Answer:
x=2, x=-8 : 2 will be taken as the answer as negative is discarded so C is the answer
Step-by-step explanation:
Apply Log Rules:
x(x+6)=16
Solve:
x=2, x=-8
6.988.880km = 4342668.7 miles
The domain of a function is the set of values of x for which a value of y exists. In this case, the only way that a value of y would not exist is for a denominator to equal to zero. If this function is f(x) = 1/(x+1) + 5, then we must find the values of x for which the denominator (x+1) = 0, which is at x = -1.
Therefore the domain is all real numbers except x = -1. In interval notation this can be written as (-infinity, -1), (-1, infinity).
Answer:
( d / c ) < ( a / d )
( b / d ) < ( a / d )
( d / a ) < ( a / d )
Step-by-step explanation:
For this problem, we need to consider the given information that a > b > c > d > 0. Note that a is the greatest number and that d is the least number.
Given this fact, we can create a fraction that will result in a maximum value by simply doing the following:
a / d
The reason the fraction ( a / d ) results in a maximum, is because of the given information where a is the furthest from 0, and d is the closest to 0. Therefore, we can say that no other combination will result in a value greater than ( a / d).
So in the three given statements, we have different combinations of fractions being compared to our maximum value fraction. Our maximum value fraction ( a / d ) will always be greater than any other combination.
Thus, we will choose the sign that makes ( a / d ) greater than the other choice fractions.
Cheers.
Answer:
a) see below
b) 40x20 meters
Step-by-step explanation:
Write down what you know:
- The area of the enclosure is length*width, so
![A = x \cdot y](https://tex.z-dn.net/?f=A%20%3D%20x%20%5Ccdot%20y)
- The length of the fencing is 80 meters, so
![2y + x = 80](https://tex.z-dn.net/?f=2y%20%2B%20x%20%3D%2080)
Now we have to combine these two equations above, and get rid of y in the process.
First rewrite the second as:
![y = 40 - \frac12 x](https://tex.z-dn.net/?f=y%20%3D%2040%20-%20%5Cfrac12%20x)
Then substitute for y in the first:
![A = x (40 - \frac12 x) = 40x - \frac12x^2](https://tex.z-dn.net/?f=A%20%3D%20x%20%2840%20-%20%5Cfrac12%20x%29%20%3D%2040x%20-%20%5Cfrac12x%5E2)
b) To maximize A, find the zero of the first derivative:
![A'(x) = 40 - x = 0 \implies x=40](https://tex.z-dn.net/?f=A%27%28x%29%20%3D%2040%20-%20x%20%3D%200%20%5Cimplies%20x%3D40)
So y = (80-40)/2 = 20 meters.