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Reptile [31]
2 years ago
9

Help me please by solving and showing the steps:)

Mathematics
1 answer:
Lorico [155]2 years ago
3 0

Answer:

-\frac{3\sqrt[3]{t} }{2}

Step-by-step explanation:

1: Write g(t) as y, resulting in y=-\frac{8}{27}t^3

2: Interchange the variables y and t, resulting in t=-\frac{8}{27}y^3

3: Multiply both sides by 27, resulting in 27t=-8y^3

4: Divide both sides by -8, resulting in -\frac{27t}{8}=y^3

5: Find the cube root of both sides, resulting in \sqrt[3]{-\frac{27t}{8} }=y

6: Apply a radical rule, resulting in -\sqrt[3]{\frac{27t}{8} } =y

7: Apply another radical rule, resulting in -\frac{\sqrt[3]{27t} }{\sqrt[3]{8} } =y

8: Simplify the denominator, resulting in  -\frac{\sqrt[3]{27t} }{2} =y

9: Apply yet another radical rule, resulting in -\frac{\sqrt[3]{27}\sqrt[3]{t}   }{2} =y

10: Simplify \sqrt[3]{27}, resulting in -\frac{3\sqrt[3]{t}   }{2} =y

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