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erastova [34]
3 years ago
8

What is the slope of the line that passes through the points (-2,3) and (-14, -5)?

Mathematics
1 answer:
TEA [102]3 years ago
8 0
Slope = 2/3 (positive 2/3)
You use the formula Y2-Y1/X2-X1 in order to get the slope

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Can someone answer this please
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Answer:

4^(-11)

Step-by-step explanation:

To divide powers, subtract the exponents.

4^(-2) / 4^9

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Step-by-step explanation:

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Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the ra
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Answer:

\frac{dh}{dt}=-\frac{1}{2\pi}cm/min

Step-by-step explanation:

From similar triangles, see diagram in attachment

\frac{r}{4}=\frac{h}{16}


We solve for r to obtain,


r=\frac{h}{4}


The formula for calculating the volume of a cone is

V=\frac{1}{3}\pi r^2h


We substitute the value of r=\frac{h}{4} to obtain,


V=\frac{1}{3}\pi (\frac{h}{4})^2h


This implies that,

V=\frac{1}{48}\pi h^3


We now differentiate both sides with respect to t to get,

\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}


We were given that water is drained out of the tank at a rate of 2cm^3/min


This implies that \frac{dV}{dt}=-2cm^3/min.


Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means h=8cm.


We substitute this values to obtain,


-2=\frac{\pi}{16}(8)^2 \frac{dh}{dt}


\Rightarrow -2=4\pi \frac{dh}{dt}


\Rightarrow -1=2\pi \frac{dh}{dt}


\frac{dh}{dt}=-\frac{1}{2\pi}






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