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.
Answer:
c
Step-by-step explanation:
Since both equations express y in terms of x we can equate the right sides
3x + 5 = - x + 3 ( add x to both sides )
4x + 5 = 3 ( subtract 5 from both sides )
4x = - 2 ( divide both sides by 4 )
x = - 0.5
substitute x = - 0.5 in either of the 2 equations
using y = - x + 3 then y = 0.5 + 3 = 3.5
solution is (- 0.5, 3.5 ) → c
Answer:
3x^2 -4x -4
Step-by-step explanation:
3x^2 – 8x – 2 + 4x – 2
Combine like terms
3x^2 -8x+4x -2 -2
3x^2 -4x -4
Answer: OPTION C.
Step-by-step explanation:
<h3>
The complete exercise is: "Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below:</h3><h3>
</h3><h3>
In this function
is the air pressure at the surface of the earth, and
is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 50% of the air pressure at the surface of the Earth"</h3><h3>
</h3>
Given the following function:

In order to calculate at what height the air pressure will be equal 50% of the air pressure at the surface of the Earth, you can follow these steps:
1. You need to substitute
into the function:

2. Finally, you must solve for
.
Remember the following property of logarithms:

Then, you get this result:
