Can u tell me what 1/3x28= Is ?
1 answer:
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Answer:
where
Step-by-step explanation:
Given that:
Amount of money to be donated by Gregory = $100
Amount of money to be donated for every book that a student will read = $15
The series becomes:
100, 115, 130, 145, 160, .....
To find:
The explicit formula to represent this problem situation.
Solution:
First of all, let us have a look at the difference of each term from its previous term.
Second term - First term = 115 - 100 = 15
Third term - Second term = 130 - 115 = 15
Fourth term - Third term = 145 - 130 = 15
The difference is same, therefore the given series is an Arithmetic Progression (AP).
We have to find the term of the given AP.
Formula for term:
is the first term and
is the common difference.
Here, = 115 (because $100 is the fixed amount so first term is taken as 115 when one book is read)
Putting the values, we get:
Therefore, formula to represent the situation is:
where
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.
