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3 years ago

PLEASE HELP! LINE DILATIONS DUE TOMORROW! ILL MARK BRAINLIEST IF YOU EXPLAIN! TYSMMMMM

Mathematics

2 answers:

Ilya [14]3 years ago

8 0

It is b
gn hope it helps

kirill115 [55]3 years ago

6 0

The answer is B. The +2 is the slope

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A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each mon

olga_2 [115]

FIRST MODEL:

Well the model for the value of the house is:

$V={ \left( \frac { 11 }{ 10 } \right) }^{ t }\cdot 120000$

V = Value

t = Years passed {t≥0}

-----------------------

When t=0, V=120000

When t=1, V=132000

When t=2, V=145200

etc... etc...

---------------------------

Now, this model is actually curved so there is no constant rate of growth each month. We can only calculate what the rate of growth is at a particular time. If we want to find out the rate of growth at a particular time, we must differentiate the formula (model) above.

--------------------------

$V={ \left( \frac { 11 }{ 10 } \right) }^{ t }\cdot 120000\\ \\ \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ t }\cdot 120000 \right) } }$

$\\ \\ \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ t } \right) } } +\ln { \left( 120000 \right) } \\ \\ \ln { V=t\ln { \left( \frac { 11 }{ 10 } \right) } } +\ln { \left( 120000 \right) }$

$\\ \\ \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \\ \\ V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\\ \\ \therefore \quad \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^{ t }\cdot 120000$

Plug any value of (t) that is greater than 0 into the formula above to find out how quickly the investment is growing. If you want to find out how quickly the investment was growing after 1 month had passed, transform t into 1/12.

The rate of growth is being measured in years, not months. So when t=1/12, the rate of growth turns out to be 11528.42 per annum.

SECOND MODEL (What you are ultimately looking for):

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

V = Value of house

t = months that have gone by {t≥0}

Formula above differentiated:

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000\\ \\ \ln { V } =\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000 \right) }$

$\\ \\ \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } } \right) } } +\ln { \left( 120000 \right) }$

$\\ \\ \ln { V=\frac { t }{ 12 } } \ln { \left( \frac { 11 }{ 10 } \right) } +\ln { \left( 120000 \right) }$

$\\ \\ \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) }$

$\\ \\ V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\\ \\ \therefore \quad \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

When t=1, dV/dt = 960.70 (2dp)

dV/dt in this case will measure the rate of growth monthly. As more money is accumulated, this rate of growth will rise. The rate of growth is constantly increasing as the graph of V is actually a curve. You can only find out the rate at which the house value is growing monthly at a particular time.

6 0

3 years ago

A square market has an area of 36 square meters. How long is each side?

podryga [215]

Answer:The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6.

Step-by-step explanation:

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3 years ago

Find the missing term in the equation below (?+5)+(3x-2)=8x+3

soldi70 [24.7K]

Answer: 5x

Step-by-step explanation:

5x + 3x = 8x

5 0

3 years ago

Read 2 more answers

What does 3y-y equal?

Novosadov [1.4K]

Answer:

$2y$

Step-by-step explanation:

You need to subtract the coefficients to get the answer.

Let's look at the equation...

$3y-y$

The coefficient is 3 and 1

So, you do 3-1

You get 2

So...

$3y-y=2y$

4 0

3 years ago

How many ways are there to travel in xyz space from the origin (0, 0, 0) to the point (4, 3, 5) by taking steps one unit in the

Virty [35]

I would think you would have to walk the 4 spaces out on the X axis. I would then turn and walk 5 spaces on the Z axis before turning up to walk the last 3 steps on the Y axis.

I think any other way would cause you to move in a negative direction. I hope this helps.

5 0

3 years ago