A cube's edge lengths are each 5 inches. A rectangular prism's length and width are also 5 inches, but its height is 7
1 answer:
The rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
<h3>What is Volume?</h3>Volume is defined as the space occupied by a three dimensional figure.
It is given that
A cube's edge lengths are each 5 inches
A rectangular prism's length and width are also 5 inches, but its height is
The volume of the cube is given by side * side * side
Volume of cube = 5 *5 * 5 = 125 cu. inches
The volume of cuboid = length * width * height
<h3>Volume of Cuboid = 5 * 5 * 15/2</h3>Volume of Cuboid = 187.5 cu.inches.
Therefore the rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.
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Answer:
55 adult tickets were sold on Friday.
Step-by-step explanation:
A linear system will be used to model the system.
Let c be the number of child tickets and a be the number of adult tickets
Then according to given statements
From equation 1
Putting this in equation 2
Putting c = 78 in equation 1
Hence,
55 adult tickets were sold on Friday.
Answer:
Only d) is false.
Step-by-step explanation:
Let be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that . 0 is a root of p, so we have that
.
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.