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3 years ago

Expanded form: (4a+4b)^3

Mathematics

1 answer:

TiliK225 [7]3 years ago

7 0

Step-by-step explanation:

use the formula: (a+b)³ = a³+3a²b+3ab²+b³

and place the corresponding values.

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NO LINKS!! Please help me with this problem

Vera_Pavlovna [14]

Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.

Now,

it's vertex is given, I.e (7 , -5)

so, length of semi transverse axis will be equal to distance of vertex from centre, i.e

a = 7 - 3 = 4 units

Now, it's focus can be represented as ;

$\qquad \sf \dashrightarrow \: (3 + ae, - 5 )$

so,

ae + 3 = 9

and we know, a = 4

$\qquad \sf \dashrightarrow \: 4e + 3 = 9$

$\qquad \sf \dashrightarrow \: 4e = 6$

$\qquad \sf \dashrightarrow \: e = \cfrac{3}{2}$

Now, let's find the measure of semi - conjugate axis (b)

$\qquad \sf \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)$

$\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)$

$\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )$

$\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )$

$\qquad \sf \dashrightarrow \: {b}^{2} = 20$

$\qquad \sf \dashrightarrow \: b = \sqrt{20}$

So, it's time to write the equation of hyperbola, as we already have the values of a and b ~

$\qquad \sf \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1$

[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]

$\qquad \sf \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1$

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2 years ago

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cameron and hunter have a push up competition and hunter did 17 push ups hunter did 2 fewer push ups than cameron how many push

GarryVolchara [31]

Answer:

Step-by-step explanation:

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3 years ago

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A family of 8 went out to dinner. Each person either ordered the lobster dinner, which costs $25, or the steak dinner which cost

defon

Answer: 6 people ordered for the lobster dinner.

2 people ordered for the steak dinner.

Step-by-step explanation:

Let x represent the number of people that ordered the lobster dinner.

Let y represent the number of people that ordered the steak dinner.

A family of 8 went out to dinner. This means that

x + y = 8

Each person either ordered the lobster dinner, which costs $25, or the steak dinner which cost $20. The total cost of all the meals is $190. This means that

25x + 20y = 190 - - - - - - - - - -- -1

Substituting x = 8 - y into equation 1, it becomes

25(8 - y) + 20y = 190

200 - 25y + 20y = 190

- 25y + 20y = 190 - 200

- 5y = - 10

y = - 10/ - 5

y = 2

x = 8 - y = 8 - 2

x = 6

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Answer:

less than

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

2 cm by 5 cm are the dimensions of the poster at one-half its current size

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