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3 years ago

Find the range of f

Mathematics

1 answer:

Ugo [173]3 years ago

8 0

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x). ...
If you can't seem to solve for x, then try graphing the function to find the range.

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Joey and Armando live on the same st as the park. The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando'

AleksandrR [38]

Let's start by assuming Armando's house is between Joey's and the park.

Let $x$ be the distance Joey walked to Armando's house.

<span>The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.

</span> $\dfrac{9}{10} = x + \dfrac{3}{5}$

$x = \dfrac{9}{10} - \dfrac{3}{5} = \dfrac{9}{10} -\dfrac{6}{10} = \dfrac{3}{10}$

That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)

Let $a, b, c$ be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

$\pm a \pm b = \pm c$

Let's get rid of the plus/minuses. Squaring,

$a^2 + b^2\pm 2ab = c^2$

$\pm 2ab = c^2-a^2-b^2$

$4a^2b^2 = (c^2-a^2-b^2)^2$

For us, that's a quadratic equation for $c^2$

$4(9/10)^2(3/5)^2= (c^2-(9/10)^2 - (3/5)^2)^2$

I'll skip right to the solutions,

$c^2=\dfrac{9}{100} \textrm{ or } c^2=\dfrac{9}{4}$

$c=\dfrac{3}{10} \textrm{ or } c=\dfrac{3}{2}$

We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.

6 0

3 years ago

The volume of a drop of a liquid is .000047 liter. Write the liquid in scientific notation

Delvig [45]

the answer would be4.7^-10^4

3 0

3 years ago

Assume that emergency medical personnel in California are planning for future resources and it has been observed that the averag

larisa [96]

Answer:

Answer is 0.5

Step-by-step explanation:

The text implies that the number of traffic accidents determines the number of ambulances required on the road. Hence, 1 traffic accident requires 1 ambulance.

The time slot and time of day remain same in both the text and the question.

The average or mean number of accidents is 1.1

QUESTION: What then is the probability that there is need for exactly 2 ambulances on that road and in that time frame?

In other words, what is the probability that there'll be 2 accidents on that road and in that time frame?

Since the mean number of accidents is 1.1, 2 is above the mean.

Probability of 1.1 accidents is 1, since that's the mean (expected value).

Probability of 2 accidents is 1/2 which is = 0.5

4 0

3 years ago

If you have 24 months to save $4,220 how much would you have to save each month

gulaghasi [49]

Answer:

$175.83

Step-by-step explanation:

All you have to do is 4220 divided by 24 = $175.83

4 0

3 years ago

A map has a scale of ¾ inch represents 6 miles. If two towns are 32 miles apart, what is their distance apart on the map?

serious [3.7K]

3/4 in = 6 mi
? In = 32 miles

32 * 0.74 / 6 = 4 in
The distance apart is 4 in

7 0

2 years ago

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