Cho nguồn phát sóng dao động điều hòa với phương trình \(u=a\cos2\pi ft\left(cm\right)\). Độ lệch pha \(\Delta\varphi\) giữa hai điểm trên phương truyền sóng cách nhau một khoảng \(\Delta d\) là

A.\(\pi\frac{\Delta d}{\lambda}\left(rad\right)\)

B.\(\pi\frac{\Delta d}{2\lambda}\left(rad\right)\)

C.\(2\pi\frac{\Delta d}{\lambda}\left(rad\right)\)

D.\(2\pi\frac{\lambda}{\Delta d}\left(rad\right)\)

Câu 1: Given that  is divisible by 9. What is the value of ? 
Câu 2: How many elements of the set A are divisible by 9?
Câu 3:A is a set of multiples of 12 less than 12. How many elements does the set A have?
Câu 4:Find the remainder when  is divided by 3.
Câu 5:Given that 511 is the sum of two prime numbers  and , . What is the value of ?
Câu 6:Given that . Find the value of .
Câu 7:Given that . How many divisors does the number A have?
Câu 8:Find the natural number  so that the product of  and 5 is a prime number.
Câu 9:
Given that . How many divisors does the number A have?
Câu 10:
Given that . How many divisors the number A have?
 

Source of Question: Câu hỏi của Hiếu Cao Huy - Toán lớp 9 | Học trực tuyến

Xét pt (1): \(\Delta=b^2-4ac\)

\(x_1=\dfrac{-b+\sqrt{\Delta}}{2a}\); \(x_2=\dfrac{-b-\sqrt{\Delta}}{2a}\)

Xét pt (2) : \(\Delta=b^2-4ac\)

\(y_1=\dfrac{-b+\sqrt{\Delta}}{2c}\) ; \(y_2=\dfrac{-b-\sqrt{\Delta}}{2c}\)

Thay vào M:

\(M=\dfrac{\left(-b+\sqrt{\Delta}\right)^2}{4a^2}+\dfrac{\left(-b-\sqrt{\Delta}\right)^2}{4a^2}+\dfrac{\left(-b+\sqrt{\Delta}\right)^2}{4c^2}+\dfrac{\left(-b-\sqrt{\Delta}\right)^2}{4c^2}\)

\(=\dfrac{b^2-2b\sqrt{\Delta}+\Delta}{4a^2}+\dfrac{b^2+2b\sqrt{\Delta}+\Delta}{4a^2}+\dfrac{b^2-2b\sqrt{\Delta}+\Delta}{4c^2}+\dfrac{b^2+2b\sqrt{\Delta}+\Delta}{4c^2}\)

\(=\dfrac{2b^2+2\Delta}{4a^2}+\dfrac{2b^2+2\Delta}{4c^2}=\dfrac{b^2+\Delta}{2a^2}+\dfrac{b^2+\Delta}{2c^2}=\dfrac{b^2c^2+\Delta c^2}{2a^2c^2}+\dfrac{a^2b^2+\Delta a^2}{2a^2c^2}\)

\(=\dfrac{b^2\left(a^2+c^2\right)+\Delta\left(a^2+c^2\right)}{2a^2c^2}=\dfrac{\left(b^2+\Delta\right)\left(a^2+c^2\right)}{2a^2c^2}=\dfrac{\left(b^2+b^2-4ac\right)\left(a^2+c^2\right)}{2a^2c^2}\)

\(=\dfrac{\left(2b^2-4ac\right)\left(a^2+c^2\right)}{2a^2c^2}=\dfrac{\left(b^2-2ac\right)\left(a^2+c^2\right)}{a^2c^2}=\dfrac{a^2b^2-2a^3c+b^2c^2-2ac^3}{a^2c^2}\)

\(=\dfrac{a^2b^2}{a^2c^2}+\dfrac{b^2c^2}{a^2c^2}-\dfrac{2a^3c}{a^2c^2}-\dfrac{2ac^3}{a^2c^2}=\dfrac{b^2}{c^2}+\dfrac{b^2}{a^2}-\dfrac{2a}{c}-\dfrac{2c}{a}\)

\(=\left(\dfrac{b^2}{c^2}-\dfrac{2ac}{c^2}\right)+\left(\dfrac{b^2}{a^2}-\dfrac{2ac}{a^2}\right)=\dfrac{b^2-2ac}{c^2}+\dfrac{b^2-2ac}{a^2}\)

\(=\left(b^2-2ac\right)\left(\dfrac{1}{c^2}+\dfrac{1}{a^2}\right)\)

Thanks a lots for your answering ^^!

Hiếu Cao Huy: Wait together!

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MD and ME are two bisectors of triangles AMB and AMC respectively.

If AM= m; BC = a . Then DE = ???

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What is the product of all real solutions to the equation above?

3) The sum of all possible natural numbers n such that

\(n^2+n+1589\) is a perfect square is.....

4) Given that x is a positive integer such that x and x+99 are perfect squares

The sum of integer x is ...

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(...((1@2)@3....@2017)

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=> \(f\left(\dfrac{1}{2016}\right)+f\left(\dfrac{2}{2016}\right)+f\left(\dfrac{3}{2016}\right)+...+f\left(\dfrac{2016}{2016}\right)\)

Các bn giúp mk vs >>> tks nha!!!