The area of a rectangle is calculated by multiplying the length of the rectangle and the width of the rectangle. In this case, the length (the longer side) is 2 2/3 feet while the width (shorter side) is 1 2/3 feet. To multiply fraction, first convert mixed numbers into improper fractions:
2 2/3 = 8/3
1 2/3 = 5/3
Multiplying the two fractions yield:
8/3 x 5/3 = 40/9 ft2
The final answer is 40/9 ft2 or 4 4/9 ft2.
Answer:
(3, 3 )
Step-by-step explanation:
Under a translation < 8, 0 > then
A(- 5, - 3 ) → (- 5 + 8, - 3 + 0 ) → (3, - 3 )
The line with equation y = 0 is the x- axis
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
(3, - 3 ) → (3, 3 )
The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is
(x - x^2)^2 * sqrt(3)/4.
Integrating from x = 0 to x = 1, we have
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
Multiplying binomial and polynomials can be easy as long as you follow the steps for example:
Let's say you were multiplying 3x-3 and x+2
(3x-3)(x+2)
remember FOIL
OR think about it like this(see attatchment)
3x^2 + 3x -6 is what you should get
