Desmond fabricates a tiny microchip. It is square in shape, measuring 7.5 millimeters on each side. Draw Desmond's chip to scale
2 answers:
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<u>Given</u>:
The 11th term in a geometric sequence is 48.
The 12th term in the sequence is 192.
The common ratio is 4.
We need to determine the 10th term of the sequence.
<u>General term:</u>
The general term of the geometric sequence is given by
where a is the first term and r is the common ratio.
The 11th term is given is
------- (1)
The 12th term is given by
------- (2)
<u>Value of a:</u>
The value of a can be determined by solving any one of the two equations.
Hence, let us solve the equation (1) to determine the value of a.
Thus, we have;
Dividing both sides by 1048576, we get;
Thus, the value of a is
<u>Value of the 10th term:</u>
The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term , we get;
Thus, the 10th term of the sequence is 12.
4x + 6 < -6
First, subtract 6 from both sides. / Your problem should look like: 3x < -6 - 6
Second, simplify -6 - 6 to -12. / Your problem should look like: 3x < -12
Third, divide both sides by 4. / Your problem should look like: x <
Fourth, simplify
to 3. / Your problem should look like: x < -3
Answer: x < -3
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First, subtract 6 from both sides. / Your problem should look like: 3x < -6 - 6
Second, simplify -6 - 6 to -12. / Your problem should look like: 3x < -12
Third, divide both sides by 4. / Your problem should look like: x <
Fourth, simplify
Answer: x < -3
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Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
Step-by-step explanation:
The given is,
Investment = $ 8000
No. of years = 15 years
Interest rate, i = 3.1 %
( compounded monthly )
Step:1
For for calculating future value with compound interest monthly,
.................(1)
Where,
A = Future amount
P = Initial investment
r = Rate of interest
n = Number of compounding in a year
t = Time period
Step:2
From given values,
P = $8000
r = 3.1%
t = 15 years
n = 12 ( for monthly)
Equation (1) becomes,
A = $ 12728.48
Result:
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.