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zalisa [80]
3 years ago
12

an object hangs from a string in a stable position and is represented by the function y=4sin(3x)+4, with time in x seconds. what

is the maximum height of the object, and when does it occur on the interval 0
Mathematics
1 answer:
Tpy6a [65]3 years ago
3 0

Answer:

Here we have the position of an object represented by the equation:

y = 4*sin(3*x) + 4

Where we can assume that y represents the height of the object.

We want to find the maximum height of the object, and for which value of x it happens in the interval 0 ≤ x ≤ 5

First let's find the maximum height.

y = 4*sin(3*x) + 4

Here the only variation is on the sin( ) part, we know that the maximum value of the sin(x) function is:

sin(x) = 1

when x = 90° = pi/2 = 3.14/2

Replacing that in the equation, we get:

y = 4*1 + 4 = 8

The maximum height of the object is 8.

Now, we know that the maximum of the sin(x) function is when x = pi/2

But in our case, we have the function sin(3*x)

Then this function is maximized when:

3*x = pi/2

x = pi/(2*3) = pi/6 = 3.14/6

And:

0 < 3.14/6 < 5

Then the first maximum occurs at x = 3.14/6 = 0.52

But it can happen again on the interval.

The next maximum of the sin(x) function is when:

x = pi/2 + 2*pi

In our case, we again have sin(3*x), then we need to solve:

3*x = pi/2 + 2*pi

x = (pi/2 + 2*pi)/3 = (3.14/2 + 2*3.14)/3 = 2.62

This is also in the interval 0 < x < 5

The next maximum of sin(x) happens at:

x = pi/2 + 2*pi + 2*pi

In our case, for sin(3*x) we need to have:

3*x = (pi/2 + 2*pi + 2*pi)

x = (3.14/2 + 2*3.14 + 2*3.14)/2 = 4.71

This again is in the interval 0 < x < 5

(is closer to the upper value, so we can expect that the next maximum does not belong to the interval)

Then the maximum height occurs at:

x = 0.52

Then occurs again at:

x = 2.62

And finally occurs again at:

x = 4.71

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What is 1.13 (where the three is repeating) written as a fraction? Someone pleaseee help!
Bess [88]

Answer:

13/90

Step-by-step explanation:

The decimal that you wrote is mixed non terminal decimal. Which means all the number don't repeat themselves.

The denominator of a non terminating decimal is always 9 even though it depends on the type of the decimal, whether it is simple or mixed

The denominator of the given decimal is 90. The denominator is 2 digit number since the given decimal is also 2 digit decimal even though it is under repeating bars.

And the numerator is 10, 13-3.

We subtract 3 since it is the one repeating itself.

Hope it helps ;) ❤❤❤

3 0
3 years ago
12)<br> Which graph represents the solution for the equation-x-1=-x+ 2?
antiseptic1488 [7]

Answer:

Find the graph that has (2,0)

Step-by-step explanation:

\frac{1}{2}x -1=-x+2

+ x          +x

\frac{3}{2}x - 1  = 2

2(\frac{3}{2}x - 1  = 2)

3x - 2 = 4

    + 2   + 2

3x = 6

/3   /3

x = 2

Your image is blurry, but the point that has (2,0)

Hope that helps!

5 0
2 years ago
Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the
sammy [17]

Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

Here, we firstly would calculate the volume of the pile

Mathematically, that will be;

V = 1/3 * pi * r^2 * h

from the question, h = 14.2

Mathematically, r = d/2

r = 34.4/2 = 17.2 m

So the volume will be:

V = 1/3 * 3.142 * 17.2^2 * 14.2

V = 4,399.7719 m^3

To find the number of sanders to be filled,

we simply divide the volume obtained by the volume a sander can take

That will be;

4,399.7719/6.9

= 637.6 which is 638

4 0
2 years ago
Which of the following points is a solution of the inequality y &lt; |x - 2|?
crimeas [40]

Answer:

(-2,0)

Step-by-step explanation:

y < |x - 2|

Substitute the points in and check

(-2,0)

0 < |-2 - 2|

0 < |-4|

0 < 4  True

(2,1)

1 < |2 - 2|

1 < |0|

1 < 0  False

(2,0)

0 < |2 - 2|

0 < |0|

0 < 0 False

3 0
3 years ago
What is one way to go about prioritizing your duties if a teacher
wlad13 [49]
Check the schedule and do the jobs as they relate to the schedule
5 0
3 years ago
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