Help me solve 6x+5-3x=26
2 answers:
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Answer:
A
Step-by-step explanation:
The base of a solid in the region enclosed by the graphs of <em>y</em> = eˣ, <em>y</em> = 0, <em>x </em>= 0, and <em>x</em> = 1. Each cross-section perpendicular to the <em>x</em>-axis is an equilateral triangle. We want to find the volume of the solid.
Please refer to the graph below. We are concerned with the red region.
In order to find the volume, we essentially sum up the area of the figure at each <em>x</em> value. So, we integrate from <em>x </em> = 0 to <em>x </em>= 1.
The area for an equilateral triangle is given by:
Where <em>s</em> is the side length of the triangle.
Since the triangle lies perpendicular on the region, the side length of the triangle at <em>x</em> is simply <em>y</em>, which is eˣ.
Therefore, our volume is:
Substitute:
Evaluate the integral. Simplify:
Integrate using u-substitution:
Evaluate:
Therefore, the volume of the solid is:
Our answer is A.
First, we are going to find the painted area of his house. We know that the total area he needs to paint is 4000 square meters, so 4000 is the area of this house. Now, to find the 62.5% of that area, we are going to multiply it by 
:
Painted area=
Now, to find <span>rate, in square feet per hour, we are going to divide the painted area by the number of hours:
Rate=</span>
We can conclude that Kyler paints at a rate of 434.78 square feet per hour.
Painted area=
Now, to find <span>rate, in square feet per hour, we are going to divide the painted area by the number of hours:
Rate=</span>
We can conclude that Kyler paints at a rate of 434.78 square feet per hour.