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.
We'll do the first one. I can't read the variable, but it looks like a
so that's what I'll use, but it doesn't matter.
First, get the variable by itself:
You get that before you multiply each side by two.
Now, you color the line so that all values that are less than 6 are shaded, so you put an open circle at 6 since it's not included and then you shade everything to the left.
Answer:
f(x) = (1/2)(x-2)^2(x+1)(x+2)
Step-by-step explanation:
You can determine this by looking at the zeroes of the graph. For any zero that goes through the x-axis, the power of that zero is odd. For any zero that that "bounces" from the x-axis, the power of that zero is even.
Starting from left to right, we can see that the first zero, -2, goes through the x-axis. That means (x+2) is raised to an odd power. The second zero, -1, also goes through, so (x+1) is raised to an odd power. The last zero, 2, bounces off the x-axis, so (x-2) is raised to an even power. The only functions that satisfy this criteria are function 1 and 2.
However, we are not done yet. We need to figure out which multiplier value (1/2, 1/4) is correct. To do this, we plug in 0 for x, since we know that the y-intercept is 4. When we plug in 0, we see that f(0) = 4 for the first function. Therefore, the first function is the answer.
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Answer:
Approx 61.554 feet
Step-by-step explanation:
Since we are dealing with the opposite and adjacent sides, we will use tangent as our ratio.
Since the angle of elevation is 72 degrees, the left side of our equation is 
.
The right side of the equation is opposite over adjacent.
Set these equal to each other.
Simplify.
x is approximately 61.554.
Answer:
it a
Step-by-step explanation:
