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vekshin1
3 years ago
13

The graph of the piecewise function f(x) is shown.

Mathematics
1 answer:
Anton [14]3 years ago
3 0

The range is virtually the answer to the question,

"In which interval can find all y-values of the function".

So you look at the y-axis and see that your function begins with y=-5 (including -5 because of the dot on the graph) and ends at including y=-1.

So the interval notation is,

y\in[-5,-1]

But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,

-5\leq y\leq-1

To specify that this is a set use curly bracelets and a bar,

\{y\mid-5\leq y\leq-1\}.

The y before bar is a step function and everything followed after the vertical bar is the range of the step function.

Hope this helps.

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you are riding a bicycle which has tires with a 25-inch diameter at a steady 15-miles per hour, what is the angular velocity of
motikmotik

Answer:

The angular velocity is 6.72 π radians per second

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The formula of the angular velocity is ω = \frac{v}{r} , where v is the linear velocity and r is the radius of the circle

The unit of the angular velocity is radians per second

∵ The diameter of the tire is 25 inches

∵ The linear velocity is 15 miles per hour

- We must change the mile to inch and the hour to seconds

∵ 1 mile = 63360 inches

∵ 1 hour = 3600 second

∴ 15 miles/hour = 15 ×  \frac{63360}{3600}

∴ 15 miles/hour = 264 inches per second

Now let us find the angular velocity

∵ ω = \frac{v}{r}

∵ v = 264 in./sec.

∵ d = 25 in.

- The radius is one-half the diameter

∴ r = \frac{1}{2} × 25 = 12.5 in.

- Substitute the values of v and r in the formula above to find ω

∴ ω = \frac{264}{12.5}

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∴ ω = 6.72 π radians per second

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3 0
3 years ago
In order to remove water from a flooded basement, two pumps, each rated at 40 gallons per minute, are used. After half an hour,
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Answer:

3600 gallons of water was removed from the basement.

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Given:

Rate of each pump = 40 gallons/min

We need to find find the number of gallons of water removed from the basement.

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Now Given:

After half an hour, the one pump burns out.

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Now for 30 mins both the pumps were working and removing the water.

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Also Given:

the second pump finishes removing the water half an hour later.

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framing in equation form we get;

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Hence 3600 gallons of water was removed from the basement.

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3 years ago
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