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vampirchik [111]
3 years ago
6

Solve for x. 4x^3 = 2x^-1

Mathematics
2 answers:
tekilochka [14]3 years ago
7 0

x
=
4
√
8
2
,
−
4
√
8
2
x
=
8
4
2
,
-
8
4
2
Sloan [31]3 years ago
3 0

Step-by-step explanation:

4x^3=2x^-1

x^3-x^-1=2-4

x^2=-2

x=√2

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"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is
sukhopar [10]

Answer:

The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

Step-by-step explanation:

Dimensions of the rectangle

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Rate of base = 3/2 cm/min

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Applying Pythagoras theorem while drawing a diagonal to the rectangle

  b^2 +h^2 =  D^2\\

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so our diagonal will be 13cm  

Upon differentiating the area of the rectangle  we get

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using  the chain rule of differentiation

h*db/dt + b*dh/dt  = 0

b*dh/dt = -h*db/dt

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dh/dt = -5/8 cm//min

so the height of the rectangle is decreasing at the rate of -5/8cm/min

now we have all the measurements we need

b = 12 , db/dt = 3/2cm/min

h = 5 , dh/dt = -5/8 cm/min

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Upon differentiating we get

2b*db/dt + 2h*dh/dt = 2D*dD/dt

b*db/dt + h*dh/dt = D*dD/dt

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18 -25/8 = 13*dD/dt

\frac{144-25}{8} = 13*dD/dt

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Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

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Answer:

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