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2 years ago

How many points of intersection are there between the graphs of the hyperbola and ellipse?

Mathematics

1 answer:

N76 [4]2 years ago

4 0

The point of intersection is the point where two or more functions meet.

The graphs of the hyperbola and ellipse have 0 point of intersection

The given parameters are:

$\mathbf{3x^2 - 4y^2 + 4x - 8y + 4 = 0}$

$\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 0}$

To determine the points of intersection, we simply equate both equations.

So, we have:

$\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 3x^2 - 4y^2 + 4x - 8y + 4 }$

Cancel out the common terms

$\mathbf{y^2 - 3y = - 4y^2 - 8y }$

Collect like terms

$\mathbf{y^2 +4y^2= 3y - 8y }$

$\mathbf{5y^2= - 5y }$

Divide through by 5

$\mathbf{y^2= - y}$

Divide through by y

$\mathbf{y= -1}$

The system of equation does not give room to calculate the x-coordinate at the x-axis.

Hence, the graphs of the hyperbola and ellipse have 0 point of intersection

Read more about points of intersection at:

brainly.com/question/13373561

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Nadusha1986 [10]

Answer:

Step-by-step explanation:

SIDE OF THE SQUARE = 6 cm = DIAMETER OF THE CIRCLE.

AREA OF THE CIRCLE = (Pi/4)*6^2 = [(22/7)/4]*36 = 22*9/7 = 28.2857 sqcm

First, find the side length of the square. (Find the square root of 36 cm^2, to get 6 cm as the side length of the square).

Second, find the radius of the circle inside the square. The side length of the square is the diameter of the circle. Radius is half of the diameter. So, half of 6 cm is 3 cm; this is the radius of the circle.

Third, find the area of the circle by using the formula, A = pi x radius x radius

so, Area = 3.14 x 3 cm x 3 cm

by calculation we get the area of the circle is 28.26 cm^2

Where pi is a constant of 22/7 or 3.14

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3 years ago

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Each person eats 2/3 of a pound of turkey. how many pounds of turkey will be needed for 8 people

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Multiply 2/3 by 8 and you will get 16/3 or 5.33 repeating.

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2 years ago

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A square pyramid has a base length of 6 inches. The height of each triangular face is 11 inches. Which expressions correctly cal

VMariaS [17]

Answer:

168 in²

Step-by-step explanation:

The square would be 36 in²

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1/2 (66) = 33 in², which is the area of a triangle.

Then you multiply 33 x 4 to get the area of all the triangles, which is 132 in²

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3 years ago

Below is the five-number summary for 144 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of

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Answer:

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days

Step-by-step explanation:

For this case we have the following 5 number summary from the data of 144 values:

Minimum: 9 days

Q1: 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

The IQR is given by:

$IQR = Q_3 -Q_1 = 28-18= 10$

If we want to find any possible outliers we can use the following formulas for the limits:

$Lower= Q_1 - 1.5 IQR$

$Upper= Q_3 + 1.5 IQR$

And if we find the lower limt we got:

$Lower= Q_1 - 1.5 IQR= 18-1.5*10 = 3$

$Upper= Q_3 + 1.5 IQR= 28+1.5*10= 43$

So then the left boundary for this case would be 3 days

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2 years ago

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dolphi86 [110]

3. Look at the picture.

We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:

$x^o+90^o+43^o=180^o\\\\x^o+133^o=180^o\ \ \ |-133^o\\\\x^o=47^o$

$Answer:\ \boxed{47^o}$

4.
Look at the picture.

Use Pythagorean theorem:

$x^2+14^2=(10+x)^2\\\\x^2+196=10^2+2\cdot10\cdot x+x^2\ \ \ \ |-x^2\\\\196=100+20x\ \ \ |-100\\\\20x=96\ \ \ |:20\\\\x=4.8$

$Used:\ (a+b)^2=a^2+2ab+b^2$

$Answer:\ \boxed{4.8\ units}$

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TRUE: 1; 2; 4

6.
We find a slope of the line OP:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\O(2;\ 6)\to x_1=2;\ y_1=6\\\\P(4;\ 3)\to x_2=4;\ y_2=3\\\\m=\dfrac{3-6}{4-2}=\dfrac{-3}{2}$

We have: $OP:\ y=-\dfrac{3}{2}x+b$

Now, we must find the slope of the line perpendicular to the line OP.
We know:

$k:y=m_1x+b;\ l:y=m_2x+c\\\\k\ \perp\ l\iff m_1m_2=-1$

therefore

$-\dfrac{3}{2}m_2=-1\ \ \ |\cdot\left(-\dfrac{2}{3}\right)\\\\m_2=\dfrac{2}{3}$

So. We have the answer! :)

$Answer:\ \boxed{y=\dfrac{2}{3}x+\dfrac{1}{3}}$

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2 years ago