Answer:
Certain
Step-by-step explanation:
In a fraction 25/25 is a whole/1 and when you find probability it is from a scale of 0 to 1. 0 is impossible and 1 is certain. So if you have 25/25 probability something will happen it is certain to happen. Hope this helped you!
Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.
Here's another way to look at it:
When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.
For any tangent on g(x), its slope is m = (dy)/(dx)
The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here.
So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.
The <u>correct answers</u> are:
<u>Perpendicular cross-section of a pyramid is a triangle</u>.
<u>Perpendicular cross-section of an oblique cylinder is an ellipse.</u>
<u>Parallel cross-section of a sphere is a circle.</u>
<u>When a rectangle is rotated about the y-axis, a cylinder is formed.</u>
<u>When a right triangle is rotated about the y-axis, a cone is formed.</u>
Explanation:
Cutting a <u>cross-section of a pyramid</u> perpendicular to the base would form a triangle. Your "slice" would go from the apex of the pyramid straight to the base. Where the cut goes through the slanted faces of the pyramid would form the slanted sides of the triangle. Where the cut goes through the base of the pyramid would make the base of the triangle.
Cutting a <u>cross-section of an oblique (non-right) cylinder</u> would form an ellipse (oval). Since the cylinder is not right, it is slanted. This means going perpendicular to the base of the cylinder would not go straight (horizontally) through the cylinder; instead it slants, which "stretches" the cross-section, forming an ellipse.
Any <u>cross-section of a sphere</u> is a circle, since a sphere is perfectly round with no base.
When <u>rotating a rectangle</u> about the y-axis, imagine rotating a piece of paper. The shape formed by doing this would "bend" the rectangle around the axis, forming a cylindrical shape.
When <u>rotating a triangle</u> about the y-axis, we can imagine the same situation we did with the rectangle; the difference is that the triangle goes in a point, which means this new figure will be as well. This would make it a cone rather than a cylinder.
Answer:
a) A = π30² = 900π cm² ≈ 2,827 cm²
b) V = Ah = 900π80 = 72000π cm³ ≈ 226,195 cm³
Step-by-step explanation: