9514 1404 393
Answer:
- graph is shown below
- absolute max and min do not exist
- local max: 0 at x=0
- local min: -500/27 ≈ -18.519 at x=10/3
Step-by-step explanation:
The function is odd degree so has no absolute maximum or minimum. It factors as ...
g(x) = x^2(x -5)
so has zeros at x=0 (multiplicity 2, meaning this is a local maximum*) and x=5.
Differentiating, we find the derivative of g(x) is zero at x = 0 and x = 10/3.
g'(x) = 3x^2 -10x = x(3x -10) ⇒ x=0 and x=10/3 are critical points
The value of g(10/3) is a local minimum. That value is ...
g(10/3) = (10/3)^2((10-15)/3) = -500/27 ≈ -18.519
__
The local maximum is (0, 0); the local minimum is (10/3, -500/27). The graph is shown below.
_____
* When a root has even multiplicity, the graph does not cross the x-axis. That means the root corresponds to a local extremum. Since this is the left-most root of an odd-degree function with a positive leading coefficient, it is a local <em>maximum</em>. (The function is <em>increasing</em> left of the left-most turning point.)
Answer:
Part A. ![\frac{84.3y}{12} = 7 +\frac{0.1\cdot y}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B84.3y%7D%7B12%7D%20%3D%207%20%2B%5Cfrac%7B0.1%5Ccdot%20y%7D%7B4%7D)
Part B. The correct quotient is (3 × 4)
Step-by-step explanation:
Part A.
To divide 84.36 by 12 we look for the Highest Common Factor of the whole number and the decimal portions of the numerator and the denominator individually as follows;
![\frac{84.36}{12} = \frac{84+0.3636}{12} = \frac{2 \times 2 \times 3 \times 7+0.01\times 12\times 3}{12} = \frac{12 \times 7+0.03\times 12}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B84.36%7D%7B12%7D%20%3D%20%5Cfrac%7B84%2B0.3636%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B2%20%5Ctimes%202%20%5Ctimes%203%20%20%5Ctimes%207%2B0.01%5Ctimes%2012%5Ctimes%203%7D%7B12%7D%20%3D%20%20%5Cfrac%7B12%20%20%5Ctimes%207%2B0.03%5Ctimes%2012%7D%7B12%7D)
Therefore, dividing 84.36 by 12 gives
= 7.03
When dividing 84.3·y by 12, therefore, we have;
![\frac{12 \times 7+0.3\times y}{12} = 7 +\frac{0.1\cdot y}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B12%20%20%5Ctimes%207%2B0.3%5Ctimes%20y%7D%7B12%7D%20%3D%207%20%2B%5Cfrac%7B0.1%5Ccdot%20y%7D%7B4%7D)
Part B.
The correct quotient should have factors of the numerator
Therefore the divisor 12 should be represented as follows
![\frac{12 \times 7+0.3\times y}{12} =\frac{12 \times 7+0.3\times y}{3 \times 4}](https://tex.z-dn.net/?f=%5Cfrac%7B12%20%20%5Ctimes%207%2B0.3%5Ctimes%20y%7D%7B12%7D%20%3D%5Cfrac%7B12%20%20%5Ctimes%207%2B0.3%5Ctimes%20y%7D%7B3%20%5Ctimes%204%7D)
The correct quotient therefore = (3 × 4)
0.000041 is the correct answer
Step-by-step explanation:
The domain is all the possible x values. Here, the smallest x value is 1, and the largest x value is 4.
1 ≤ x ≤ 4
Answer:
30.2 - 13.7=n
Step-by-step explanation:
To get how far he ran you have to subtract 30.2 from 13.7 therefore giving you 16.5 which will be the total distance he ran after lunch.