You have to use the geometric mean of right triangles here. Your ratio is set up like this: 
. That gives you 
and that 
. To find z in the second part, use the Pythagorean Theorem. 
and z = 6. In the third part, the student should have had the length of the hypotenuse as the denominator in the second ratio, which is 8. So your answer there is the second one down. In order to do that last one you need to find the hypotenuse in the triangle that has legs of 4 and 10. Using Pythagorean's theorem we find that that length is 
. Now set up your geometric mean: 
. Cross multiply to get 4x + 16 = 116 and that 4x = 100. Solve for x to get x = 25
What are the next three terms in the sequence? -3, 6, 15, 24
1 answer:
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Answer:
A) 277 million years
Step-by-step explanation:
Here, decay of U-238 is first order reaction. (since most of the nuclear decays are first order).
so, the equation t = × ln(
)
where, t = time from start of reaction
k = reaction constant
A(0) = initial concentration; A = present concentration.
⇒ 4.5 billion = 4500 million years = × ln2.
Now, given 95.82% of parent U-238 isotope is left.
⇒ t = × ln(
)
t = × ln(
)
⇒ t ≅ 277 million years.