Rate of change: 25L of water per minute
1. Look on the x axis at the 1
2. Look at the y coordinate to identify the rate of change.
(You can do extra steps with rise and run and scaling down but this is the easier way ;) )
To do this, change into common denominators. The common denominator is 21 so change the problem from 1/3 + 1/7 to 7/21 + 3/21. This gives you 10/21. It is already in simplest form.
The area of a shape is the amount of space it can occupy.
- <em>The same hallway be painted with the same pattern, but using twice as much black paint as white paint</em>
- <em>The length of the hallway is 40 feet</em>
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From the complete question (see attachment), the length of the white area is:
The width is:
So, the area of the white segment is:
The length of the black area is:
The width is:
So, the area of the black segment is:
So, their areas are:
--- white area
--- black area
<u>The paints</u>
The equation is given as:
Substitute the areas
Collect like terms
Divide both sides by 36
Because x has a positive real value, then the <em>same hallway be painted with the same pattern, but using twice as much black paint as white paint</em>
<u>Length of the hallway</u>
To calculate the length of the hallway, we simply equate both areas;
Collect like terms
Divide both sides by 6
So, the length of the hallway is the sum of the following lengths:
So, we have:
Substitute 4 for x
So, the length of the hallway is 40 feet
Read more about areas at
brainly.com/question/5688437
Answer:
-5.99, -3, -6, -5.9, -1, -5.999, -5, 2
Step-by-step explanation:
this symbol: ≥, means that d is greater than or equal to -6, so you select everything that is either greater than, or equal to -6.
Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,
The integral with respect to <em>x</em> is trivial:
For the remaining integral, integrate term-by-term to get
Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.