Total distance = 16 + 3 + 22 + 7 = 48 miles

Distance she covered by running = 16 miles

Required answer = 16/48 = 1/3 = 0.33........ it's non-terminating

Hope This Helps You!

7 0

3 years ago

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Which portion of the unit circle satisfies the trigonometric inequality cos^2theta + sin^2theta is greater than or equal to 1. A

liberstina [14]

Answer:

Only points on the circle satisfy the given inequality.

Step-by-step explanation:

Given: Unit circle

To find: portion of the unit circle which satisfies the trigonometric inequality $\sin ^2\theta +\cos ^2\theta \geq 1$

Solution:

In the given figure, OA = 1 unit (as radius of the unit circle equal to 1)

$\sin \theta$ = side opposite to $\theta$ /hypotenuse

$\cos \theta$ = side adjacent to $\theta$ /hypotenuse

$\sin \theta =\frac{AB}{AO}\\\sin \theta =\frac{AB}{1}\\AB=\sin \theta$

$\cos \theta=\frac{OB}{AO}\\\cos \theta =\frac{OB}{1}\\OB=\cos \theta$

So, coordinates of A = $\left ( \cos \theta ,\sin \theta \right )$

For any point (x,y) on the unit circle with centre at origin, equation of circle is given by $x^2+y^2=1$

Put $(x,y)=\left ( \cos \theta ,\sin \theta \right )$

$\cos ^2\theta +\sin ^2\theta =1$

So, $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ satisfies the equation $x^2+y^2=1$

For points $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ inside the circle, $\cos ^2\theta +\sin ^2\theta$

For points $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ outside the circle, $\cos ^2\theta +\sin ^2\theta >1$

So, only points on the circle satisfy the given inequality.

4 0

3 years ago

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What is the equation of the line passing through the points (-3,7) and (3,3)

Sav [38]

$\text{Given that,}\\\\(x_1,y_1) = (-3,7)~~ \text{and}~~(x_2,y_2) =(3,3)\\\\\\\text{Slope, }~~ m =\dfrac{y_2-y_1}{x_2 - x_1}= \dfrac{3-7}{3-(-3)} = -\dfrac{4}{3+3} = -\dfrac 46 = -\dfrac 23\\\\\\\text{Equation with given points ,}\\\\y- y_1 = m(x-x_1)\\\\\implies y -7 = -\dfrac 23 (x +3)\\\\\implies y -7= -\dfrac 23 x - 2\\\\\implies y = -\dfrac 23 x -2 +7 \\\\\implies y = -\dfrac 23 x +5\\\\\implies 3y = -2x +15 \\\\\implies 2x +3y = 15$

6 0

3 years ago

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