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denis-greek [22]
1 year ago
15

a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in sti

ll water and what is the rate of current?
Mathematics
1 answer:
Galina-37 [17]1 year ago
4 0
\begin{gathered} \text{Let;s assume the sp}e\text{d of boat in still water is x.} \\ And\text{ the spe}ed\text{ of stream is y.} \\ For\text{ upstream,} \\ (x-y)\times8=456 \\ x-y=57\ldots(1)_{} \\ (x+y)\times9=783 \\ x+y=87 \\ x=87-y\ldots(2) \\ \text{Now, substitute the value of x in the equation (1).} \\ 87-y-y=57 \\ -2y=57-87 \\ 2y=30 \\ y=15\text{ km/hours (rate of current)} \\ \text{Substitute the value of y in the equation (2).} \\ x=87-15 \\ x=72\text{ km/hours (boat in still water)} \end{gathered}

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Using the Extended Euclidean Algorithm, find integers x and y such that 26x + 9y = 1.
Xelga [282]

Answer:

The solution is: x=-1 and y=3.

Step-by-step explanation:

Let's find the solution, but first let's remember the following:

A / B = C + R where:

A=dividend, B=divisor, C=quotient, and R=remainder. This can be express as follows:

A = (C * B) + R, which is the structure we are going to use next.

Using the Euclidian Algorithm we need to find the highst common factor (HCF) between the coefficients from your equation, this means:

The original equation: 26x+9y=1 is in the form Ax+By=C, so A=26, B=9 and C=1.

We need to find the HCF of 'A' and 'B'. Using the Euclidan Algorithm (EA), so we have:

A = (C * B) + R, using our values:

26 = (2 * 9) + 8, look that the divisor (B) is 9 and the remainder (R) is 8.

Now using the (EA) we divide the divisor (B=9) by the obtained remainder (R=8). And we do the same for each obtained result until the las remainder (R) is equal to 0, like this:

A = (C * B) + R

9 = (8 * 1) + 1

using the divisor (B=8) and the remainder (R=1) we obtain:

A = (C * B) + R

8 = (1 * 8) + 0, look that the remainder is now 0, so in summary we can use the method as follows:

26 = (2 * 9) + 8

9 = (8 * 1) + 1

8 = (1 * 8) + 0; and this equations are the ones we are going to use in order to find a solution.

Next step is to use the equation before R=0, so:

9 = (8 * 1) + 1, which is:

9 - (8 * 1) = 1; but if you consider the first obtained equation: 26 = (2 * 9) + 8, we can write:

26 - (2 * 9) = 8, and we can use this expression in the previous one, so:

9 - (8 * 1) = 1, is:

9 - ((26 - (2 * 9)) * 1) = 1, simplifying:

9 - 26 + (2*9) = 1

9 - 26 + (9 + 9) = 1

-26 + (9 + 9 + 9) = 1

-26 + (3 * 9) = 1

26*(-1) + 9*(3) = 1; if you compare the last expression with the original equation, which is: 26x+9y=1, you can see the similarity, where x=-1 and y=3.

So, the solution is: x=-1 and y=3.

8 0
3 years ago
Write an equivalent expression to present patricia total earnings this week 7h + 135 + 5h = ?h + ?​
Paul [167]

Answer: 12 h + 135

Step-by-step explanation: 7h +135 + 5h = ?h + ?​

                                             7h +5h +135  

                                            =12h +135

So u combine like terms together  which are 7h and 5h which gives you 12 h.And then you have 135 left,so you add 12h to 135.

Ps.If you don't know what like terms are.I will explain down below.

Like terms are  variable that are the same.For an example 4y and 3y are like terms .Another example is 1/3 xy and 6xy .

Hope this helps :) and if it does please give brainliest .

8 0
2 years ago
One way to compute a 20% tip for a bill is to multiply it by 0.20. A restaurant bill was $35.70. Calculate the tip.
Dafna1 [17]

Answer:

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Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Which is the correct first step for solving this equation? 2x-7=5?
scZoUnD [109]

Answer:

to get x by itself so divide 5 by 2 and then add 7 to the other side

Step-by-step explanation:

2x-7=5

x-7=2.5

x=2.5+7

x=9.5

4 0
3 years ago
Please help I have no clue how to do this​
Alinara [238K]

Step-by-step explanation:

It's a question of trigonometry.

You need to remember that tangent (tan) stands for Perpendicular / Base.

So, tan P = QR / PR

By Pythagoras Theorem,

34² = 30² + x²

x² = 34² - 30²

x² = 1156 - 900

x² = 256

x = 16

Now, placing the values,

tan P = 30 / 16

tan P = 1.875

HOPE IT HELPS ^_^

5 0
2 years ago
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