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4 years ago

Suppose the value of a rare quarter is increasing exponentially. In 2009 it was worth

Mathematics

1 answer:

morpeh [17]4 years ago

7 0

In 2029 worth in $1.60 because each year go up $0.04

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Find the equation of ellipse passing throgh (1,4) and (-3,2)

irinina [24]

Answer:

$\displaystyle \frac{ {3x}^{2} }{ 35 } + \frac{{2y}^{2} }{ 35 } = 1$

Step-by-step explanation:

we want to figure out the ellipse equation which passes through (1,4) and (-3,2)

the standard form of ellipse equation is given by:

$\displaystyle \frac{(x - h {)}^{2} }{ {a}^{2} } + \frac{(y - k {)}^{2} }{ {b}^{2} } = 1$

where:

(h,k) is the centre
a is the horizontal redius
b is the vertical radius

since the centre of the equation is not mentioned, we'd assume it (0,0) therefore our equation will be:

$\displaystyle \frac{ {x}^{2} }{ {a}^{2} } + \frac{{y}^{2} }{ {b}^{2} } = 1$

substituting the value of x and y from the point (1,4),we'd acquire:

$\displaystyle \frac{ 1}{ {a}^{2} } + \frac{16}{ {b}^{2} } = 1$

similarly using the point (-3,2), we'd obtain:

$\displaystyle \frac{ 9}{ {a}^{2} } + \frac{4 }{ {b}^{2} } = 1$

let 1/a² and 1/b² be q and p respectively and transform the equation:

$\displaystyle \begin{cases} q + 16p = 1 \\ 9q + 4p = 1 \end{cases}$

solving the system of linear equation will yield:

$\displaystyle \begin{cases} q = \dfrac{3}{35} \\ \\ p = \dfrac{2}{35} \end{cases}$

substitute back:

$\displaystyle \begin{cases} \dfrac{1}{ {a}^{2} } = \dfrac{3}{35} \\ \\ \dfrac{1}{ {b}^{2} } = \dfrac{2}{35} \end{cases}$

divide both equation by 1 which yields:

$\displaystyle \begin{cases} {a}^{2} = \dfrac{35}{ 3} \\ \\ {b}^{2} = \dfrac{35}{2} \end{cases}$

substitute the value of a² and b² in the ellipse equation , thus:

$\displaystyle \frac{ {x}^{2} }{ \dfrac{35}{3} } + \frac{{y}^{2} }{ \dfrac{35}{2} } = 1$

simplify complex fraction:

$\displaystyle \frac{ {3x}^{2} }{ 35 } + \frac{{2y}^{2} }{ 35 } = 1$

and we're done!

(refer the attachment as well)

8 0

3 years ago

Write this number in expanded form.4,408,730

Elena L [17]

4,000,000 +400,000 +0 +8,000 +700 +30 +0

6 0

3 years ago

Read 2 more answers

he population of a city grows at a rate of 5% per year. The population in 1990 was 400,000. What would be the predicted current

SVETLANKA909090 [29]

5 percent of 400,000 is 20,000
It is about 28 years from 1990
20,000 * 28 = 560,000
560,000 + 400,000 = 960,000
So the estimated current popu;ation in a city is 960,000.
Hope this helps!

7 0

3 years ago

I need the answer to (6)(-5)

Mama L [17]

Answer:-30

Step-by-step explanation: you do 6 time 5 which is 30 and it is a negative times a positive which equals a negative so it is a negative

6 0

3 years ago

Given that f(x)= 2/x^2, what is the value of f(x) when x = 2?

Butoxors [25]

Answer:

0.5

Step-by-step explanation:

2/2^2

= 2/4

= 1/2

= 0.5

3 0

3 years ago