Tyler is preparing a speech on skateboarding for his physics class. For speech support, he is using facts. To make his speech mo
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The coefficients for the binomial expansion of (a + b)³ are 1, 3, 3, 1.
We have,
The binomial expansion (a + b)³,
So,
Now,
We know that,
Formula for binomial expansion,
i.e.
(u + v)ⁿ = ⁿC₀ · uⁿ · v⁰ + ⁿC₁ · uⁿ⁻¹ · v¹ + ⁿC₂ · uⁿ⁻² · v² + ⁿC₃ · uⁿ⁻³ · v³
Now,
According to the question,
Here,
u = a,
v = b,
And, n =3
Now,
Putting values,
i.e.
(a + b)³ = ³C₀ · a³ · b⁰ + ³C₁ · a³⁻¹ · b¹ + ³C₂ · a³⁻² · b² + ³C₃ · a³⁻³ · b³
We get,
(a + b)³ = ³C₀ · a³ · b⁰ + ³C₁ · a² · b¹ + ³C₂ · a¹ · b² + ³C₃ · a⁰ · b³
Now,
Using combination formula,
On solving we get,
(a + b)³ = a³ + 3 a² b + 3 a b² + b³
So,
Now,
The coefficients of :
a³ = 1,
3a²b = 3,
3ab² = 3,
b³ = 1,
So,
The coefficients of the given binomial expansion are 1, 3, 3, 1.
Hence we can say that the coefficients for the binomial expansion of (a + b)³ are 1, 3, 3, 1.
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A long string can be easily stretched. The Two points on the string are labeled A and B is that A should be at 90 degrees with same magnitude and B should be at 270 degrees with same magnitude.
<h3>What is Angle magnitude</h3>- This is known as the amount of rotation via which one of the arms is said to be rotated about vertex to result in a given position of the other.
Equal vectors are known to have the same magnitude and direction. Two vectors are said to be equal when their magnitude and direction are said to be same.
See the full question below
A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B.At the instant shown, orient v(A) and v(B) to correctly represent the direction of the wave velocity at points A and B.At each of the points A and B, rotate the given vector to indicate the direction of the wave velocity.Figure:A string is attached and moving up and down
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