Answer:
see explanation
Step-by-step explanation:
the domain is the set of x- coordinates from the ordered pairs , that is
domain : { - 7, - 3, 0, 5 }
the range is the set of y- coordinates from the ordered pairs, that is
range : { - 2, 1, 2, 5 }
Answer:
The volume of this pyramid is 16 cm³.
Step-by-step explanation:
The volume 
of a solid pyramid can be given as:
,
where
is the area of the base of the pyramid, and
is the height of the pyramid.
Here's how to solve this problem with calculus without using the previous formula.
Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.
Refer to the sketch attached. Let the vertical distance from the vertice be 
cm.
- At the vertice of this pyramid,
and the length of a side of the square is also 
. - At the base of this pyramid,
and the length of a side of the square is 
cm.
As a result, the length of a side of the square will be
.
The area of the square will be
.
Integrate the area of the horizontal cross-section with respect to
- from the top of the pyramid, where ,
- to the base, where .
.
In other words, the volume of this pyramid is 16 cubic centimeters.
The only difference between the two following expressions is
their exponent though it’s equal. If you would analyze carefully, the two
expressions are equal since 2/4 is just equal to ½. The two expressions are
equal in value so the presentation of the exponent is their only difference.
Answer:
-8.5 is a rational number
Step-by-step explanation:
The whole numbers are all the numbers you can reach if you start at 1 (or 0, if that's your thing) and count forward - 1, 2, 3, 4, on and on forever. The integers are all the numbers we can get by adding and subtracting two whole numbers - this includes situations like 3 - 4, where we're "taking away" more than we have: we simply invent numbers less than zero, the negatives, and that gives 3 - 4 a value - the number -1.
So we can add, subtract and multiply any of these numbers together and we end up somewhere else our world of integers, but the moment we want to ask a question like "what numbers are between 0 and 1?" the integers just aren't enough. We need fractions, and for that purpose we create the rational numbers, which include all the fractional parts between integers, as well as the integers themselves.
-8.5 is halfway between the integers -8 and -9, and since it has a fractional part, it must be a rational number.
Answer:
5.5
Step-by-step explanation:
The y-intercept of the line graph shown above is the value of the point where the line cuts the y-axis. The y-intercept of this graph is between 5 and 6. However, we can get an accurate value by calculation. This can be done by generating an equation of the line.
Recall the slope-intercept equation, 
, where m = slope of the line, b = y-intercept.
To generate the equation of the line, first find slope using the points (-2, 7) and (6, 1):
.
Substitute m = ¾ and the coordinates (6, 1) into the slope-intercept equation to find the y-intercept (b):
Therefore, b = y-intercept = 5.5.
To generate the equation of the line, plug in the values of m and b, we would have:
y = ¾x + 5.5
The y-intercept of the line of the graph is 5.5.
