This graph shows the relationship between distance and time for the three turtles.

Mathematics

2 answers:

Charra [1.4K]3 years ago

4 0

Answer:

the lane 1 turtle is the fastest.

ohaa [14]3 years ago

3 0

Answer:

lane 1

Step-by-step explanation:

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Answer the following questions.

serg [7]

39 is <span>312% </span>of 12.5

To find this you just divide 12.5 into 39 which gives you 3.12. To change that to a percentage you multiply by 100 which gives you 312%

7.5 is <span>102% </span>of 7.38

To find this you just divide 7.38 into 7.5 which gives you 1.0162, which I rounded to 1.02. To change that to a percentage you multiply by 100 which gives you 102%

I hope this helped! :)

6 0

3 years ago

How to do question 1?Had no idea how to do both parts

givi [52]

$y=\dfrac{\ln x}{3x-6}$

Differentiate both sides with respect to $x$ :

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{3x-6}x-3\ln x}{(3x-6)^2}$

When $x=1$ , you have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{3-6}1-3\ln1}{(3-6)^2}=\dfrac{-3}9=-\dfrac13$

For part (b), we now assume that $x$ and $y$ are functions of an independent variable, which we'll call $t$ (for time). Now differentiating both sides with respect to $t$ , we have

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{\frac{3x-6}x-3\ln x}{(3x-6)^2}\dfrac{\mathrm dx}{\mathrm dt}$

where the chain rule is used on the right side. We're told that $y$ is decreasing at a constant rate of 0.1 units/second, which translates to $\dfrac{\mathrm dy}{\mathrm dt}=-0.1$ . So when $x=1$ , you have

$-0.1=\dfrac{\frac{3-6}1-3\ln1}{(3-6)^2}\dfrac{\mathrm dx}{\mathrm dt}$
$-0.1=-\dfrac13\dfrac{\mathrm dx}{\mathrm dt}$
$\dfrac{\mathrm dx}{\mathrm dt}=0.3$

where the unit is again units/second.

6 0

3 years ago

Which triangle would be most helpful in finding the distance between the points (-4, 3) and (1,-2) on the coordinate

earnstyle [38]

Answer:

On a coordinate plane, a triangle has points (negative 4, 3), (negative 4, negative 2), (1, negative 2).

Step-by-step explanation:

The points (-4,3), (1,2) and (-4, -2) would form a right triangle when graphed and connected by lines.

(-4,3), (1,2) and (1,3) would also work as well