Xiao Wang goes to the stadium to do morning exercises every day, and he sees an uncle of the track and field team doing exercises. They run along the 400 meter track. Each time Xiao Wang runs 2 laps, uncle runs 3 laps. One day, they run in the same direction. Xiao Wang looks at the clock and finds that they meet for the first time after 32 seconds. Ask for their speed. The next day, Xiao Wang plans to run in the same direction with his uncle Run to see how many times my uncle meets him again. Can you predict for Xiao Wang first?

Xiao Wang goes to the stadium to do morning exercises every day, and he sees an uncle of the track and field team doing exercises. They run along the 400 meter track. Each time Xiao Wang runs 2 laps, uncle runs 3 laps. One day, they run in the same direction. Xiao Wang looks at the clock and finds that they meet for the first time after 32 seconds. Ask for their speed. The next day, Xiao Wang plans to run in the same direction with his uncle Run to see how many times my uncle meets him again. Can you predict for Xiao Wang first?

Suppose uncle's speed is 3vm / s, then Xiao Wang's speed is 2vm / s. according to the meaning of the title, we get (3V + 2V) × 32 = 400, the solution is v = 2.5, 〈 3V = 3 × 2.5 = 7.5m/s, 2V = 2 × 2.5 = 5m / s, that is, uncle's speed is 7.5m/s, Xiao Wang's speed is 5m / s. when running in the same direction the next day, let XS meet for the first time

An enterprise produces a product with a cost of 400 yuan per piece and a sales price of 510 yuan. In this quarter, it has sold M pieces. In order to further expand the market, the enterprise decides to reduce the cost while reducing the sales price. After market research, it is predicted that the sales price of this product will decrease by 4% and the sales will increase by 10% in the next quarter, so as to keep the sales profit (sales profit = sales price cost price) unchanged How much should the cost price of each product be reduced?

Suppose that the cost price of each piece of the product should be reduced by X Yuan, then according to the meaning of the question, we get [510 (1-4%) - (400-x)] × (1 + 10%) M = (510-400) m, and solve this equation, we get x = 10.4. Answer: the cost price of each piece of the product should be reduced by 10.4 yuan

If we know the points m (4,3) and n (1, - 2), P is on the Y axis, and PM + PN is the shortest, we can find the coordinates of P
But I want to know how it came about and what concepts were used,

M is Q about the symmetric point of Y axis
Then it is PQ + PN
The sum of the two sides of a triangle is greater than the third side
When three points of triangle are in a straight line and P is between Q and n
PN+PQ=NQ
This is the minimum
So p is the intersection of the line NQ and the y-axis

Given that a ^ 2-3a-1 = 0, the value of a ^ 3-10a is

a^2-3a-1=0
a^2-3a=1
Original formula = a ^ 3-3a ^ 2 + 3A ^ 2-9a-a
=a(a^2-3a)+3(a^2-3a)-a
=a+3-a
=3

In the right angle trapezoid ABCD, ad ⊥ CD, BC ⊥ CD, and AC + CB = AB, take the oblique waist AB as the diameter to make the circle O, prove that CD is the tangent of the circle o

It is proved that OE ⊥ CD over O is equal to E
∵AD⊥CD,BC⊥CD,OE⊥CD
∴AD∥OE∥BC
∵AO＝BO
The OE is the median line of ladder shaped ABCD
∴OE＝（AD+BC）/2
∵AD+BC＝AB
∴AO＝AB/2＝（AD+BC）/2
∴OE＝AO
The tangent of circle O is CD

If p1p2 = 2 (Q1 + Q2), it is proved that at least one of the equations x2 + P1x + Q1 = 0 and X2 + P2X + Q2 = 0 has real roots

Suppose that the original proposition does not hold, that is, X2 + P1x + Q1 = 0 and X2 + P2X + Q2 = 0 ∧ △ 1 = p12-4q1 < 0, △ 2 = p22-4q2 < 0, two formulas are added to get: p12 + p22-4q1-4q2 < 0, that is, p12 + P22 < 4 (Q1 + Q2) and ∧ p1p2 = 2 (Q1 + Q2), ∧ p12 + P22 < 2p1p1p2, that is: (P1-P2) 2 < 0, this formula obviously does not hold

As shown in the figure, fold rectangle ABCD along EF so that point d coincides with point B. given AB = 3 and ad = 9, find the length of be

Let be = x, then de = be = x, AE = ad-de = 9-x, in RT △ Abe, AB2 + AE2 = be2, then 32 + (9-x) 2 = X2, the solution is: x = 5. So the length of be is 5

Let f (x) = x2 + AlN (x + 1) + 1 / 2ln2 (1) find the monotone interval (2) if the function has two extreme points x1, X2, (X11 / 4)

The definition field of function f (x) = x2 + AlN (x + 1) + 1 / 2ln2 is (- 1, + ∞) (1) f '(x) = 2x + [A / (x + 1)] = (2x ^ 2 + 2x + a) / (x + 1) = [2 (x + 1 / 2) ^ 2 + A-1 / 2] / (x + 1) 1, when a ≥ 1 / 2, 2 (x + 1 / 2) ^ 2 + A-1 / 2 > 0, then f' (x) > 0, f (x) increases monotonically on (- 1, + ∞); 2, when AX2, when x2 = [- 1

On the plane rectangular coordinate system of mathematical problems' please help
In plane rectangular coordinate system
Point a (- 1,0) point B (1,2) point P makes the triangle ABP an isosceles triangle on the coordinate axis
How many such points are there?
(note that point P is on the axis)
A: 6 B: 7 C: 8 D: 9

Option C
Two on the positive half axis and two on the negative half axis of y-axis
There are three on the positive half axis and one on the negative half axis of X axis
Special attention: the midpoint C (0,1) of AB is on the positive half axis of Y axis, so it can't form an isosceles triangle of AC = BC

If the expansion of (x to the second power + PX + Q) (2x-3) does not contain the terms of X to the second power, the value of P and Q can be obtained
If the expansion of (X & # 178; + PX + Q) (2x-3) does not contain x, X & # 178;, find the value of P and Q

(X²+PX+Q)(2X-3)
=x³+2Px²+2Qx-3x²-3Px-3Q
=x³+(2P-3)x²+(2Q-3P)x-3Q
Does not contain x, X & #; items
therefore
The coefficients are all 0
therefore
2P-3=0
P=3/2
2Q-3P=0
Q=9/4