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const2013 [10]
3 years ago
10

Thanks in advance to all the people who provided support to my problem!

Mathematics
1 answer:
sashaice [31]3 years ago
5 0

Answer as an improper fraction:  7/4

Answer as a mixed number:  1 & 3/4

Answer in decimal form:  1.75

Each answer above is a different way to represent the same distance

=========================================

Explanation:

I'm assuming the total distance is 5&1/4. This converts to the improper fraction 21/4 through the use of the formula below

a & b/c = (a*c+b)/c

In this case, a = 5, b = 1 ,c = 4

If each leg of the race is x miles, then the three legs add to x+x+x = 3x miles total. Set this equal to 21/4 and solve for x

--------------------------

3x = 21/4

(1/3)*3x = (1/3)*(21/4)

x = (1*21)/(3*4)

x = (21/3)*(1/4)

x = 7*(1/4)

x = 7/4

-------------------------

Each leg is 7/4 miles. Lets convert this to a mixed number through long division.

7/4 = 1 remainder 3

The two results above indicate that 7/4 = 1 & 3/4

To help confirm this, imagine you had 7 slices of pie and 4 people to divide those 7 slices among. Each person will get 1 slice meaning there are 7-4 = 3 slices leftover, aka the remainder.

If you need the answer in decimal form, then 1 & 3/4 = 1 + 3/4 = 1+0.75 = 1.75

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A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per lit
Veronika [31]

Answer:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

Step-by-step explanation:

1) Identify the problem

This is a differential equation problem

On this case the amount of liquid in the tank at time t is 1600−24t. (When the process begin, t=0 ) The reason of this is because the liquid is entering at 16 litres per second and leaving at 40 litres per second.

2) Define notation

y = amount of chlorine in the tank at time t,

Based on this definition, the concentration of chlorine at time t is y/(1600−24t) g/ L.

Since liquid is leaving the tank at 40L/s, the rate at which chlorine is leaving at time t is 40y/(1600−24t) (g/s).

For this we can find the differential equation

dy/dt = - (40 y)/ (1600 -24 t)

The equation above is a separable Differential equation. For this case the initial condition is y(0)=(1600L )(0.0125 gr/L) = 20 gr

3) Solve the differential equation

We can rewrite the differential equation like this:

dy/40y = -  (dt)/ (1600-24t)

And integrating on both sides we have:

(1/40) ln |y| = (1/24) ln (|1600-24t|) + C

Multiplying both sides by 40

ln |y| = (40/24) ln (|1600 -24t|) + C

And simplifying

ln |y| = (5/3) ln (|1600 -24t|) + C

Then exponentiating both sides:

e^ [ln |y|]= e^ [(5/3) ln (|1600-24t|) + C]

with e^c = C , we have this:

y(t) = C (1600-24t)^ (5/3)

4) Use the initial condition to find C

Since y(0) = 20 gr

20 = C (1600 -24x0)^ (5/3)

Solving for C we got

C = 20 / [1600^(5/3)] =  20 [1600^(-5/3)]

Finally the amount of chlorine in the tank as a function of time, would be given by this formula:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

7 0
3 years ago
30 Points please help!! Please explain too!
sergiy2304 [10]
Initial: 200 feet = opp. side
Angle = 17.31, adj. Side = a
So tan (17.31) = opp. Side / adj. Side
tan (17.31) = 200 / a
--> a = 200/tan17.31 = 641.73
When stopped: adj. Still = a
Opp. Side still = 200, angle = 46.41
tan46.41 = 200 / a
--> a = 200/tan46.41 = 190.39
Now subtract those two distances to get the distance traveled from initial to when it stopped:
641.73 - 190.39 = 451.34 feet
3 0
3 years ago
The midpoint between (-4, 4) and (-2, 2)
Sav [38]
The midpoint is (-3,3)
5 0
3 years ago
Read 2 more answers
If you have time help, please!
Viefleur [7K]

Answer:

The point on the y-axis is (0,-3) and the point on the x-axis is (6,0)

Step-by-step explanation:

Start by plotting -3 on the y-axis

Then move up 1 and over 2 from there

7 0
3 years ago
Suppose each laptop of a certain type is assigned a series number, which consists of a sequenceof eight symbols: number, letter,
Varvara68 [4.7K]

Answer:

Step-by-step explanation:

There are 5numbers and 3 letters. Each number can be one among the 10 possible.

Each letter is 1 among the 26 available.

a)The number of possible unique serial numbers are

10^5x 26³

The number of 5 number combinations each different (order important) is 5!(10/5)= 30240

The number of 3 letter combinations each different (order important) is 3!(26/3)=15600

The required probability (that all symbols are different if one laptop is picked at random with equal probability) is

15600x3240/ 10^5x 26³=0.2684

b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..

The number of 5 number combinations each different and starting with 4 (order important) is .

4!=24

The number of 5 number combinations each different and starting with 5 (order important) is .

4!(5/4)= 120

The number of 5 number combinations each different and starting with 6 (order important) is .

4!(6/4)= 360

The number of 5 number combinations each different and starting with 7 (order important) is .

4!(7/4)= 840

The number of 5 number combinations each different and starting with 8 (order important) is

4!(8/4)= 1680

The number of 5 number combinations each different and starting with 9 (order important) is .

4!(9/4)= 3024

Thus, there are

The required probability ( that all symbols are different and the first number is the largest among the numbers) is

15600* 6040/10^5x 26³= 0.0537

5 0
3 years ago
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