There is a point P in the equilateral triangle ABC. If the distances from point P to points a, B and C are 3, 4 and 5 respectively, what is the degree of ∠ APB

There is a point P in the equilateral triangle ABC. If the distances from point P to points a, B and C are 3, 4 and 5 respectively, what is the degree of ∠ APB

∵ PC = 5, Pb = 4, PA = 3, ∵ PC & sup2; = Pb & sup2; + PA & sup2; rotate the triangle BCP about point B clockwise for 60 ° to make the rotated point C coincide with point a. the new position of point P is Q ∵ AQ = PC. It is easy to prove that △ bpq is an equilateral triangle ∵ Pb = PQ ∵ AQ & sup2; = PA & sup2; + PQ & sup2; ∵ QPA = 90 & ordm; ∵ BPA =}

[mathematical proof problem] as shown in the figure: in RT △ ABC, ∠ ACB = 90 °, CD ⊥ AB at point D. (1) prove: the square of AC = ad × ab
As shown in the figure: in RT △ ABC, ∠ ACB = 90 ° CD ⊥ AB is at point D
(1) Proof: the square of AC = ad × ab
(2) If AC = 12, BC = 5, find the length of AD

∵CD⊥AB∴∠CDA=90∵∠ACD=90∴∠CDA=∠ACD∵∠A=∠A∴△ACD∽△ABC∴AC/AB=AD/AC∴AC²= AB×AD2、∵AB²=AC²+BC²AC=12BC=5∴AB=13∵AC²= AB×AD12²=13ADAD=144/13...

Write down the proposition and conclusion of the following question, and use the method of counter example to show that the following question is a false proposition: if ab

For example, if AB < 0, then a + B < 0
Counterexample: let a = 4, B = - 3, ab = 4 × (- 3) = - 12 < 0, and a + B = 4 + (- 3) = 1 > 0
Therefore, this proposition is false

If the number a is divided by the number B, the quotient is 3 and the remainder is 2, the number a, the number B, the quotient and the remainder are 89?

Let B be x, then a be 3x + 2
(3x+2)+x+3+2=89
4x+7=89
4x=82
x=20.5
The number of a is 3x + 2 = 3 × 20.5 + 2 = 63.5

It is known that the radius of the bottom of the cone is 40 cm and the length of the generatrix is 90 cm, then the center angle of the expanded side view of the cone is 0______ Degree

According to the arc length formula L = n π R180: 80 π = n π· 90180, the solution is n = 160 degrees. The center angle of the side view is 160 degrees

(1 / 3) log 2 times with the base of 3

=Log (9 cube)
=log2.08
=0.3181

High one inequality properties. Urgent urgent!
1. The monthly rent of a supermarket is 5000 yuan, the salary of the staff is 3000 yuan, and the prescribed expenses are about 1500 yuan. If the average gross profit of the goods is 40%, how much is the monthly turnover at least to ensure the monthly profit of no less than 2500 yuan?
2. When k takes what value, the value of algebraic formula 1 / 2 (1-5k) - 2 / 3K is nonnegative
3. When x is not equal to - 1, compare the square of 5x + 6x-8 with the square of 3x + 2x-10
4. For any real number x, compare the square of (x + 1) with the size of 2x + 1

1. Let x yuan be reached
4x-5000-3000-1500 > = 2500,
The solution is x > = 30000
2.1/2(1-5K)-2/3K>=0
Then 3 (1-5k) - 6K > = 0
K0
The square of (x + 1) is greater than 0
If x is not equal to - 1, the former is greater than the latter
4. Expand the square of (x + 1) to the square of X + 2x + 1
Because the square of X ≥ 0, the square of (x + 1) is greater than or equal to 2x + 1

Roughly like this, divide the circle into a rectangle with a circumference of 8.28cm. What is the area of the circle?
1. Cut a round piece of paper into several parts, and you can put it together into an approximate rectangle. It is known that the circumference of the rectangle is equal to 8.28cm, and the original area of this round piece of paper is () square centimeter?
2 the area of a square is 8 square centimeters. Find the area of the shadow part. The shadow is a quarter of the circle, take the top right quarter, and place it in the square.

Rectangle circumference = 2 μ R + 2R = 8.25, so r = 1, the area of the circle is equal to μ R ^ 2 = 3.14 * 1 ^ 2 = 3.14 square centimeter

In quadrilateral ABCD, angle a = angle B, angle B = angle D is used to find that the quadrilateral is a parallelogram

∵∠A=∠C,∠B=∠D
∠A+∠B+∠C+∠D=360°
∴∠A+∠B=180°,∠B+∠C=180°
∴AB‖CD,AD‖BC
The quadrilateral ABCD is a parallelogram

Try to write at least two polynomials with the letter x.y, and satisfy the following conditions: the coefficient of each term of the cubic equation is 1 or - 1, and each term must contain X and y at the same time
Try to write at least two polynomials with the letter x.y, and satisfy the following conditions: the coefficient of each term of the sixth power trinomial is 1 or - 1, and each term must contain x at the same time. Y cannot contain other letters
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The square of x times the cubic of Y + XY + the square of x times y
X times the fifth power of Y + xy-x times the square of Y