Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
- a² = b² +c² -2bc·cos(A)
- k² = 31² +53² -2·31·53·cos(37°)
<h3>Comparison</h3>
Comparing the two equations, we note these correspondences:
Comparing these values to the given information, we see that ...
- KN = c = 53 . . . . . . . . . . matching values 53
- NM = a = k . . . . . . . . . . . matching values k
- KM = b = n = 31 . . . . . . . matching values 31
- ∠K = ∠A = 37° . . . . . . . matching side/angle names
Abby apparently knew that ∠K = 37° and n = 31.
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<em>Additional comment</em>
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
Answer:
the answer is 31.9 years
Step-by-step explanation:
initial mass, 
= 150 gram
half life, 
= 32 years
new mass = half of initial mass = M = 0.5
formula , M = 
where x is the number of years required.
therefore 0.5 = 
therefore -0.0217 x = 
therefore x = 
= 31.942
3 because 3 packs of 12 is 36 and that is the same product as 4 packs of 9
<u><em>Answer:</em></u>
volume of sphere = 288π ft³
<u><em>Explanation:</em></u>
volume of sphere = 
where pi is a constant and r is the radius of the sphere
<u>We are given that: </u>
The diameter of the sphere is 12 ft.
<u>This means that</u> the radius = 
<u>Substitute with the radius in the above equation to get the volume as follows:</u>
volume = 
ft³
Hope this helps :)
