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4 years ago

Write an equation in standard form for the parabola that has a vertex (3,-2) and passes through the point (1,14)

Mathematics

1 answer:

guajiro [1.7K]4 years ago

3 0

You could use math way its an online calculator thats what i use to get these answers

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Someone help me with this one

Montano1993 [528]

Answer:

p' (4,-2)

Step-by-step explanation:

P is at ( -1,5)

We are moving it 5 units to the right so add 5 to the x

We are moving it 7 units down so subtract 7 from the y

p'( -1+5, 5-7)

p' (4,-2)

5 0

4 years ago

Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parr

Tcecarenko [31]

Answer:

The least possible number of coins the Pirate has = 81

Step-by-step explanation:

Given:

Pirate Jack has equal number of gold and silver coins.

When the pirate splits the coins into 7 equal piles he has 4 coins left.

When the pirate splits the coins into 11 equal piles he has 4 coins left.

Every pile has at least 1 coin.

To find the least possible number of coins Pirate Jack has.

Solution:

In order to find the least possible number of coins pirate Jack has, we must find the least common multiple of the number of piles the coins are split into.

So, the least common multiple of 7 and 11 can be found by listing the multiples.

$7= 7,14,21,28...............,77$

$11=11,22,33,44,55,66,77$

So, we find the least common multiple of 7 and 11 is 77.

Number of coins left = 4

Total number of coins the pirate must have = $77+4 =81$

We can check the answer by dividing 81 by 7 and 11. I both cases we get remainder = 4.

So, the least possible number of coins the pirate has = 81

6 0

4 years ago

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

I need help doing this problem

SIZIF [17.4K]

40 degrees I believe

4 0

3 years ago

LenKa [72]

The answer would be C because they say if 3 new students arrived each year.

4 0

3 years ago