Answer:
its the 3cm i did it
Step-by-step explanation:
Answer:
1.) 8.09g ; 2) 206.7 years
Step-by-step explanation:
Given the following :
Half-life(t1/2) of Uranium-232 = 68.9 years
a) If you have a 100 gram sample, how much would be left after 250 years?
Initial quantity (No) = 100g
Time elapsed (t) = 250 years
Find the quantity of substance remaining (N(t))
Recall :
N(t) = No(0.5)^(t/t1/2)
N(250) = 100(0.5)^(250/68.9)
N(250) = 100(0.5)^3.6284470
N(250) = 100 × 0.0808590
= 8.0859045
= 8.09g
2) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?
Using the relation :
N / No = (1/2)^n
Where N = Amount of remaining or left
No = Original quantity
n = number of half-lifes
N = 12.5g ; No = 100g
12.5 / 100 = (1/2)^n
0.125 = (1/2)^n
Converting 0.125 to fraction
(1/8) = 1/2^n
8 = 2^n
2^3 = 2^n
n = 3
Recall ;
Number of half life's (n) = t / t1/2
t = time elapsed ; t1/2 = half life
3 = t / 68.9
t = 3 × 68.9
t = 206.7 years
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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.
