Potential energy , hope this helps :)
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.
Answer:
T=1022.42 N
Explanation:
Given that
l = 32 cm ,μ = 1.5 g/cm
L =2 m ,V= 344 m/s
The pipe is closed so n= 3 ,for first over tone
f= 129 Hz
The tension in the string given as
T = f²(4l²) μ
Now by putting the values
T = f²(4l²) μ
T = 129² x (4 x 0.32²) x 1.5 x 10⁻³ x 100
T=1022.42 N
Its the first one with the circle and the arrows going around it
Answer:
a. 340.13 m/s b. 680.26 m/s c. our wavelength doubles
Explanation:
a. speed of wave, v = fλ were f = frequency = 301 Hz and λ = wavelength = 1.13 m.
v = fλ = 301 Hz × 1.13 m = 340.13 m/s
b. If we double the frequency then f = 2 × 301 Hz = 602 Hz
v = fλ = 602 Hz × 1.13 m = 680.26 m/s
c. If the speed of the wave is still 340.13 m/s, if we cut the frequency in half, then frequency now equals f = 301 Hz/2 = 150.5 Hz.
Since v = fλ,
λ = v/f = 340.13 m/s ÷ 150.5 Hz = 2.26 m.
Since our initial wavelength λ₀ = 1.13 m,
λ/λ₀ = 2.26 m/1.13 m = 2.
So, λ = 2λ₀ our wavelength doubles
