Answer:
dV = - 5.73*10⁹ m³/s
Step-by-step explanation:
Question: What is the rate of change of the volume of the prism at that instant (in cubic meters per second) ?
A function can be dependent on one or more variables. The change in the function due to a change in one o its variables is given by the functions derivative with respect to that variable. For functions that are composed of products of its variables, we may use the product rule to determine its derivative.
The volume of a square prism with base a and height h is given by
V = a²h
When the base and height are changing, we have
dV = 2ah(da/dt) + a²(dh/dt)
Given
a = 4 Km
h = 9 Km
da/dt = - 7 Km/min
dh/dt = 10 Km/min
we have
dV = 2(4 Km)(9 Km)(- 7 Km/min) + (4 Km)²(10 Km/min)
⇒ dV = - 504 Km³/min + 160 Km³/min = - 344 Km³/min
⇒ dV = - 5.73*10⁹ m³/s
The surface area increases by a factor of 4. 2^2= 4.
The area of the long side is 3×1= 3cm^2 on the small prism.
The area of the long side is 6×2= 12cm^2 on the large prism.
12/3= 4.
Answer by JKismyhusbandbae: 8 × 4
Explanation/Work: There are 8 snack bags with 4 muffins in each. Multiply 8 × 4 to find the total number of muffins.
The lines mean that they are parallel
