Which of these is the algebraic expression for "some number to the power of 6?"
2 answers:
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Split up the interval [2, 5] into 
equally spaced subintervals, then consider the value of 
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be 
. This means the first rectangle's height would be taken to be 
when 
, so that the height is 
, and its base would have length 
. So the area under over the first subinterval is 
.
Continuing in this fashion, the area under over the 
th subinterval is approximated by 
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
The length of the interval is
Continuing in this fashion, the area under
and its value is given exactly by taking
Answer:
The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.
Step-by-step explanation:
Let the variable <em>X</em> represent the amount of land used for planting trees and <em>Y</em> represent the amount of land purchased.
The goal of the environmental initiative is to save at least 25 million hectares of rain forest.
That is:
<em>X</em> + <em>Y</em> = 25....(i)
Now it is provided that:
- The cost of planting trees is $ 400 per hectare.
- The cost of purchasing land is $ 260 per hectare.
- The initiative has a budget of $8,250 million.
Using the above data it can be said that:
400<em>X</em> + 260<em>Y</em> = 8250....(ii)
Solve equations (i) and (ii) simultaneously.
Then the value of <em>y</em> is:
Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.