To find the total area of the octagon you can find the area of the rectangle that is created by the entire figure and subtract the areas of the four congruent right triangles.
(10 cm x 6 cm) - [4(1/2 x 2 x 2)]
60 cm² -8 cm² = 52 cm²
The total area of the octagon is 52 cm².
Answer:
for this type of question, integral by parts should be used . This involves using the formula for intregation by parts:
intudv=uv-intvdu.
lets first break apart the x and e10x into two parts - "u" and "v"
where u = x.
however, we need to find the value of v. in order to do this, we can integrate dv/dx in order to get to v.
the value of dv/dx is : e10x
u = x dv/dx = e10x
as seen in the formula, you need to have a value for u, dv, v and du.
therefore in order to get du you must differentiate u:
u = x
du/dx = 1
du = 1dx = dx
du = dx
in order to get v you need to integrate dv/dx:
\displaystyle \inte10x dx = 1/10 x10x
now that we have both parts, we can put this back into the formula.
intudv=uv-intvdu.
\displaystyle \intxe10x = x * 1/10e10x - \displaystyle \int1/10e10x dx
Step-by-step explanation:
1. The x-intercepts are x = 0 and x = 6. You can find these by looking for where the line crosses the x-axis. You can see here that it does so at 0 and 6.
2. The maximum value for this function is looking for the f(x) value at the highest point. In this case, you will see that f(x) at the highest point is 120. This happens at x = 3. Once again, this can be found just by looking for the highest point on the graph.
3. Since that is the absolute highest point, it is also the point where is goes from increasing to decreasing. As a result, we know the increasing interval is x<120 and the decreasing interval is x > 120.
4. Finally, the average rate of change between 3 and 5 is -30. You can find this by determining the amount of change in f(x) and dividing it by the amount of change in x. The basic formula is below.
-30
The cost of 8 pounds of oranges based on the total cost of 5 pounds bought is 12.00
What is the cost for a pound of oranges?
The cost of a pound of oranges based on the rate at which 5 pounds were bought and 8 pounds would also be bought is determined as the amount paid for 5 pounds of oranges divided by the number of pounds of oranges bought
cost per pound of oranges=cost of 5 pounds/5 pounds
cost per pound of oranges=7.50/5
cost per pound of oranges=1.50
Based on the 1.50 per pound, the cost of 8 pounds is the cost per pound multiplied by 8 pounds
cost of 8 pounds of oranges=1.50*8pounds
cost of 8 pounds of oranges=12.00
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