Answer:
Step-by-step explanation:
Mathematical Sentence:
[tex]d=rtk[/tex]
Solution for the constant of variation or k:
Given: [tex]d=45[/tex], [tex]r=15[/tex], [tex]t=14[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]d=rtk[/tex]
Solution:
[tex]d=rtk\\45=(15)(14)k\\45=210k\\\frac{45}{210}=\frac{210k}{210}\\\frac{45}{210}=k\\k=\frac{3}{14}[/tex]
Final solution for d:
Given: [tex]r=21[/tex], [tex]t=8[/tex], [tex]k=\frac{3}{14}[/tex]
Find: [tex]d=?[/tex]
Formula: [tex]d=rtk[/tex]
Solution:
[tex]d=rtk\\d=(21)(8)(\frac{3}{14})\\d=(3)(8)(\frac{3}{2})\\d=(3)(4)(3)\\\boxed{d=36}[/tex]
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