The question asks: "Let
. Find the largest integer n so that <span>f(2) · f(3) · f(4) · ... · f(n-1) · f(n) < 1.98"
The answer is n = 98</span>Explanation:
First thing, consider that the function can be written as:
Now, let's expand the product, substituting the function with its equation for the requested values:
As you can see, the intermediate terms cancel out with each other, leaving us with:
This is a simple inequality that can be easily solved:
200n < 198(n + 1)
200n < 198n + 198
2n < 198
n < 99
Hence, the greatest integer n < 99 (extremity excluded) is
98.
Area of the figure is 71.13
Step-by-step explanation:
- Step 1: Area of the figure can be found out by considering the parts individually as a semicircle, rectangle and a right triangle. Then add all the areas.
Find the area of the semicircle. Here, radius = 3.
Area = 1/2 πr² = 1/2 × 3.14 × 3² = 14.13
- Step 2: Find the area of the rectangle. Here, width = 6 and length = 8
Area = length × width = 8 × 6 = 48
- Step 3: Find the area of the right triangle. Here the height = width of the rectangle = 6 and base = 11 - 8 = 3
Area = 1/2 × base × height = 1/2 × 3 × 6 = 9
- Step 4: Find the total area.
Area of the figure = 14.13 + 48 + 9 = 71.13
I'm not exactly sure but I really want to say 1,6
The first step would be the square of the parenthesis.
-5x²(4x∧6-x∧4)
4x∧6 means 4x to the sixth power.
I hope that helps.