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anzhelika [568]
1 year ago
10

Please help!!! What is the slope of a line perpendicular to the following line:

Mathematics
1 answer:
AleksAgata [21]1 year ago
7 0

Answer:

b.) 2

Explanation:

Parallel slopes have same slope.

Perpendicular slopes have negatively inverse slope.

\sf Here  \ given \  equation:  y = -\dfrac{1}{2} x  - 6

Comparing it with slope intercept form, "y = mx + b" where m is slope.

Here parallel slope: -1/2

Perpendicular slope: -(-1/2)⁻¹ = 2

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Answer: D

Step-by-step explanation:

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3 years ago
the volume v of a right circular cylinder of radius r and heigh h is V = pi r^2 h 1. how is dV/dt related to dr/dt if h is const
laiz [17]
In general, the volume

V=\pi r^2h

has total derivative

\dfrac{\mathrm dV}{\mathrm dt}=\pi\left(2rh\dfrac{\mathrm dr}{\mathrm dt}+r^2\dfrac{\mathrm dh}{\mathrm dt}\right)

If the cylinder's height is kept constant, then \dfrac{\mathrm dh}{\mathrm dt}=0 and we have

\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dt}{\mathrm dt}

which is to say, \dfrac{\mathrm dV}{\mathrm dt} and \dfrac{\mathrm dr}{\mathrm dt} are directly proportional by a factor equivalent to the lateral surface area of the cylinder (2\pi r h).

Meanwhile, if the cylinder's radius is kept fixed, then

\dfrac{\mathrm dV}{\mathrm dt}=\pi r^2\dfrac{\mathrm dh}{\mathrm dt}

since \dfrac{\mathrm dr}{\mathrm dt}=0. In other words, \dfrac{\mathrm dV}{\mathrm dt} and \dfrac{\mathrm dh}{\mathrm dt} are directly proportional by a factor of the surface area of the cylinder's circular face (\pi r^2).

Finally, the general case (r and h not constant), you can see from the total derivative that \dfrac{\mathrm dV}{\mathrm dt} is affected by both \dfrac{\mathrm dh}{\mathrm dt} and \dfrac{\mathrm dr}{\mathrm dt} in combination.
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2 years ago
Make all the factors of 15 1 through 6 make group
stealth61 [152]
1, 3, and 5 because you can multiply all these numbers to get 15


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