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Allushta [10]
3 years ago
7

Find the equation of the line that contains the points (4,2) and (6,10). Write the equation in the form y=mx+b and identify m an

d b.
Mathematics
1 answer:
Fantom [35]3 years ago
3 0
Points (4,2) and (6, 10)

Eqn:
y - y = m(x - x)
y - 2 = [(2-10)/(4-6)] (x - 4)
y - 2 = (-8/-2) (x - 4)
y - 2 = 4(x-4)
y - 2 = 4x - 16
y - 2 + 2 = 4x - 16 + 2
y = 4x - 14

Therefore the slope (m) would be 4 and the y intercept (b) would be -14.
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5 0
3 years ago
1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is
solong [7]

Answer:

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

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h: is the height

The rate of change of the volume can be calculated by using the chain rule:

\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]

Since h = 4/3 r we have:

\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]

\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]        

\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]    (1)    

With:

\frac{dr}{dt} = 3 in/min

r = 3 ft*\frac{12 in}{1 ft} = 36 in

And by entering the above values into equation (1) we have:

\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]

\frac{dV}{dt} = 16286 in^{3}/min

Therefore, the volume is increasing at a rate of 16286 in³/min.

I hope it helps you!                                    

3 0
3 years ago
Liliana and Marcus are playing a word game. Liliana spells a word incorrectly and loses 18 points. Then Marcus spells a word cor
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2 years ago
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