4 years ago

How do you find the Constant of variation

1 answer:

6 0

If y
y
varies directly as x
x
and y=15
y
=
15
when x=24
x
=
24
, find x
x
when y=25
y
=
25
.

Find the constant of variation.

k=yx=1524=58y=58x k=
y
x
=
15
24
=
5
8
y=
5
8
x
To find x
x
, substitute 25
25
for y
y
.

25=58xx=40

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A sheet of metal that is 30cm wide and 600cm long is to used to make a rectangular eavestrough by bending the shett an equal amo

tensa zangetsu [6.8K]

Answer:

The sheet should be turned up 7.5cm on each side to obtain maximum volume.

Step-by-step explanation:

If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.

Height of eaves trough = x cm

Length of eaves trough = 600 cm

Width of eaves trough = (30 - 2x) cm

We know that Volume is given by:

V = Length · Width · Height

V = (x)(30 - 2x)(600)

V = -1200x² + 18000x

To maximize the volume, we take the derivative and put it equal to zero.

$\frac{dV}{dx} =\frac{d}{dx}( -1200x^2 +18000x)=0\\\frac{d}{dx}( -1200x^2 +18000x) = 0\\-(2)1200x+18000=0\\-2400x+18000=0\\x=\frac{18000}{2400}\\ x=7.5cm$