Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
The acceleration of a rocket engine is given here, and after 50 seconds of flight, the engine fails, and we must determine the altitude of the rocket at the time the engine fails. Because the rocket starts from rest, the time taken is 50 seconds, the initial velocity is zero, and the acceleration is 22.9 meters per second square. So we use the kinamatics equation s equal to v. I t plus half 8 square. There is no acceleration at the start. 22.9 and t is 50 seconds, so displacement 2.86 times 10 to the power 4 is met. This is the rocket's displacement in 50 seconds, so this is the rocket's altitude when the engine fails.
<h3>What exactly is accelerate?</h3>
- In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.
- In his second law of motion, Sir Isaac Newton (1642-1727) defined acceleration as the ratio of a force acting on an object to its mass: a = f/m.
- Accelerate is a verb that means to speed up. When you press the gas pedal, the car accelerates. If you know someone who works at the consulate, you can speed up the process.
- Acceleration is the rate at which velocity changes over time, both in terms of speed and direction. A point or object moving in a straight line is accelerated if it accelerates or decelerates.
- Even if the speed is constant, motion on a circle is accelerated because the direction is constantly changing. Both effects contribute to acceleration in all other types of motion.
Hence, There is no acceleration at the start. 22. This is the rocket's displacement in 50 seconds, so this is the rocket's altitude when the engine fails.
To know more about Accelerate refer to:
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Answer:
a Doe
A baby mouse is called a 'pinky', a male is called a 'buck' and a female is called a 'doe'.
(hope that helped)
Answer:
Explanation:
Mass: M, Length: L.
The formula that gives center of mass is
In the case of a non-uniform mass density, this formula converts to
where the denominator is the total mass and the nominator is the mass times position of each point on the rod.
We have to integrate the mass density over the total rod in order to find the total mass. Likewise, we have to integrate the center of mass of each point (xσ(x)) over the total rod. And if we divide the integrated center of mass to the total mass, we find the center of mass of the rod:
Here x's are cancelled. Otherwise, the denominator would be zero.
