Answer:
(a) 0.4
(b) a = 3
Step-by-step explanation:
(a) The area under the curve from x=4 to x=6 is 0.2 units high and 2 units wide, so is 0.2·2 = 0.4. (The area of a rectangle is the product of length and width.)
(b) The area is 0.2 and the height of the curve is 0.2, so the width of the region of concern is 0.2/0.2 = 1. (Again, area = height·width, or width = area/height.) 1 unit from the left end is found at X=3, so a = 3.
Answer: This is true because everything in the first equation was multiplied equally to get to the second equation. Every part was multiplied by three. The first equation is x-7=3 and the second can be seen as 3(x-7=3). The three will not affect x seeing that the entire equation had the same thing done to it.
If you picture a cylinder rolled out flat. there would be two circles for top and bottom and then a rectangle for the side. The rectangle would have width equal to height and length equal to circumference.
So then the areas of the pieces are added together to get total surface area.
= 2pi(3x-2)^2 + 2pi(3x-2)(x+3)
and you can simplify this is you want by multiplying through and combining like terms.
= 2pi(12x^2 - 5x -2)
or factor more to simplify the solution.
= 2pi(3x-2)(3x-2+x+3)
= 2pi(3x-2)(4x+1)