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Anika [276]
3 years ago
6

Maya can run 18 miles in 3 hours, and she can bike 18 miles in 2 hours.

Mathematics
1 answer:
polet [3.4K]3 years ago
4 0

Answer:

36 miles

Step-by-step explanation:

Maya can bike 9 miles in one hours, meaning that she can bike 27 miles in 3 hours. Since Maya can run 18 miles in 3 hours, and half of 3 is 1.5, she can run 9 miles in 1.5 hours.

Biking Miles + Running Miles= Total Miles

27 + 9= 36 total miles

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po
sladkih [1.3K]

Answer:

\displaystyle C=\left(\frac{26}{9}, 2\right)

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

\displaystyle \frac{dy}{dx}=3x^2-3

Point A has an <em>x-</em>coordinate of -1. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0

Find the <em>y-</em>coordinate of Point A using the original equation:

y(-1)=(-1)^3-3(-1)=2

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

y-2=0(x-(-1))

Simplify:

y=2

Point B has an <em>x-</em>coordinate of 4. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45

Find the <em>y-</em>coordinate of Point B:

y(4)=(4)^3-3(4)=52

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

y-52=45(x-4)

Simplify:

y=45x-128

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for <em>x: </em>

2=45x-128

We acquire:

\displaystyle x=\frac{26}{9}

Since one of our equations is <em>y</em> = 2, the <em>y-</em>coordinate is 2.

Hence, Point C is:

\displaystyle C=\left(\frac{26}{9}, 2\right)

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