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2 years ago

Find a function of the form y=Asin(kx)+C or y=Acos(kx)+C whose graph matches this one:

Mathematics

1 answer:

kumpel [21]2 years ago

4 0

Answer:

y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

k·10 = 2π

k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

y = 4cos((π/5)x) +3

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The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.

EastWind [94]

Answer:

$P(t) = 200\cdot 0.95^t$

Step-by-step explanation:

The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.

Write a function that gives the lion population size,

Each year, the population drops to 95% of its previous value. (100 - 5)%

That is, the population is multiplied by 0.95 each year.

Repeated multiplication is signified by an exponent.

Here, that exponent is the number of years from today (t).

<h3>There fore, The population function can be written as ...</h3><h3 /><h3> P(t) = 200·0.95^t</h3><h3> $P(t) = 200\cdot 0.95^t$ </h3>

8 0

2 years ago

In 1603, German astronomer Christoph Scheiner began to copy and scale diagrams using an instrument that came to be known as the

Softa [21]

Answer:

1. The pin’s location aids to create two drawings simultaneously. This is that while drawing an image, a copy, which may vary in size, is created at the same time.

2. The pantograph relates to dilation and similarity due to the use of similar triangles that affect the scale of the second drawing.

3. The use of similar triangles illustrates the process of the pantograph because the ratio of similitude is set when determining where to place the pin. When a triangle is moved while tracing a line, along with the outline of the image, an enlarged/reduced version of the image is created by the other pantograph's end.

4. The pantograph is now obsolete and has been replaced by several different ways of producing duplicates such as photocopying, mass printing, and digital filing.

4 0

2 years ago

Ronnie wants to lower his utility bills to save money on his monthly expenses. He discovers that if he replaces his water heater

Soloha48 [4]

Alright, lets get started.

Last year, Ronnie's utility expenses were = 1935.67 $

After switching to electric water heater to solar water heater, his yearly utility bills get reduced.

This year, Ronnie's utility expenses are = 862.40 $

So the difference on utility bills Ronnie saved = $1935.67 - 862.40$

so, difference Ronnie saved = 1073.27 $

So, the percentage of amount Ronnie saved = $\frac{1073.27}{1935.67} *100$

Percentage of amount Ronnie saved = 55.45 %

Hence, 55.45 % Ronnie save on his utlility bills by switching to a solar water heater. : Answer

Hope it will help :)

5 0

2 years ago

Read 2 more answers

The Fibonacci sequence was first discovered during a study of rabbits. If newborn rabbits become adults in one month, each pair

Rina8888 [55]

Answer:

There will be 233 pairs of rabbits would be produced after thirteen months.

Step-by-step explanation:

Consider the provided information.

In the Fibonacci sequence we can find the next term by adding the two numbers before it.

Let us consider that we have 1 pair of newborn rabbits in first month.

Then in the second month they will fully grow.

On the next month 1 more pair of baby rabbits were born.

Next month the baby rabbits were grown and the first pair had two more baby rabbits.

Thus the sequence will look like:

Sequence: 1, 1, 2, 3

It is given that the it follows the Fibonacci sequence. Now use the above rule to generate the Fibonacci sequence.

The required Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

We need to find the number of pairs of rabbits would be produced after thirteen months.

Now from the above sequence we can find the number of rabbits produced after thirteen months.

Hence, there will be 233 pairs of rabbits would be produced after thirteen months.

4 0

2 years ago

The center of a hyperbola is located at (0, 0). One focus is located at (0, 5) and its associated directrix is represented by th

Lady bird [3.3K]

For a hyperbola $\dfrac{y^{2}}{a^{2}}-\dfrac{x^{2}}{b^{2}}=1$
where $a^{2}+b^{2}=c^{2}$
the directrix is the line $y=\dfrac{a^{2}}{c}$
and the focus is at (0, c).

Here, we have c = 5, a² = 9, so b² = 5² - 9 = 16.
a = √9 = 3
b = √16 = 4

Your hyperbola's constants are ...
a = 3
b = 4

______
Please note that the equation of a hyperbola has a negative sign for one of the terms. The equation given in your problem statement is that of an ellipse.

8 0

2 years ago

Read 2 more answers