Answer:
I. 37+0.2m≤95
II. The greatest Distance you can drive each day is 290 miles.
Step-by-step explanation:
The cost of a car rental is $37 per day plus 20 cents per mile.
Let the number of miles driven be represented by m.
Therefore costs of miles driven
=20 cents X m =$0.2 X m= $0.2m
Total Cost Per day= Rental Cost + Cost of Miles Driven = 37+0.2m
Since the daily budget is $95, the total cost must be less than or equal to $95.
That is,
37+0.2m≤95.....(I)
This is the inequality that represents the greatest distance possible.
Next, we solve for m
37+0.2m≤95
0.2m≤95-37
0.2m≤58
m≤58/0.2
m≤290
The greatest Distance you can drive each day is 290 miles.
Answer:
I'm pretty sure it is 7.4% or 0.074.
Step-by-step explanation:
The rate of increase is found by differentiating with resepect to time. The product rule comes into play here.
A = LW
dA/dt ≈ (dL/dt)·W + L·(dW/dt)
... = (6 cm/s)·(5 cm) + (7 cm)·(3 cm/s)
... = 30 cm²/s + 21 cm²/s
... = 51 cm²/s . . . . rate of area increase
Answer:
![p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%20%7Bx%7D%5E%7B4%7D%20%20%2B%20%20%7Bx%7D%5E%7B3%7D%20%20%20-%207%20%7Bx%7D%5E%7B2%7D%20-%20x%20%2B%206)
Step-by-step explanation:
The polynomial function has zeros
x=1, x=2,x=-3,x=-1
This means the factored form of the polynomial is
![p(x) = (x - 1)(x + 1)(x + 3)(x - 2)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x%20-%201%29%28x%20%2B%201%29%28x%20%2B%203%29%28x%20-%202%29)
We expand to get:
![p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%201%29%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%20x%20-%206%29)
We expand further to get:
![p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%7Bx%7D%5E%7B2%7D%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%20x%20-%206%29%20-%201%28%7Bx%7D%5E%7B2%7D%20%20%2B%20x%20-%206%29)
![p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%20%7Bx%7D%5E%7B4%7D%20%20%2B%20%20%7Bx%7D%5E%7B3%7D%20%20-%206%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20%2B%206)
This simplifies to:
![p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%20%7Bx%7D%5E%7B4%7D%20%20%2B%20%20%7Bx%7D%5E%7B3%7D%20%20%20-%207%20%7Bx%7D%5E%7B2%7D%20-%20x%20%2B%206)
This is the standard form of the polynomial since it is written in descending powers of x.