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3 years ago

What is the slope of the line graphed below? -3,4) 3,2)

Mathematics

2 answers:

insens350 [35]3 years ago

5 0

Answer:

-0.33

Step-by-step explanation:

x1 = -3, y1 = 4, x2 = 3 y2 = 2

m = y2 - y1 / x2 -x1

m = 2 - 4 / 3 - (-3)

m = -2/ 6

m = -0.33

Lilit [14]3 years ago

4 0

Answer:

y = -0.33333333333333x + 3

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

-1

= -0.33333333333333

θ =

arctan( ΔY ) + 360°

ΔX

= 341.56505117708°

ΔX = 3 – -3 = 6

ΔY = 2 – 4 = -2

Distance (d) = √ΔX2 + ΔY2 = √40 = 6.3245553203368

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A 15-ft ladder leans against a wall. The lower end of the ladder is being pulled away from the wall at the rate of 1.5 ft/sec. L

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Answer:

The top of the ladder is sliding down at a rate of 2 feet per second.

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Refer the image for the diagram. Consider $\Delta ABC$ as right angle triangle. Values of length of one side and hypotenuse is given. Value of another side is not known. So applying Pythagoras theorem,

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Now to calculate $\dfrac{dy}{dt}$ again consider following equation,

$\left ( y \right )^{2}+\left ( x \right )^{2}=\left ( l \right )^{2}$

Differentiate both sides of the equation with respect to t,

$\dfrac{d}{dt}\left(y^2+x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

Applying sum rule of derivative,

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(225\right)$

Applying power rule of derivative,

$2y\dfrac{dy}{dt}+2x\dfrac{dx}{dt}=0$

Simplifying,

$y\dfrac{dy}{dt}+x\dfrac{dx}{dt}=0$

Substituting the values,

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Subtracting both sides by 18,

$9\dfrac{dy}{dt}=-18$

Dividing both sides by 9,

$\dfrac{dy}{dt}= - 2$

Here, negative indicates that the ladder is sliding in downward direction.

$\therefore \dfrac{dy}{dt}= 2\:\dfrac{ft}{sec}$

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What is the slope of the line graphed below? -3,4) 3,2) ​

What is the slope of the line graphed below? -3,4) 3,2)