Given that the image of function f (x) = SiNx + acosx passes through the point (- π / 3,0), the value of real number a is obtained

Given that the image of function f (x) = SiNx + acosx passes through the point (- π / 3,0), the value of real number a is obtained

Sin (- π / 3) = - radical 3 / 2
cos(-π/3)=1/2
F (- π / 3) = - radical 3 / 2 + A / 2 = 0
A / 2 = root 3 / 2
So a = root 3

Find the maximum value of function y = - cos2x + acosx + 5 / 8a-1 / 2, X ∈ [0, π / 2]
In a hurry

y=-cos2x+acosx+5/8a-1/2=y=1-2(cosx)^2+acosx+5/8a-1/2=-2(cosx-a/4)^2+5/8a+1/2+a^2/8
Discussion: 0

Given the function f (x) = 1 / 2 (cos2x) + asinx-a / 4, the definition field is [0, п / 2], and the maximum value is 2, find the value of real number a

The idea is as follows:
If cos2x = 1-2sin ^ 2x, then 1 / 2 (cos2x) = 1 / 2-sin ^ 2x
fx=1/2-sin^2x+asinx-a/4
The method of matching is adopted
fx=1/2-(sin^2x+asinx+a^2/4-a^2/4)-a/4
=1/2-(sinx+a/2)^2+a^2/4-a/4
It can be seen from the definition field that the value range of SiNx is [0,1]. There is no doubt that when SiNx = - A / 2, FX has the maximum value (because the square of any number is greater than = 0, take the minimum of 0 square and the maximum of subtraction rule)
That is 1 / 2 + A ^ 2 / 4-A / 4 = 2, the solution is a = - 2 or a = 3
A = 3 is not in line with the meaning of the question, because SiNx = - 3 / 2 is not in the range
Topic summary:
If the topic changes to acosx, then you need to change cos2x to 2cosx-1, and then make the formula. If there is such a problem of finding the maximum and minimum, you should make the formula flexibly
In addition, whenever there is a domain, your function must be within that range
Classmate, your foundation is not very solid

Given that the definition field of function f (x) = 12cos2x + asinx − A4 is [0, π 2], and the maximum value is 2, find the value of real number a

The definition domain of the function is [0, π [0 [0, π 2] for [0, π 2] and [0, π 2] for [12 (1 − 2s2x2x) + 12 (1 − 2s2x2x2x) + asinx {12 (x (x) = 12cos2x (12cos2x) + 12cos2x + asinx cos2x + asinx {12 (12) 2x + asinx2x x x} = 12 (12, the definition of [12, π [0, π 2 [12, π [12, π [12 {A4 = 12} A4 = 12} 4 = 12 \\\\\\\\\\\\\\thevalue is - 1 + A + 12 − A4 = 2 & nbsp; & nbsp; In conclusion, a = - 6 or a = 53

How to solve the equation of 5x + (20-x) △ 2 × (- 2) = 64

5x+(20-x)×(-1)=64
5x+x-20=64
6x=84
x=14

If the values of X and y are equal, then K − 3Y = 1kx + (K − 1) y = 3=______ ．

From the question meaning: y = x, substitute into the equation system: 4x − 3x = 1kx + (K − 1) x = 3, the solution: x = 1, k = 2, then k = 2

Solving equation 5x + 3 * (x-0.7) = 22.1

5X+3*（X-0.7)=22.1
5X+3X-2.1=22.1
8X=22.1+2.1=24.2
X=24.2÷8
X=3.025

Detailed steps to solve the equation with x + 1.5x = 250
I want to solve the equation of X + 1.5x = 250, the steps of solving the equation
Please, I can't solve this equation
(for example: x + 50 = 80)
x=80-50
x=30 ）

x=1x
1x+1.5x=250
2.5x=250
x=100

To solve the equation: x square - 5x + 10 > 0, a complete process is needed,

Xsquare - 5x + 10 > 0
Xsquare - 5x + 25 / 4 + 15 / 4 > 0
（x-5/2）²+15/4>0
（x-5/2)² >-15/4
equation holds good under all circumstances
So x ∈ R

(only use the formula or the equation to find an unknown number)
If there is a car with a wheel circumference of 5.5/12 meters and a rear wheel circumference of 6.1/3 meters, how many meters can we advance so that the number of turns of the front wheel is 99 more than that of the rear wheel?
The cost of a mobile phone in the telecommunication city is 80% of the price. The price of the electric board is 300 yuan, and the cost is 240 yuan. Now the telecommunication city supplies a mobile phone with two electric boards, and sells it according to 95% of the sum of their prices. In this way, each set can still make a profit of 480 yuan. How much is the cost of the mobile phone?

1. If the rear wheel turns x times, the front wheel turns 99 times more than the rear wheel, then the front wheel turns x + 99 times
Then (x + 99) * (5 + 5 / 12) = (6 + 1 / 3) x
X = 585 turns
So 585 * (6 + 1 / 3) = 3705 meters
2. If the price of mobile phone is x yuan, then the cost is 80% x = 0.8x yuan,
Then (x + 300 * 2) * 95% - (0.8x + 240 * 2) = 480
The solution is x = 2600
The cost of mobile phone is 2600 * 0.8 = 2080