Invasive species often unbalance the ecosystems into which they are introduced because _______. a. they did not co-evolve with t
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The normal force acting on the legs of the table is 175 N
The weight of the books is the force exerted by the books on the table, and it is given as:
The force exerted by the table is given as:
The parameters above imply that:
- The table and the books are stationary,
- The force exerted by both act in the same downward direction.
So, the normal force acting on the legs of the table is calculated as follows:
Substitute known values
Hence, the normal force acting on the legs of the table is 175 N
Read more about normal force at:
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.
Learn more about binomial expansion here
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