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Luda [366]
3 years ago
13

Write the expression 2/3 [ln(x) + ln(x^3-2) -ln(x+4)] as a logarithm of a single quantity.

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0
Lnx+lny=ln(xy)
lnx-lny=ln(x/y)
xlny=ln(y^x)

(2/3)(lnx+ln(x^3-2)-ln(x+4))=
(2/3)(ln((x)(x^3-2))-ln(x+4))=
(2/3)(\frac{ln((x)(x^3-2))}{ln(x+4)}=
(\frac{2ln((x^4-2x))}{3ln(x+4)}=
(\frac{ln((x^3-2x)^2)}{ln((x+4)^3)}



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Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. -2, 6, -18, 54,
aleksandrvk [35]

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Step-by-step explanation:

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r = 6/- 2 = - 18/6 = - 3

Therefore, the sequence is geometric.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

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a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = - 2

r = - 3

The explicit formula is

Tn = - 2 × (- 3)^(n - 1)

To find the 8th term, T8,

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3 years ago
Use the information frompart a to write an equation representing the number of colories burned each minute while bowling. Let m
Fofino [41]

Answer:

To find the number of calories burned:

Find the Metabolic Equivalent of Task (MET) value of the task.

Calculate the number of calories burned per minute. (MET x body weight in kg x 3.5) / 200.

Multiply the calories burned per minute by the number of minutes of activity.

Now, as per the question, weight is 125 pounds (lb), we will convert the weight in kilogram (kg) which is 1 lb = 0.453 kg, it means 125 lb = 56.7

Now we have to find the MET,

A metabolic equivalent (MET) value is a measurement of the energy cost of a specific physical activity for a specific period of time.

For example. A MET of 1 would be roughly equivalent to a person's energy expenditure from sitting still in a room temperature and not actively digesting food.

As per the Calorie guide value of MET for bowling is 3.9

Now the overall formula is

Calorie Burn (x) = ((MET * body weight in kg * 3.5) / 200) * (Number of minutes) m

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Finally, x = 3.87 m represents the number of calorie burned (x) while bowling m minutes.

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