Given that the left and right focus of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) are F1, F2, Pf1 / PF2 = e respectively, the value range of eccentricity e is

Given that the left and right focus of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) are F1, F2, Pf1 / PF2 = e respectively, the value range of eccentricity e is

According to the definition of ellipse: Pf1 + PF2 = 2A, and Pf1 / PF2 = E

4 - [3.75 × (1.2-1 / 3) + 3 / 4]

4 - [3.75 × (1.2-1 / 3) + 3 / 4]
=4 - [15 / 4 × (6 / 5-1 / 3) + 3 / 4]
=4 - [15 / 4 × 13 / 15 + 3 / 4]
=4 - [13 / 4 + 3 / 4]
=4-4
=0

If the system of equations x square + y square = 16, X-Y = k with X and y as unknowns has real solutions, then the value range of K is

Change the binary into one
From X-Y = k to x = K + y
Substituting x = K + y into X & # 178; + Y & # 178; = 16 leads to
（k+y)²+y²=16
2y²-2ky+k²-16=0
△=(-2k)²-4×2×﹙k²-16﹚
=-4k²+128
=-4(k²-32﹚
∵ the equation has real roots
∴-4(k²-32﹚≧0
That is K & # 178; - 32 ≤ 0
∴-4√2≤K≤4√2

20 mathematical problems
4 / 7 + 2 / 7 △ 2 = 1 / 25% = 3 / 5 3 / 3 = 4-1 / 5 1 / 1 = 1-12 / 5-12 / 5 = 2.4 × 6 / 5 = 254-97 = 3624-2994=
3 = 1 / 4 + 1 / 3-1 / 4 + 1 / 4 = 19 / 19%=
3 of 8-37.5% = 22 of 51 × 33, 17 of 8 = 0.75 × 99 + 0.75=
1 and 4 of 1 × 3 of 2 = 2 and 4 of 3-8 of 3-8 of 5 = 40 ／ 10 of 11=
2 △ 11 / 33 △ 2 = 5 and 3 / 4 △ 5.75 = 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2=

4 / 7 + 2 / 7 = 5 / 7 1 / 25% = 4 3 / 5 3 / 3 = 6 / 5
4-1 / 5 △ 1 / 5 = 31-12 / 5-12 / 5 = 12.4 × 6 / 5 = 2
254-97=157 3624-2994=630
4 and 1 / 3 △ 1.3 = 2.5 1 / 4 + 1 / 3-1 / 4 + 1 / 4 = 7 / 12 19 △ 19% = 100
3-37.5% = 0.51:22 × 33:17 = 2 / 90.75 × 99 + 0.75 = 75
1 and 4 / 1 × 3 / 2 = 5 / 6 2 and 4 / 3-8 / 3-8 / 5 = 1 and 4 / 3
40 △ 11 / 10 = 400 / 11
11 / 33 / 2 = 3.5 and 3 / 4 / 5.75 = 1
1 / 2 + 1 / 2 △ 1 / 2 + 1 / 2 = 2

Cut out the largest square on a 20 cm long and 15 cm wide rectangular paper. What is the area of the remaining part? Draw a picture

（20-15）×15
=5×15
=75 square centimeters

Given a sinusoidal alternating current I = 14.14sin (314t-45 ·) a, find the effective value and period of I and the algebraic form of current phasor

Effective value u = 14.14 / √ 2 = 10 A, angular frequency ω = 2 π f = 314, frequency f = 50 Hz, so period T = 1 / F = 20 ms
Algebraic form of current phasor u = 10 ∠ - 45 °

There is a rectangular cardboard, 80 cm long and 50 cm wide. Cut four squares with 8 cm sides at its four corners. Find the perimeter of the remaining cardboard

The perimeter of the remaining paperboard is equal to that of the original rectangle, so the perimeter = (80 + 50) × 2 = 260 cm

Is pulse the same as heart rate

In general, it is consistent. But some diseases can lead to inconsistency, such as atrial fibrillation, heart rate can be faster than pulse rate, which is called pulse shortness in medicine. It is because the contractility of myocardium in some cardiac cycles is weak, and it is not enough to output blood to peripheral blood vessels, so there is no pulse. If you feel sick, please go to the hospital for diagnosis and treatment. The network is very difficult to solve

The radius of the bottom of the cone is r, the length of the generatrix is 6R, and M is a point on the circumference of the bottom. Pull a rope from m, circle the side of the cone, and then return to M. the shortest rope length is?

When unfolding a cone, the shortest distance is the chord length after unfolding, the bottom radius is r, the generatrix length is 6R, and the center angle of the arc can be calculated as 60, so the chord length = generatrix length = 6R (equilateral triangle)

The checking method of fraction addition and subtraction and the checking method of integer ()

The checking method of addition and subtraction of fractions is the same as that of integers