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IrinaVladis [17]
3 years ago
13

Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter

val 0<_t<_0.5. Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).

Mathematics
1 answer:
hoa [83]3 years ago
5 0

Answer:

0.20 and 0.36

Step-by-step explanation:

y(t) = 2 sin (4π t) + 5 cos (4π t)

We wish to convert this to:

y = A sin(ωt + φ)

We know that ω = 4π.  We also know the following:

5 = A sin φ

2 = A cos φ

Divide the first equation by the second equation:

5/2 = tan φ

φ = tan⁻¹(5/2)

Now, square the two equations and add them together.

5² + 2² = (A sin φ)² + (A cos φ)²

29 = A²

A = √29

The equation of the wave is therefore:

y = √29 sin(4π t + tan⁻¹(5/2))

The maximum negative position is -√29.  And half of that is -½√29.

-½√29 = √29 sin(4π t + tan⁻¹(5/2))

-½ = sin(4π t + tan⁻¹(5/2))

7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)

7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π

t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24

Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.

t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24

t ≈ 0.20 or 0.36

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Nutka1998 [239]

Answer:

yes because |x+y|=|x|+|y| is just the same equation just splitting the numbers

They both are the same absolute value equation

Step-by-step explanation:

|x+y|=|x|+|y|

x+y=|x|+|y|

x+y=x+y

7 0
3 years ago
Please help me please<br><br>​
kenny6666 [7]

Answer:

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4 0
3 years ago
Please help me with this !!
Sergio [31]

Answer: AC = 7√3

tan 30° = \frac{BC}{AC}

=> \frac{BC}{AC}=\frac{1}{\sqrt{3} }\\\\\=> AC=BC\sqrt{3} =7\sqrt{3}

Step-by-step explanation:

3 0
3 years ago
Fill in the missing information. Tim Worker is doing his budget. He discovers that the average miscellaneous expense is $45.00 w
nlexa [21]

Answer:

P(38.6

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

z=\frac{X -\mu}{\sigma}

And replacing we got:

z=\frac{38.6- 45}{16}= -0.4

z=\frac{57.8- 45}{16}= 0.8

We can find the probability of interest using the normal standard table and with the following difference:

P(-0.4

Step-by-step explanation:

Let X the random variable who represent the expense and we assume the following parameters:

\mu = 45, \sigma 16

And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:

P(38.6

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

z=\frac{X -\mu}{\sigma}

And replacing we got:

z=\frac{38.6- 45}{16}= -0.4

z=\frac{57.8- 45}{16}= 0.8

We can find the probability of interest using the normal standard table and with the following difference:

P(-0.4

6 0
3 years ago
I need help with this problem
Tju [1.3M]
2 x 2 x 3 x 3



This is really easy to search up btw
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2 years ago
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