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zzz [600]
3 years ago
9

What is the domain of the function

Mathematics
1 answer:
Anon25 [30]3 years ago
7 0
The answer is -2,2,3,4
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A boat covers 25 km upstream and 44 km downstream in t hours. Also, it covers 15 km upstream and 22 km downstream in 5 hours. Fi
aniked [119]

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.

7 0
2 years ago
Read 2 more answers
Can you guys help me I need It now​
KIM [24]
1. 7 17/42
2. 42 5/6
3. 7 3/4
4. 12 2/3
5. 2 8/35
7 0
2 years ago
Read 2 more answers
What is the value of the expression 100 - 92 ÷ 3?
lora16 [44]

Answer:

2.67

Step-by-step explanation:

100-92=8

8÷3

\sqrt[3]{8}

=2.67

8 0
3 years ago
Read 2 more answers
How many three-digit positive integers <img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle"
Anastaziya [24]

Answer:

  40

Step-by-step explanation:

Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.

As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.

_____

The equation reduces, mod 23, to ...

  10x = 11

Its solutions are x = 23n +8.

3 0
2 years ago
Could somebody please answer this?
jok3333 [9.3K]
Here are the resulting percentages:
LEAH = 3.5%
RATHA = 2.3%
ED = 1.8%
CHRIS = 4.2%
MARY = 2.5%

You arrive at this answer by dividing the bonus by the wages

BONUS/WAGE = PERCENTAGE OF BONUS TO WAGE.

Chris had the greatest percentage of wages in his bonus
3 0
3 years ago
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