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3 years ago

31. Each day, Talisa exercises by first

Mathematics

1 answer:

GaryK [48]3 years ago

5 0

Answer:

Step-by-step explanation:

Given the following :

Laps - - - - - - - - 5 - - - 6 - - - 7 - - - 8 - - - 9

Total time - - - 25 - - 28 - - 29 - - 30 - - 32

Using online graphing tool:

The y - axis named dependent variable represents the total time taken.

The x-axis, represents the number of laps.

The equation of the trend line attached to the plot is in the form :

y = mx + c

y = 1.6x + 17.6

Where y = total time taken

x = number of laps

m = 1.6 = gradient of the line (change in y / change in x)

C = 17.6 = intercept (whee the trndline intersects the y-axis).

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3 years ago

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Basile [38]

Answer:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

Step-by-step explanation:

We know that given the polynomial with real coefficients, if x = 3 + i is a root, then x = 3 - i must be another root. These two roots can combine multiplicative factors as shown:

(x - 3 - i) * (x - 3 + i) = (x-3)^2 + 1 = x^2 - 6 x + 9 + 1 = x^2 - 6 x + 10

Then we divide the given polynomial: x^4 - 10x^3 + 29x^2 - 10x - 50 by the quadratic one we just found, and get a perfect division:

{x^4 - 10x^3 + 29x^2 - 10x - 50} / {x^2 - 6 x + 10} = x^2 - 4 x - 5

which can be factored out by grouping as shown below:

x^2 - 4 x - 5 = x^2 - 5 x + x - 5 = x (x - 5) + x - 5 = (x - 5 ) * (x + 1)

then the full factor form of the quartic polynomial given is:

(x - 3 - i) * (x - 3 + i) * (x - 5 ) * (x + 1)

and therefore the associated roots are:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

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3 years ago