A carousel has 56 horses 3/8 of them are white how many horses are not white

Given the parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π. convert to a rectangular equation and sketch the curve

Temka [501]

The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

For given question,

We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.

We need to convert given parametric equations to a rectangular equation and sketch the curve.

Given parametric equations can be written as,

x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.

We know that the trigonometric identity,

sin²t + cos²t = 1

⇒ (x/2)² + (- y/3)² = 1

⇒ $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.

The rectangular equation is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

The graph of the rectangular equation $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ is as shown below.

Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

Learn more about the parametric equations here:

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7 0

1 year ago

I need help on 5a, I forgot how to set it up(algebra2)

GalinKa [24]

The answer is 12t because i said so<span />

3 0

2 years ago

Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real

adoni [48]

Step-by-step explanation

<h3>Prerequisites:</h3>

$b^2 - 4ac = 0 \Rightarrow 1 solution$

$b^2 - 4ac > 0 \Rightarrow 2 solutions$

$b^2 - 4ac < 0 \Rightarrow No\ real\ solutions$

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$2x^2-7x-9 = 0$

$b^2 - 4ac$

$-7^2 - 4(2)(-9) = 121$

2 Solutions

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$x^2-4x+4 = 0$

$b^2 - 4ac$

$-4^2 - 4(1)(4) = 0$

1 Solution

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$4x^2-3x-1 = 0$

$b^2 - 4ac$

$-3^2 - 4(4)(-1) = 25$

2 Solutions

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$x^2-2x-8 = 0$

$b^2 - 4ac$

$-2^2 - 4(1)(-8) = 36$

2 Solutions

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$3x^2+5x+3 = 0$

$b^2 - 4ac$

$5^2 - 4(3)(3) = -11$

No Solutions

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3 0

3 years ago

Read 2 more answers

WILL MARK BRAINLIEST! Please help me. :(

OLga [1]

Answer:

A

Step-by-step explanation:

Distribute the (-)

6x^3y^3+x^3y^3 + 5x^2y^2 - x^2y^2 - x^2y+x^2y +xy^2 +3x+3x +2-4

Cancel out bold and add:

7x^3y^3 + 4x^2y^2 +xy^2+6x-2

7 0

3 years ago

How many pennies could you have if: When you break the pennies into groups of 2, you have 1 penny left over, AND when you break

dsp73

Answer:

31 pennies

Step-by-step explanation:

Given that:

Breaking the number of pennies into 2 groups, there is 1 penny left over.

Breaking the pennies into 3 groups, there is 1 penny left over.

Breaking the pennies into 5 groups, there is 1 penny left over.

Breaking the pennies into groups implies that the same number of pennies are in each group for each case. Since there is no restriction to the number of pennies in the groups for all cases, then the total number of pennies would be 31.

So that;

31 = 15 + 15 + 1 = 2 groups + 1

31 = 10 + 10 + 10 + 1 = 3 groups + 1

31 = 6 + 6 + 6 + 6 + 6 + 1 = 5 groups + 1

There are 31 pennies.

8 0

3 years ago