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3 years ago

If you vertically stretch the linear parent function f(x)=x, by a factor of 2, what is the equation of the new function?

Mathematics

1 answer:

pentagon [3]3 years ago

4 0

Answer:

y=2x

Step-by-step explanation:

The condition about stretching is that when the stretch factor is greater than 1, the function will be closer to OY axis; when the stretch factor is between 0 and 1, the function will be closer to OX axis.

We can observe this end result in the attached graphs.

The red line represent the original function and the blue line is y=2x

As we can observe that the condition still holds.

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Roberto rowed 20 miles downstream in 2.5 hours. The trip back, however, took him 5 hours. Find the rate that Roberto rows in sti

almond37 [142]

Answer:

<em>Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour</em>

Step-by-step explanation:

<u>Relative Speed</u>

When a body is moving at a constant speed v, the distance traveled in a time t is:

$d=v.t$

When Roberto rows downstream, his speed in still water is added to the speed of the water, making it easier to travel the required distance.

When Roberto rows upstream, his speed in still water is affected by the speed of the water, both are subtracted and the required distance is covered in more time.

Let's call

x = Roberto's rowing speed in still water

y = Speed of the river current

The speed when rowing downstream is x+y, thus the distance traveled is

$d=(x+y).t_1$

Where t1=2.5 hours. Substituting values:

$20=(x+y)*2.5$

Rearranging, we find the downstream equation:

$2.5x+2.5y=20\qquad[1]$

The speed when rowing upstream is x-y, and the distance traveled is

$d=(x-y).t_2$

Where t2=5 hours. Substituting values:

$20=(x-y)*5$

Rearranging, we find the upstream equation:

$5x-5y=20\qquad[2]$

Multiplying [1] by 2:

$5x+5y=40$

Adding this equation to [2]:

$10x=60$

Solving:

$x=60/10=6$

Dividing [2] by 5:

$x-y=4$

Solving for y

$y=x-4=6-4=2$

Thus, Roberto's speed in still water is 6 miles/hour and the river speed is 2 miles/hour

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3 years ago

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olga_2 [115]

Answer:

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2 years ago

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