Answer:
44.2 years
Step-by-step explanation:
If we assume the interest is compounded annually and the investment is a one-time deposit into the account, its value each year is multiplied by 1+6.25% = 1.0625. After n years, the value in the account will be ...
19000 = 1300·1.0625^n
Dividing by 1300 and taking logs, we have ...
log(19000/1300) = n·log(1.0625)
log(190/13)/log(1.0625) = n ≈ 44.24 . . . . years
It will take about 44.2 years for the account to reach $19,000.
Problem 2
Part (a)
The 3D shape formed when rotating around the y axis forms a pencil tip
The shape formed when rotating around the x axis is a truncated cone turned on its side.
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Part (b)
Check out the two diagrams below.
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Problem 3
Answer: Choice A and Choice C
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Explanation:
Think of stacks of coins. Let's say we had 2 stacks of 10 quarters each. The quarters are identical, so they must produce identical volumes. Those sub-volumes then add up to the same volume for each stack. Now imagine one stack is perfectly aligned and the other stack is a bit crooked. Has the volume changed for the crooked stack? No, it hasn't. We're still dealing with the same amount of coins and they yield the same volume.
For more information, check out Cavalieri's Principle.
With all that in mind, this leads us to choice C. If the bases are the same, and so are the heights, then we must be dealing with the same volumes.
On the other hand, if one base is wider (while the heights are still equal) then the wider based block is going to have more volume. This leads us to choice A.
Answer:
y = 3
Step-by-step explanation:
The vertex of the parabola is (1,4) and the axis of the parabola is parallel to the positive y-axis.
So, the equation of the parabola will be (x - 1)² = 4a(y - 4) ....... (1)
Now, we have to get the value of a since the equation id the directrix is y = 4 - a.
Now, the parabola passes through the point (3,5) {Obtained from the graph).
Therefore, from equation (1), we get, 2² = 4a × 1, ⇒a = 1
Therefore, the equation of the directrix is y = 4 - 1 = 3. (Answer)
80 * 3.5 = 280
she travels around 280km in 3.5 hours.
2 parallel lines with shading in opposite directions.