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alisha [4.7K]
3 years ago
6

It takes three hours for a boat to go 18 miles downstream, and nine hours to return. What is the rate of the boat in calm water

and the rate of the current?​
Mathematics
1 answer:
vampirchik [111]3 years ago
5 0

Step-by-step explanation:

Distance = rate × time

If B is the rate of the boat, and C is the rate of the current, then we can write two equations:

18 = (B + C) × 3

18 = (B − C) × 9

Simplifying the equations:

6 = B + C

2 = B − C

Add the equations together to eliminate C:

8 = 2B

B = 4

Plug into either equation to find C:

C = 2

The boat's rate is 4 mph, and the current's rate is 2 mph.

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Find the magnitude of the vector from the origin to (8. - 6) and write the vector as the sum of unit vectors.
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The magnitude of the vector from the origin is 10

The unit vector in of the vector from the origin as   (8/10, -6/10

<u>Step-by-step explanation:</u>

<u>1.Finding the magnitude,</u>

we have the formula,

magnitude=√a²+b²

we have the values as a=8 and b=-6

Finding the magnitude we get,

magnitude=√a²+b²

magnitude=√8²+6²

magnitude=√100

magnitude=10

The magnitude of the vector from the origin is 10

<u>2.Finding the  unit vector</u>

Divide by the magnitude

Unit vector: (8/10, -6/10)

The unit vector in of the vector from the origin as   (8/10, -6/10

3 0
3 years ago
One number is nine more than a second number. Four times the first is 6 less than 2 times the second. Find the numbers.
Masteriza [31]

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Answer:

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Step-by-step explanation:

Let x represent the first number. Then the second is x-9. The other relation is ...

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The first number is -12; the second number is -21.

6 0
3 years ago
(02.03)Figure ABC is reflected about the x-axis to obtain figure A'B'C':
faust18 [17]

Answer:

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Step-by-step explanation:

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3 years ago
Which of the following transformations will result in an image that maps onto itself
Anestetic [448]

The transformations that maps image onto itself are D) reflect over the y axis and then reflect again over the y axis.

Complete question

Which sequence of a transformation will result in an image that maps onto itself? A) rotate 180 degrees counterclockwise and then reflect across the x axis b) reflect over the y axis and then reflect over the x axis c) rotate 180 degrees counterclockwise and then reflect across the y axis d) reflect over the y axis and then reflect again over the y axis

Step-by-step explanation:

Reflecting a figure across the y axis then repeating the same procedure will take you to the original position. This means mapping the figure onto itself.When coordinates(x,y) are reflected on the y axis the image coordinates are (-x,y) thus repeating this will form the second image coordinates as (x,y).

Learn More

Transformation : brainly.com/question/10656536

Keyword : transformation

#LearnwithBrainly

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