Answer:
19 years
Step-by-step explanation:
The attached spreadsheet shows the balance will be zero at the beginning of year 19, when the last $10,423.27 is withdrawn from the account.
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One could argue that the "nearest year" is year 18, when the balance after the withdrawal is less than $10,000.
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In the attached spreadsheet, the ending balance is 1.082 times the beginning balance (after deposits and withdrawals), which is the ending balance of the year before (after deposits).
In year 1 the beginning balance has 100,000 added. In year 2, the ending balance has 55,000 added. In year 4 and every year after, the beginning balance as 20,000 subtracted.
One. If one of the angles is 90° then there are only 90° degrees left for the other two angles. If angle two is half of 90°, that would make it a 45° angle meaning there is only another 45° left. Every triangle can have a total of 180° when you add all their angles together.
Answer:
x:y:z = 12:3:2
Step-by-step explanation:
x = 4y
2y = 3z ⇒ 4y = 6z
⇒ x = 4y = 6z
To find x:
Multiply the coefficients of y & z: 4 × 6 = 24
To find y:
Multiply the coefficients of x & z: 1 × 6 = 6
To find z:
Multiply the coefficients of x & y: 1 × 4 = 4
⇒ x:y:z = 24:6:4 = 12:3:2
Answer:
DA = 285.7 m
Step-by-step explanation:
First we need to find the side AB in the triangle ABC, and we can do this using Pythagoras' theorem:
AB^2 = BC^2 + AC^2
AB^2 = 300^2 + 400^2
AB^2 = 25000
AB = 500 m
We can find the angle ABC with the tangent relation:
tangent(ABC) = 400/300 = 4/3
ABC = 53.13°
From triangle ABC, we have:
ABC + BCA + CAB = 180°
53.13 + 90 + CAB = 180
CAB = 36.87°
From triangle DAC, we have:
DAC + ACD + CDA = 180
36.87 + 45 + CDA = 180
CDA = 98.13°
Now to find the side of DA, we can use law of sines in triangle DAC:
DA/sin(DCA) = AC/sin(CDA)
DA/sin(45) = 400/sin(98.13)
DA = 400 * 0.7071 / 0.9899 = 285.7258 m
Rounding to nearest tenth, we have DA = 285.7 m
