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2 years ago

Find the equation of the line with slope = -6 and passing through (-6,32).write your equation

Mathematics

1 answer:

Lemur [1.5K]2 years ago

4 0

Point slope form says the line through (a,b) with slope m is

y - b = m(x - a)

Here that's

y - 32 = -6(x - -6)

y -32 = -6(x + 6) = -6x - 36

y = -6x - 4

Check:

-6(-6) - 4 = 36 - 4 = 32, good

Answer: y = -6x - 4

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A group of hikers walked 2 1/4 km in 3/4 hour.The distance here varies directly with time. What is the constant of variation?

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3 years ago

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20 points!!!!!!!

castortr0y [4]

See the attached figure to better understand the problem
let
L-----> length side of the cuboid
W----> width side of the cuboid
H----> height of the cuboid

we know that
One edge of the cuboid has length 2 cm-----> <span>I'll assume it's L
so
L=2 cm
[volume of a cuboid]=L*W*H-----> 2*W*H
40=2*W*H------> 20=W*H-------> H=20/W------> equation 1

[surface area of a cuboid]=2*[L*W+L*H+W*H]----->2*[2*W+2*H+W*H]

100=</span>2*[2*W+2*H+W*H]---> 50=2*W+2*H+W*H-----> equation 2
substitute 1 in 2
50=2*W+2*[20/W]+W*[20/W]----> 50=2w+(40/W)+20
multiply by W all expresion
50W=2W²+40+20W------> 2W²-30W+40=0

using a graph tool------> to resolve the second order equation
see the attached figure

the solutions are
13.52 cm x 1.48 cm
so the dimensions of the cuboid are
2 cm x 13.52 cm x 1.48 cm
or
2 cm x 1.48 cm x 13.52 cm

<span>Find the length of a diagonal of the cuboid
</span>diagonal=√[(W²+L²+H²)]------> √[(1.48²+2²+13.52²)]-----> 13.75 cm

the answer is
the length of a diagonal of the cuboid is 13.75 cm

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2 years ago

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Brilliant_brown [7]

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