If XY satisfies (x-1) ^ 2 + (y + 2) ^ 2 = 4, find the maximum and minimum of S = 2x + y

If XY satisfies (x-1) ^ 2 + (y + 2) ^ 2 = 4, find the maximum and minimum of S = 2x + y

XY satisfies (x-1) ^ 2 + (y + 2) ^ 2 = 4
Let x = 1 + 2cost, y = - 2 + 2sint
s=2x+y=4cost+2sint=sqrt(20)sint(t+n)
S Max sqrt (20)
S min - sqrt (20)

If x and y satisfy (x-1) 2 + (y + 2) 2 = 4, find the maximum and minimum of S = 2x + y

(x-1) 2 + (y + 2) 2 = 4 denotes a circle with radius equal to 2 centered on (1, - 2). From S = 2x + y, y = - 2x + s is obtained. When the line is tangent to the circle, s obtains the maximum and minimum values. From | 2 × 1 − 2 − s | 22 + 12 = 2, s = ± 25, ｜ Smax = 25, smin = − 25

The odd function f (x) defined on [- 1,1] is known. When x ∈ [- 1,0], f (x) = 1 / 4x-a / 2x (a ∈ R)
(1) Find the analytic expression of F (x) on (0,1);;
(2) Find the maximum value of F (x) on (0,1);;
(3) If f (x) is an increasing function on (0,1), find the value range of real number a

(1)D=[-1,1]
x=[-1,0] -x=[0,1]
f(-x)=-1/4x+a/2x
The analytic expression of F (x) on (0,1) is y = - 1 / 4x + A / 2x
(2) When a > 1 / 2, X (max) = 1 / 4 + A / 2
When a = 1 / 2, x = 0
When A0
a>1/2

It is known that f (x) is an odd function defined on R, and when x > 0, f (x) = 1-x2. (1) find the analytic expression of F (x); (2) draw the image of F (x); (3) if f (x) is monotone in the interval [a, a + 1], write the value range of real number a directly

(1) 1 ° because the function is odd, so when x = 0, f (0) = 0 -------- (2 points) 2 ° let x < 0, then - x > 0, according to when x > 0, f (x) = 1-x2, f (- x) = 1 - (- x) 2 = 1-x2 ∵ f (x) is an odd function defined on R ∵ f (x) = - f (- x) = x2-1 -------- (4 points) to sum up: F (x) = 1 − X2, x > 00 & nbsp; & nbsp;, x = 0x2 − 1, X < 0 & nbsp; (2) when x ＞ 0, the function image is on the right side of the open downward parabola, when x ＜ 0, the function image is on the left side of the open upward parabola, and f (0) = 0, thus the function image can be obtained as shown in the right figure -------- (10 points) (3) according to the function image of (2), when [a, a + 1] ⊊ (- ∞, 0), the function f (x) can be obtained ）It is a decreasing function in the interval [a, a + 1]; when [a, a + 1] ⊊ (0, + ∞), the function f (x) is an increasing function in the interval [a, a + 1]. The solution is: a ＜ - 1 or a ＞ 0 ------ (15 points)

If Party A, Party B and Party C jointly buy a TV set, half of the amount paid by Party A is equal to one third of the amount paid by Party B and three seventh of the amount paid by Party C,
It is known that C pays 120 yuan more than A. how much is the TV set?

3 / 7 of the amount paid by Party C is equivalent to 1 / 2 of the amount paid by Party A. then, the amount paid by Party C is equivalent to (1 / 2) / (3 / 7) = 7 / 6 of Party A. the amount paid by Party B is 720 * 1 / 2 / (1 / 3) = 1

Fractions and percentages
84 kg peanut kernel, 47.3 kg oil can be extracted, and the oil yield is ()
2.10 △ () = 62.5% = 15 () = 8 ()
3. In the four numbers of π, 3, 20, 7 and 3.14315%, the maximum number is (), and the minimum number is ()
4. The oil in an oil barrel accounts for 5.3% of the oil in the whole barrel. After 18 kg is sold, 60% of the original oil is left. How many kg of oil can this oil barrel hold? The correct formula is: () a.18 × (1-60%) × 5.3 moleculars b.18 × (1-60%) + 5.3 moleculars c.18 × (1-60%) / 5.3 moleculars d.18 × (1-60%) × 5.3 moleculars
5. A basket of apples weighs 7kg more than a basket of oranges, while the weight of a basket of oranges is less than the weight of a basket of apples by 5 moles1, so a basket of oranges weighs () kg
6. A molecule of the simplest fraction is reduced to 1 by adding 3, and 2 is obtained by subtracting 1. This fraction is ()
7. The master and the apprentice make a batch of parts together. The master makes 25% more parts than the apprentice, and the apprentice makes less parts than the master ()
8. For a and B welding rods, first use 10 moleculars 1 and then 10 moleculars 1 decimeter from a, and first use 10 moleculars 1 decimeter and then 10 moleculars 1 from B. at this time, the length of the remaining parts of the two welding rods is equal. It turns out that () A. length B. length B. length C. length D. is not sure

Child, do these questions by yourself, what do you do in the future? It's so easy to ask here!

Number a is 1 / 3 of number B, number B is 1 / 3 of number C, number a is () a.1 / 3 B.1 / 6 C.1 / 9 d.9 times of number C

C.1/9

It is known that the binary linear equations x + y = - 1, ax by = 1 and ax + by = 7, 2x-y = 4 have the same solution, so we can find the value of a and B

Because x + y = - 1,2x-y = 4
The solution is: x = 1, y = - 2
Substituting x = 1, y = - 2 into ax by = 1 and ax + by = 7,
We get a - (- 2) y = 1
a+(-2)y=7
The solution is a = 4
b=-3/2

What is 120 × (1 / 3 + 1 / 4 + 1 / 6)?

Original formula = 120 × 1 / 3 + 120 × 1 / 4 + 120 × 1 / 6 = 40 + 30 + 20 = 90, hope to help you, please accept in time, your adoption is the power of my answer!

To solve the ternary linear equations 1) 2x + y-3z = 3,3x-y + 2Z = 1, X-Y-Z = 5,2) x: y = 3:2, Y: z = 5:4, x + y + x = 66

1. Formula 1 Plus Formula 2, get 5x - z = 4, formula 1 Plus Formula 3, get 3x - 4Z = 8, then 4 * (5x - z) - (3x - 4Z) = 16-8 = 8, that is 17x = 8, the solution is x = 8 / 17, then z = 5x-4 = - 28 / 17, y = x-z-5 = - 49 / 17, so the solution of the equation is x = 8 / 17, y = - 49 / 17, z = - 28 / 172, x = 1.5y, z = 0.8y, then x + y + Z = 3.3