Answer:
The volume of the second rectangular prism is 576 cm³ .
Step-by-step explanation:
As given
The volume of a rectangular prism varies jointly with the length and width when the height remains constant.
Let us assume that the length is denoted by L .
Let us assume that the Breadth is denoted by B.
Thus
V = L × B × H
where H is the constant of variation
The volume of a rectangular prism is 672 cubic centimeters and has a length of 8 centimeters and a width of 14 centimeters.
Volume (V) = 672 cm
Length (L) = 8 cm
Width (B) = 14 cm
Put all the values in the above
672 = 8 × 14 × H
672 = 112H
H = 6
As given
A second prism has a length of 12 centimeters and a width of 8 centimeters.
Length = 12 cm
Width = 8 cm
Height = 6cm
Put all the values in V = L × B × H .
V = 12 × 8 × 6
V = 576 cm³
Therefore the volume of the second rectangular prism is 576 cm³ .
The missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
<h3>What is unit conversion?</h3>It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
Make subject C and solve:
Plug F = 41
41 degrees F = 5 degrees C
Thus, the missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.
Learn more about the unit conversion here:
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Answer:
University of Texas has 46,500 students, University of California has 34,000 students and University of Miami has 15,500 students.
Step-by-step explanation:
Represent Texas with T, Miami with M and California with C. With the given information, the following equations were obtained.
T = 3 × M
T – 3M = 0 ………………………….(i)
C = 3,000 + 2 × M
C – 2M = 3,000…………………..(ii)
T + C + M = 96,000…………….(iii)
By rearranging, we have:
1T + 0C – 3M = 0 ………………………….(i)
0T + 1C – 2M = 3,000…………………..(ii)
1T + 1C + 1M = 96,000………….…….(iii)
The Augmented Matrix is:
=
Making the subject of the formula we have:
=
Let’s say matrix A = , the inverse of matrix A =
is determined by the formula
. This can also be computed directly on a scientific calculator.
=
=
T = 46,500
C = 34,000
M = 15,500