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ser-zykov [4K]
2 years ago
9

Find the absolute maximum and absolute minimum values of f on the given interval.

Mathematics
1 answer:
kvasek [131]2 years ago
5 0

Answer:

absolute max= (4.243,18)

absolute min =(-1,-5.916)

absolute max=(pi/6, 2.598)

absolute min = (pi/2,0)

Step-by-step explanation:

a) f(t) = t\sqrt{36-t^2} \\

To find max and minima in the given interval let us take log and differentiate

log f(t) = log t + 0.5 log (36-t^2)\\Y(t) = log t + 0.5 log (36-t^2)

It is sufficient to find max or min of Y

y'(t) = \frac{1}{t} -\frac{t}{36-t^2} \\\\y'=0 gives\\36-t^2 -t^2 =0\\t^2 =18\\t = 4.243,-4.243

In the given interval only 4.243 lies

And we find this is maximum hence maximum at  (4.243,18)

Minimum value is only when x = -1 i.e. -5.916

b) f(t) = 2cost +sin 2t\\f'(t) = -2sint +2cos2t\\f"(t) = -2cost-4sin2t\\

Equate I derivative to 0

-2sint +1-2sin^2 t=0

sint = 1/2 only satisfies I quadrant.

So when t = pi/6 we have maximum

Minimum is absolute mini in the interval i.e. (pi/2,0)

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timurjin [86]

Answer:

CD = 27

Step-by-step explanation:

Given the triangles are similar then the ratios of corresponding sided are equal, that is

\frac{CD}{KD} = \frac{CB}{KL} , substitute values

\frac{CD}{9} = \frac{30}{10} = 3 ( multiply both sides by 9 )

CD = 27

7 0
2 years ago
46. Order these numbers from least to greatest:<br> 1/2, 0.4, 1/3, 1/5
e-lub [12.9K]

Answer:

1/5, 1/3, 0.4, 1/2

Step-by-step explanation:

1/5 = 0.2

1/3 = 0.33

1/2 = 0.5

4 0
2 years ago
3x+2y+4+9y=<br> Plz answer
fomenos
<span>3x+2y+4+9y=


Combine like terms:
2y+9y=11y


I believe the answer is 3x+11y+4

(That is unless you know the numbers that y & x equals)</span>
5 0
3 years ago
Susan threw a softball 42 years on her first try and 51 1/3 yard on her second try. How much farther did she throw the softball
Andru [333]

Answer:

28 feet farther than 1st ball.

Step-by-step explanation:

We have been given that Susan threw a softball 42 yards on her first try and 51\frac{1}{3} yard on her second try.

To find second ball is how much farther from the 1st ball, we will subtract 42 yards from 51\frac{1}{3} yards.

\text{The second ball is farther from 1st ball}=51\frac{1}{3}\text{ yards}-42\text{ yards}

\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-42\text{ yards}

Let us have a common denominator.

\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-\frac{42*3}{3}\text{ yards}  

\text{The second ball is farther from 1st ball}=\frac{154}{3}\text{ yards}-\frac{126}{3}\text{ yards}

\text{The second ball is farther from 1st ball}=\frac{154-126}{3}\text{ yards}

\text{The second ball is farther from 1st ball}=\frac{28}{3}\text{ yards}

\text{1 yard}=3\text{ feet}

\frac{28}{3}\text{ yards}=\frac{28}{3}\times 3\text{ feet}

\frac{28}{3}\text{ yards}=28\text{ feet}

Therefore, Susan thrown the second ball 28 feet farther from the 1st ball.

7 0
3 years ago
Currently the exchange rate between the US Dollar and the Euro is 1 USD = .85 Euro. If you bring $150 to Ireland with you, how m
vesna_86 [32]

Answer:

127.50 euros

Step-by-step explanation:

In order to do this you can just multiply 150 by .85 to find the amount of euros you would get for it.

Hope this helped!

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7 0
3 years ago
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