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solong [7]
3 years ago
15

Solve -2/3x > 8 or -x < 4.

Mathematics
1 answer:
horrorfan [7]3 years ago
8 0

Answer:

<u>x < -12</u>

Step-by-step explanation:

-2/3x > 8

-2/3x * (-3/2) < (-3/2)

cancel the common factor of 2

-x/3*-3<8* (-3/2)

Multiply

x<8 * (-3/2)

Simplify

x < 4 * -3

Multiply

x<-12

-2/3x > 8

= x < -12

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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustra
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Answer:

x = t

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Step-by-step explanation:

Given

x=t

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z=2t-t^2

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The vector equation is given as:

r(t) = (x,y,z)

Substitute values for x, y and z

r(t) = (t,\ e^{-t},\ 2t - t^2)

Differentiate:

r'(t) = (1,\ -e^{-t},\ 2 - 2t)

The parametric value that corresponds to (0, 1, 0) is:

t = 0

Substitute 0 for t in r'(t)

r'(t) = (1,\ -e^{-t},\ 2 - 2t)

r'(0) = (1,\ -e^{-0},\ 2 - 2*0)

r'(0) = (1,\ -1,\ 2 - 0)

r'(0) = (1,\ -1,\ 2)

The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)

It should be noted that:

The equation of a line through position vector a and parallel to vector v is given as:

r(t) = a + tv

Such that:

a = (0,1,0) and v = r'(0) = (1,-1,2)

The equation becomes:

r(t) = (0,1,0) + t(1,-1,2)

r(t) = (0,1,0) + (t,-t,2t)

r(t) = (0+t,1-t,0+2t)

r(t) = (t,1-t,2t)

By comparison:

r(t) = (x,y,z) and r(t) = (t,1-t,2t)

The parametric equations for the tangent line are:

x = t

y = 1 - t

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<h3>Answer:</h3>

48 1/8

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... = 47 + 1 1/8 . . . . . . then division

... = 48 1/8 . . . . . . . . then addition

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A decent calculator will evaluate this for you according to the order of operations. A Google or Bing search box will do that, too.

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