Answer:
rule: f(n) = n³
missing numbers: 125, 216, 343, 512, 729
Step-by-step explanation:
Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.
1 = 1·1·1 = 1³
8 = 2·2·2 = 2³
27 = 3·3·3 = 3³
64 = 4·4·4 = 4³
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The rule is ...
f(n) = n³
The cubes of 5 through 9 will complete the set of numbers ...
1, 8, 27, 64, 125, 216, 343, 512, 729
Answer:
k = - 6.6667
Step-by-step explanation:
this is quite very simple to begin. I would encourage you take other practice questions similar to help with understanding it.
let us begin.
Given that ;
dT/dt = k ( Tm - T) where Tm is the temp of the medium
dT/dt = 5 degrees Celsius per minute when T = 70
so we have that, 5 = k ( 25 - 70)
remember to convert 5 degree celsius per minute to seconds
we have that;
5*60(sec) = k ( 25 - 70)
k = 5*60 / ( 25 - 70)
k = - 6.6667
note K is negative because we consider it for cooling process (temp decreasing).
cheers i hope this helps!!!
Answer:
3 groups of 5 sopranos and 12 altos
Step-by-step explanation:
Step 1. Convert 3 1/4 to an improper fraction.
3 * 4 + 1/4 - 1 5/8
Step 2. Simplify 3 * 4 to 12
12 + 1/4 - 1 5/8
Step 3. Simplify 12 + 1 to 13
13/4 - 1 5/8
Step 4. Convert 1 5/8 to an improper fraction.
13/4 - 1 * 8 + 5/8
Step 5. Simplify 1 * 8 to 8
13/4 - 8 + 5/8
Step 6. Simplify 8 + 5 to 13
13/4 - 13/8
Step 7. Find the Least Common Denominator (LCD) of 13/4, 13/8
LCD = 8
Step 8. Make the denominators the same as the LCD
13 * 2/ 4 * 2 - 13/8
Step 9. Simplify. Denominators are now the same
26/8 - 13/8
Step 10. Join the denominators
26 - 13/8
Step 11. Simplify
13/8
Step 12. Convert to a mixed fraction
1 5/8
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