The general equation of a line is:
When m is the gradient and x1 and y1 are the coordinates of the points on the line
Therefore:
When m is the gradient and x1 and y1 are the coordinates of the points on the line
Therefore:
The diagram shows several planes, lines, and points.
1 answer:
Answer:
The true statement is <u>Line h has points on planes R, P, and T</u>
Step-by-step explanation:
The rest of the question is the attached figure
According to the graph, we will check which option is true.
a. Line h intersects line f at two points, A and B (<u>Wrong</u>)
<u>Because</u>: h intersects line f at B only.
b. Line h is the intersection of planes R and T (<u>Wrong</u>)
<u>Because</u>: g is the intersection of planes R and T
c. Line h intersects plane P at point C (<u>Wrong</u>)
<u>Because</u>: h intersects plane P at point B
d. Line h has points on planes R, P, and T (<u>True</u>)
<u>Because </u>h has the point B on the plane P, h has the point A on the plane T
and the points of h on the plane R
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Answer:
Part A: The value of the simple interest investment at the end of three years is $12,220
Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08
Part C: The simple interest investment is better over the first three years
Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time
Step-by-step explanation:
Part A:
A = P + P r t, where
- A represents the value of the investment
- P represents the original amount
- r represents the rate in decimal
- t represents the time in years
∵ George deposits $10,000
∴ P = 10,000
∵ First option offers 7.4% per year simple interest
∴ r = 7.4% = 7.4 ÷ 100 = 0.074
∵ He may not withdraw any of the money for three years after
the initial deposit
∴ t = 3
- Substitute all of these values in the formula above
∴ A = 10,000 + 10,000(0.074)(3)
∴ A = 10,000 + 2,220
∴ A = 12,220
The value of the simple interest investment at the end of three years is $12,220
Part B:
, where
- A represents the value of the investment
- P represents the original amount
- r represents the rate in decimal
- n is a number of periods of a year
- t represents the time in years
∵ George deposits $10,000
∴ P = 10,000
∵ The second option offers a 6.5% interest rate compounded quarterly
∴ r = 6.5% = 6.5 ÷ 100 = 0.065
∴ n = 4 ⇒ quarterly
∵ He may not withdraw any of the money for three years after
the initial deposit
∴ t = 3
- Substitute all of these values in the formula above
∴
∴
∴ A = 12,134.08
The value of the compounded quarterly interest investment at the end of three years is $12,134.08
Part C:
∵ 12,220 > 12,134.08
∴ The simplest interest investment is better than the compounded
interest investment at the end of three years
The simple interest investment is better over the first three years
Part D:
I advise George to invest his money in the compounded interest investment if he will keep the money for a long time
Look to the attached graph below
- The red line represents the simple interest investment
- The blue curve represents the compounded interest investment
- (Each 1 unit in the vertical axis represents $1000)
- After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest
- After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest
