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
Answer:
sum = -15h+2
Step-by-step explanation:
The distance flown by plane is 750 kilometers.
Step-by-step explanation:
Let,
Distance traveled by plane = x
Distance traveled by car = y
Total distance = x+y
According to given statement;
The distance by car was 125 kilometers less than the distance by plane.
y = x - 125 => x=y+125 Eqn 1
The total distance was 500 kilometers less than three times the distance traveled by car.
Total distance = 3y - 500
x+y=3y-500 Eqn 2
Putting value of x from Eqn 1;
Putting y=625 in Eqn 1
The distance flown by plane is 750 kilometers.
Keywords: linear equations, substitution method
Learn more about linear equations at:
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4. First find how much sauce is used for 1 person:
2 ÷ 7 = 0.285714285714286
0.285714285714286cups of sauce will make spaghetti for one person.
0.285714285714286 • 210 = 60
60 cups of sauce for 210 people.
5. Found out how much he read in one minute:
40 ÷ 50 = 0.8
0.8 • 80 = 64
In 80 minutes, she will read 64 pages.
6. Found out how much he earns after one month:
9 ÷ 6 = 1.5
1.5 • 12 = 18
18 • 2 = 36
After two years, he will have 36 days of vacationing time
