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3 years ago

Find the range of possible values of x

Mathematics

1 answer:

mamaluj [8]3 years ago

5 0

Answer:

I dont have time to answer but i explained c:

Step-by-step explanation:

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).

Find the domain of g(y), and this will be the range of f(x).

If you can't seem to solve for x, then try graphing the function to find the range.

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3 years ago

(c). Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in s

Bezzdna [24]

(i) Since P(t) gives the population of the culture after t seconds, the population after 1 second is

P(1) = 3•1² + 3e¹ + 10 = 13 + 3e ≈ 21.155

In Mathematica, it's convenient to define a function:

P[t_] := 3t^2 + 3E^t + 10

(E is case-sensitive and must be capitalized. Alternatively, you could use Exp[t]. You can also specify that the argument t must be non-negative by entering a condition via P[t_ ;/ t >= 0], but that's not necessary.)

Then just evaluate P[1], or N[P[1]] or N <at symbol> P[1] or P[1] // N to get a numerical result.

(ii) The average rate of change of P(t) over an interval [a, b} is

(P(b) - P(a))/(b - a)

Then the ARoC between t = 2 and t = 6 is

(P(6) - P(2))/(6 - 2) ≈ 321.030

In M,

(P[6] - P[2])/(6 - 2)

and you can also include N just as before.

(iii) You want the instantaneous rate of change of P when t = 60 (since 1 minute = 60 seconds). Differentiate P :

P'(t) = 6t + 3e^t

Evaluate the derivative at t = 60 :

P'(60) = 6•60 + 3e⁶⁰ = 360 + 3e⁶⁰

The approximate value is quite large, so I'll just leave its exact value.

In M, the quickest way would be P'[60], or you can differentiate and replace (via ReplaceAll or /.) t with 60 as in D[P[t], t] /. t -> 60.

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3 years ago

Help pls ????????!!!!!!

7nadin3 [17]

Answer:

let the number of steps taken by friend 1, 2 and 3 be: x, y and z respectively

we know that the mean of the total steps taken by all the friends is 10,350

Since the formula for mean is: sum of all values / number of values

here, the total values is the total number of steps taken

So,

steps taken by friend 1 +steps taken by friend 2 +steps taken by friend 3 +steps taken by friend 4 +steps taken by friend 5 +steps taken by friend 6

all that divided by 6 will give us the mean

so, 7800 + 8000 + 9800 + x + y + z / 6

(25600 + x + y + z)/6 = 10350

25600 + x + y + z = 10350 * 6

x + y + z = 62100 - 25600

x + y + z = 36500

So since the sum of x, y and z is 36500,

we can say that the average value of x , y and z is 12167 (36500/3)

So the next thing to make an equation out of is Median

to find the median, we need to arrange the values in any order you like, i will arrange in descending order

so since the estimated value of all x , y and z is greater than the greatest known value:

x > y > z > 9800 > 8000 > 7800

Since this set of values has an even number of values, we will take the average of the middle 2 values as the median

(9800 + z)/2 = 10000

9800 + z = 20000

z = 10200 -------- we have found one of the three values! getting closer

Now, the final equation will be found from the range

since we already have sorted our data, and the difference of the highest and lowest is the range

x > y > z > 9800 > 8000 > 7800

So, x - 7800 = 7500

x = 15300 ------- now that we have x and z, we can use the first equation to find the value of y and we will be done!

x + y + z = 36500

replacing the values

15300 + y + 10200 = 62100

y = 36500 - 25500

y = 11000

So the three remaining friends walked

15300, 11000 and 10200 steps

6 0

3 years ago