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kkurt [141]
3 years ago
9

If juliana and brody hiked both trails, how far did they hike? 3 2/3 and 2 5/6

Mathematics
1 answer:
Andreyy893 years ago
8 0

Juliana trails = 3\frac{2}{3}

Brody trails = 2\frac{5}{6}.

In order to find total how far they hiked, we need to add Juliana trails and Brody trails.

Juliana trails + Brody trails  = 3\frac{2}{3} +2\frac{5}{6}.

Adding whole number in front 3+2 = 5.

Now, adding fractions 2/3 and 5/6 by taking common denominator (lcd).

Least common denominator(lcd) of 3 and 6 is = 6.

So, we need to make both denominator = 6.

Muilplying 2/3 by 2 in top and bottom we get 2*2/3*2 = 4/6.

Now, adding 4/6 and 5/6.

We got the common denominator 6. So, we can just add numerators.

\frac{4}{6} +\frac{5}{6}  = \frac{4+5}{6} = \frac{9}{6}

Converting 9/6 into improper fraction:

If we divide 9 by 6, we get quotent 1 and 3 remainder.

So, we get fraction 1 \frac{3}{6} .

3/6 could also be reduced to 1/2 by dividing 3 and 6 by 3.

We get,

\frac{3}{6}  = \frac{1}{2}

Therefore, 1 \frac{3}{6}  = 1 \frac{1}{2}

Adding 5 into 1\frac{1}{2}.

We get,

6\frac{1}{2}.

So, we could say

They hiked total 6\frac{1}{2} far.

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Answer:

First part

The answer is (5 square root 2, 45°), (-5 square root 2, 225°) ⇒ answer (d)

Second part

The equation in standard form for the hyperbola is y²/81 - x²/19 = 1 ⇒ answer(b)

Step-by-step explanation:

First part:

* Lets study the Polar form and the Cartesian form

- The important difference between Cartesian coordinates and

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# In Cartesian coordinates there is exactly one set of coordinates

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# In polar coordinates there is an infinite number of coordinates

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# In the polar the coordinates the origin is called the pole, and

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# The angle measurement θ can be expressed in radians

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- To convert from Cartesian Coordinates (x , y) to

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# r = ± √(x² + y²)

# θ = tan^-1 (y / x)

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∵ x = 5 and y = 5

∴ r = ± √(5² + 5²) = ± √50 = ± 5√2

∴ tanФ = (5/5) = 1

∵ tanФ is positive

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∵ Ф = tan^-1 (1) = 45°

∴ Ф in the first quadrant is 45°

∴ Ф in the third quadrant is 180 + 45 = 225°

* The answer is (5√2 , 45°) , (-5√2 , 225°)

Second part:

* Lets study the standard form of the hyperbola equation

- The standard form of the equation of a hyperbola with  

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• the coordinates of the vertices are (0 , ±a)

• the length of the conjugate axis is 2b

• the coordinates of the co-vertices are (±b , 0)

•      the coordinates of the foci are (0 , ± c),  

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∵ The vertices are (0 , 9) and (0 , -9)

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∵ The foci at (0 , 10) , (0 , -10)

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∴ (10)² = (9)² + b² ⇒ 100 = 81 + b² ⇒ subtract 81 from both sides

∴ b² = 19

∵ The equation is  y²/a² - x²/b² = 1

∴  y²/81 - x²/19 = 1

* The equation in standard form for the hyperbola is y²/81 - x²/19 = 1

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