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2 years ago

Find the 30th derivative of y=cos(2x)

Mathematics

1 answer:

Sladkaya [172]2 years ago

8 0

I got this answer from someone else so I’m not sure this is correct but I really hope it helps...

Step-by-step explanation:

Look for patterns in the derivatives.

y=cos2x

y'=-2sin2x

y''=-4cos2x

y'''=8sin2x

y''''=16cos2x

Notice that sin and cos alternate every derivative. Also, they alternate positive and negative every 2 derivatives.

The constant is just 2^(derivative#).

Every odd derivative has sin and every even derivative has cos, so you know that the 30th derivative will be cos.

If you follow the pattern of negatives and positives, you find that the 30th derivative will be negative.

y^(30)= -2^30cos2x

y^(30)= -1073741824cos2x

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Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of

ehidna [41]

Answer:

The required system of equations is,

$y=25+x$

$y=20+2x$ .

Step-by-step explanation:

Let the number of hours spent by Lucy = x

It is given that,

Local zoo charges initial fee $25 and per hour fee $1.

So, the equation representing the cost if Lucy stays 'x' hours is,

$y=25+x$ in dollars.

Also, Local citcus charges initial fee $20 and per hour fee $2.

So, the equation representing the cost if Lucy stays 'x' hours is,

$y=20+2x$ in dollars.

Since, the objective function for the situation is to 'minimize the cost'.

So, upon solving the equations, we will get the minimum value as,

25+x = 20+2x

i.e. x= 5

Thus,

$y=25+x$ implies $y=25+5$ i.e. y= $30

$y=20+2x$ implies $y=20+2\times 5$ i.e. $y=20+10$ i.e. y= $30

Thus, the minimum value is $30.

The required system of equations is,

$y=25+x$

$y=20+2x$ .

8 0

2 years ago

During batting practice, two pop flies are hit from the same location, 2 s apart. The paths are modeled by the equations h = -16

jolli1 [7]

To find the time at which both balls are at the same height, set the equations equal to each other then solve for t.
h = -16t^2 + 56t
h = -16t^2 + 156t - 248
-16t^2 + 56t = -16t^2 + 156t - 248
You can cancel out the -16t^2's to get
56t = 156t - 248
=> 0 = 100t - 248
=> 248 = 100t
=> 2.48 = t
Using this time value, plug into either equation to find the height.
h = 16(2.48)^2 + 56(2.48)
Final answer:
h = 40.4736
Hope I helped :)

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masya89 [10]

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2 * 3 = 6.

2 * 3 * r = 96

Find r: 96/6 = 16.

2 * 3 *16 = 96.

r = 16.

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2 years ago

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Nimfa-mama [501]

Answer:

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Svet_ta [14]

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