Let
x--------> the time in minutes
y-------> an altitude in feet
we know that
For x=0 min y=0 ft
For x=50 min y=52,000 ft
so
the rate of change is equal to calculate the slope of the linear equation
![\frac{52,000-0}{50-0}=\frac{52,000}{50}=1,040\frac{ft}{min}](https://tex.z-dn.net/?f=%5Cfrac%7B52%2C000-0%7D%7B50-0%7D%3D%5Cfrac%7B52%2C000%7D%7B50%7D%3D1%2C040%5Cfrac%7Bft%7D%7Bmin%7D)
Round to the nearest hundred-------->
therefore
<u>the answer is</u>
![1,000\frac{ft}{min}](https://tex.z-dn.net/?f=1%2C000%5Cfrac%7Bft%7D%7Bmin%7D)
A unit rate in math is the expression of a rate in a quantity of one.<span> For example, 60 miles per hour represents a commonly used unit rate. Similarly, 30 students per school bus also represents a unit rate.</span>
Solution:- Given that the total revenue function
,where x is the number of rooms filled
Now, differentiating the function w.r.t. x,we get
![r'(x)=300-0.4x](https://tex.z-dn.net/?f=r%27%28x%29%3D300-0.4x)
To find critical points ,Put ![r'(x)=0](https://tex.z-dn.net/?f=r%27%28x%29%3D0)
![\Rightarrow300-0.4x=0\\\Rightarrow0.4x=300\\\Rightarrow x=750\\\text{Now}\\r"(x)=-0.4](https://tex.z-dn.net/?f=%5CRightarrow300-0.4x%3D0%5C%5C%5CRightarrow0.4x%3D300%5C%5C%5CRightarrow%20x%3D750%5C%5C%5Ctext%7BNow%7D%5C%5Cr%22%28x%29%3D-0.4%20%3C0%5Ctext%7B%28by%20second%20derivate%20test%29%7D%29%5C%5C%5Ctext%7BMaximum%20revenue%20will%20produce%20by%20filling%20x%3D750%20rooms%20in%20dante%27s%20villas.%7D)
Given:
The system of equations that represent the constraints for the given situation is
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Multiply equation (i) by 4.
...(iii)
Subtracting (iii) from (ii), we get
![16.90x+4y-(4x+4y)=36.35-17](https://tex.z-dn.net/?f=16.90x%2B4y-%284x%2B4y%29%3D36.35-17)
![16.90x+4y-4x-4y=19.35](https://tex.z-dn.net/?f=16.90x%2B4y-4x-4y%3D19.35)
![12.90x=19.35](https://tex.z-dn.net/?f=12.90x%3D19.35)
Divide both sides by 12.90.
![x=\dfrac{19.35}{12.90}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B19.35%7D%7B12.90%7D)
![x=1.5](https://tex.z-dn.net/?f=x%3D1.5)
Put this value in (i).
![1.5+y=4.25](https://tex.z-dn.net/?f=1.5%2By%3D4.25)
![y=4.25-1.5](https://tex.z-dn.net/?f=y%3D4.25-1.5)
![y=2.75](https://tex.z-dn.net/?f=y%3D2.75)
The solution of system of equations is x=1.5 and y=2.75. It means, the yards of silk are 1.5 and yards of cotton are 2.75.
Answer:
Do they have enough?
Nope, they don't have enough.
Step-by-step explanation:
They would not have enough because 3/4 times 4 would not equal 5...it would equal 3. Mario and his 3 friends each have 3/4 foot of rope. They needed 5 feet of rope altogether. Do they have enough rope? They would need 2 more feet of rope to complete the 5 feet. But they do not have enough feet of rope to make 5 feet.
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