PAB is ()
A. 12B. 22C. 33D. 63

Take any point D in PC and make do ⊥ plane APB, then ⊥ DPO is the angle formed by the line PC and plane PAB. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; through point O, make OE ⊥ PA, of ⊥ Pb, because do ⊥ plane APB, then de ⊥ PA, DF ⊥ Pb. △ dep ≌ DFP, ⊥ EP =

Solve the equation. 0.1 x + 0.3 x + 0.8 0.2 + 0.3 x = 8
0.1 x + 0.3 x + 0.2 of 0.8 + 0.3 x = 8
0.1 x + 0.3 X are molecules

5 (0.1X + 0.3x) + 0.8 (0.2 + 0.3x) = 8
4x/5+5x/8=8
32x+25x=320
57x=320
x=320/57

In the parallelogram ABCD, the diagonals AC and BD intersect at point O, Mn is a straight line passing through point O, BC intersects at m, ad intersects at n, BM = 2, an = 2.8, and BC and AD are calculated

Is there a problem with the title? There is no answer to such a condition, and BC = ad. why do you ask for BC and ad?

Solve equation 5 (X-7) = 26.54 (x + 8.2) = 40.8 (x-0.52) △ 4 = 1.121.5
solve equations
5（x-7）＝26.5
4（x＋8.2）＝40.8
（x-0.52）÷4＝1.12
1.5（x-8）＝60
4x＋2x＝5.4
x-0.52x＝12
whole

①x-7=5.3
x=12.3
②x+8.2=10.2
x=2
③x-0.52=4.48
x=5
④x-8=40
x=48
⑤6x=5.4
x=0.9
⑥0.48x=12
x=25
Hope to adopt

Given the point a (- 3.5), B (2,15), there is a point P on the line L; 3x-4y + 4 = 0, which makes PA + Pb minimum

P (8 / 3,3) (| PA | + | Pb |) min = 5 √ 13. Because the distance between two points is the shortest, we only need to make a '(x0, Y0) symmetric point of point a (or point B) with respect to line L, and then connect the intersection point of a'B and line L to obtain P. first, we need to find a' (x0, Y0) 3 (x0-3) / 2 - 4 (Y0 + 5) / 2 + 4 = 0 (1) formula (y0-5) / (x0 + 3) = -

Simple calculation: 5 * 6 and 4 / 5 + 6 * 7 and 5 / 6 + 7 * 8 and 6 / 7 + 8 * 9 and 7 / 8! Hurry!

34+47+62+79=222
5, 6, 7, 8 can be about five, six, seven, eight
I don't know if it's what you want

For any real number x, it is proved that the value of the algebraic formula - 2x ^ 2 + 8x + 2 is greater than 10

Certification:
-2x²+8x+2
=-2(x²-4x+4)+10
=-2(x-2)²+10
∵ for any real number x, there is always - 2 (X-2) &# 178; ≤ 0, and the equal sign is obtained only when x = 2,
∴-2(x-2)²+10≦10
That is to say, the value of - 2x & # 178; + 8x + 2 is no more than 10