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Leokris [45]
3 years ago
6

Plot two points that are 888 units from Point \blueD{B}Bstart color #11accd, B, end color #11accd and also share the same xxx-co

ordinate as Point \blueD{B}Bstart color #11accd, B, end color #11accd.
Stuck

Mathematics
1 answer:
Debora [2.8K]3 years ago
4 0

Answer:

B' = (-6,-8)

Step-by-step explanation:

Given

Point\ B = (-6,0)

Required

Plot a new point that is 8 units down and also has the same x coordinate

Represent the new point with B'

In Point\ B = (-6,0)

x = -6 and y = 0

This means that B' has an x coordinate of -6

Next, is to determine the y coordinate

If a point (x,y) is translated b units down, the new point is (x, y - b)

In this case:

The y coordinate of B is 0 and b = 8. So, the new y coordinate is: 0 - 8 = -8

So, we have:

B' = (-6,-8)

See attachment

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Here is the answer for prove that cos theta by 1 minus tan theta + sin theta by 1 minus cot theta equal to sin theta + cos theta

3 0
3 years ago
On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

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