BuilderBoi

Note that in every term, the numerator increases by 1, and the denominator decreases by 1. 

Because the first term starts in 1 and increases by 1, the number of terms is the last term. 

Can you take it from here?

Note that the area of the overlapping region is basically the area of the triangle without the 2 smaller triangles in the corner. 

Because the distance from the center vertice to the edge of the square is \(10 \div 2 = 5\), the smaller triangle has a height of 1. 

This means that the 2 smaller triangles are congruent and similar to the larger triangle by a ratio of \(1:6\) 

So, the area of each triangle is \({1 \over 6} ^2 \times 18= {{1 \over 2}}\), meaning the area of the overlapping region is \(18 - (2 \times {1 \over 2}) = \color{brown}\boxed{17}\)

Use the distance formula to calculate the distance between the 2 points (this is the radius)

Now, use the radius to find the area of the circle. 

There are \(4!\) ways to order the chickens 

There are \(6!\) ways to order the cats. 

There is only 1 way to order the dog. 

There are \(3!\) ways to order the chickens, cats, and dogs. 

So, there are \(4! \times 6! \times 3 = \color{brown}\boxed{51840}\) ways. 

The equation has asympotes when the denominator is 0.

This means that \(3x^2 + 6x + 2 = 0\).

Now, use Vieta's to solve for the sum...

Here's hint: Draw a line with points \((1,7)\) and \((13,-16)\).

K will be the integer that is closest to the y-value when x = 5. 

Note that n is always exactly 1 less than a. 

Can you take it from here?

Note that only the inside 4 x 4 x 4 cube will not be painted. 

Can you take it from here?

answered

https://web2.0calc.com/questions/percent_93