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astra-53 [7]
3 years ago
13

A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element r

emaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.
Which statement describes how the reasonable domain compares to the mathematical domain?

1The reasonable domain is restricted to integers.
2The reasonable domain is restricted to positive real numbers.
3The reasonable domain has a minimum value of 1,500.
4The reasonable domain has a maximum value of 1,500.
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

Answer:

2. The reasonable domain is restricted to positive real numbers.

Step-by-step explanation:

The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.

___

I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.

__

x might be restricted to integers if you're only measuring the remaining amount once a year.

The maximum value of 1500 applies to the *range* of the function, not its domain.

The minimum value of 1500 has nothing to do with anything.

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Find the endpoint:
scZoUnD [109]

Answer:

The coordinates of Point D are: (-5,-8)

Step-by-step explanation:

The formula for mid-point is given by:

M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})

For the point (x1,y1) and (x2,y2)

Given that

M = (-3, -6)

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(-3,-6) = (\frac{-1+x_2}{2} , \frac{-4+y_2}{2})

Putting respective coordinates equal

-3 = \frac{-1+x_2}{2}\\-6 =-1+x_2\\x_2=-6+1\\x_2 = -5\\AND\\-6 = \frac{-4+y_2}{2}\\-12 = -4+y_2\\y_2 = -12+4\\y_2 = -8

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3 0
2 years ago
A long distance runner does a first lap around a track in exactly 50 seconds.As she tires.Each subsequent lap takes 20% longer t
madreJ [45]

Answer:

182 seconds

Step-by-step explanation:

Given:

Time taken for first lap is 50 seconds and each subsequent lap takes 20% longer than previous

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Time taken for first lap = 50 sec

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Previous lap time = 50 sec

second lap = 50 + 20% of 50

second lap =50+(\frac{20}{100}\times 50)

second lap = 50 + 10

second lap = 60\ sec

For third lap

Each subsequent lap takes 20% longer than previous

Previous lap time = 60 sec

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Third\ lap = 60+2\times 6

Third\ lap = 60+12

Third\ lap = 72\ sec

Time taken for 3 laps is equal to sum of all three laps time.

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Tiem\ taken\ for\ 3\ lap = 182\ sec

Therefore, it takes 182 seconds (3 min, 2 seconds) to run three laps

6 0
3 years ago
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