Cheyenne drove 3,000 miles in 75 hours. At this rate, how long will it take her to drive 4,000 miles?

1 answer:

8 0

First step=
we need to find time for i mile
which is
75/3000=1/40
then to find for 4000 miles we multiply that by 4000
which is 1/40x4000
cancel zeros
1/4x400
=100 hours for 4000 miles

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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:

brainly.com/question/14289251

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