Answer: only the third option. [Vector A] dot [vector B + vector C]
The dot between the vectors mean that the operation to perform is the "scalar product", alson known as "dot product".
This operation is only defined between two vectors, not one scalar and one vector.
When you perform, in the first option, the dot product of any ot the first and the second vectors you get a scalar, then you cannot make the dot product of this result with the third vector.
For the second option, when you perform the dot product of vectar B with vector C you get a scalar, then you cannot make the dot product ot this result with the vector A.
The third option indicates that you sum the vectors B and C, whose result is a vector and later you make the dot product of this resulting vector with the vector A. Operation valid.
The fourth option indicates the dot product of a scalar with the vector A, which we already explained that is not defined.
Answer:
1.022 x 103 N.m
Explanation:
Solution
Given:
The weight of the block of mass m₂ is :
w₂ = m₂*g
Where
w₂ = 39 x 9.8 = 382.2 N
Then,
The weight of the block of mass m₁
w₁= m₁*g;
so,
w₁ = 12 x 9.8 = 117.5 N
Thus,
The tension wrapped in cord on drum (80 cm) T₁ = F - w₁
Now,
T₁ = 1200 - 117.5
T₁ = 1082.5 N
The tension wrapped in the cord on drum (41 cm) T₂ = w₂;
T₂ = 382.2 N
Hence,
We calculate net torque on the center of the drum:
The net torque = T₁ x 0.8 + T₂ x 0.41;
= 1082.5 x 0.8 + 382.2 x 0.41;
= 1.022 x 103 N.m
Therefore, the resulting torque applied to the system is 1.022 x 103 N.m
It is called a metric system!
Answer:
The second statement is true: If the concentration of Y is increased by a factor of 1.5, the rate will increase by a factor of 2.25.
Explanation:
Hi there!
Let´s write the rate law for the original reaction and the reaction with X increased by 1.5:
rate 1 =k [X][Y]²
rate 2 = k[1.5 X][Y]²
Now we have to demonstrate if rate 2 = 2.25 rate 1
Let´s do the cocient between the two rates:
rate 2/ rate 1
if rate 2 = 2.25 rate 1
Then,
rate 2 / rate 1 = 2.25 rate 1 / rate 1 = 2.25
Let´s see if this is true using the expressions for the rate law:
rate 2 / rate 1
k[1.5 X][Y]² / k [X][Y]² = 1.5 k [X][Y]² / k[X][Y]² = 1.5
2.25 ≠ 1.5
Then the first statement is false.
Now let´s write the two expressions of the rate law, but this time Y will be increased by 1.5:
rate 1 = k[X][Y]²
rate 2 = k[X][1.5Y]²
Again let´s divide both expressions to see if the result is 2.25
rate 2 / rate 1
k[X][1.5Y]²/ k [X][Y]²
(distributing the exponent)
(1.5)²k [X][Y]² / k [X][Y]² = (1.5)² = 2.25
Then the second statement is true!
