Let f(x)=1/x and g(x)=x^3. Find f(x) -g(x)

1 answer:

6 0

To find f(x) - g(x), simply subtract g(x) from f(x).

$\frac{1}{x} -x^3$

If you need to simplify, we can find a common denominator:

$\frac{1-x^4}{x}$

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A factory makes rods by cutting platic pipes that are 5 feet long into 8 rods. How long is each rod

CaHeK987 [17]

If you divide 8 by 5 you should get 1.6

8 0

3 years ago

The altitude to the hypotenuse of a right triangle divides the hypotenuse into 15 inches and 30 inch segments. Explain or show h

e-lub [12.9K]

9514 1404 393

Answer:

CX = 15√2 inches

BC = 15√3 inches

AC = 15√6 inches

Step-by-step explanation:

In this geometry, all of the triangles are similar:

ΔABC ~ ΔACX ~ ΔCBX

Corresponding segments are proportional in similar triangles, so we have ...

AX/CX = CX/BX = (long leg)/(short leg)

Filling in the numbers, we get

30/CX = CX/15

CX² = 15×30

CX = 15√2 . . . . . exact length of the altitude (inches)

Similarly, we can form proportions with the legs:

AB/BC = CB/BX

BC² = (BX)(AB) = (45)(15)

BC = 15√3 . . . inches

and

AC/AB = AX/AC

AC² = (AX)(AB) = (30)(45)

AC = 15√6 . . . inches

_____

<em>Additional comment</em>

You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...

altitude = geometric mean of hypotenuse segments

short side = geometric mean of short segment and whole hypotenuse

long side = geometric mean of long segment and whole hypotenuse

Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.