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2 years ago

Find any relative extrema of the function. (Round your answers to three decimal places.)

Mathematics

1 answer:

Strike441 [17]2 years ago

8 0

(x) = arcsec(x) − 8x

f'(x) = d/dx( arcsec(x) − 8x )

1/xsqrt( x^2 - 1) - 8

f'(x) = 0

1/xsqrt( x^2 - 1) - 8 = 0

8 x sqrt (x^2-1) = 1

( 8 x sqrt (x^2-1) )^2 = 1

64 x^2 ( x^2 - 1) = 1

64 x^4 - 64 x^2 =1

64 x^4 - 64 x^2 - 1 = 0

x = 1.00766 , - 1.00766

x = - 1.00766

f(- 1.00766) = arcsec(- 1.00766) − 8( - 1.00766)

f( - 1.00766 ) = 11.07949

x = 1.00766

f(1.00766) = arcsec(1.00766) − 8( 1.00766)

f(1.00766 ) = -7.93790

relative maximum (x, y) = (- 1.00766 , 11.07949 ) relative minimum (x, y) = ( 1.00766 , -7.93790 )

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You and three friends own a paint shop. The shop's profit was $536 in the first month. You always divide the profits equally. In

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C. $360

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2 years ago

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There are some nickels dimes and quarters in a large piggy bank for every two nickels there are 3 dimes for every two dimes that

creativ13 [48]

We are given

piggy bank has nickels , dimes and quarters

Let's assume

number of nickels =n

every two nickels there are 3 dimes

so, number of dimes are

$=\frac{3}{2}n$

$=1.5n$

every two dimes that are 5 quarters there

so, number of quarters are

$=\frac{5}{2}\times 1.5n$

$=3.75n$

so, total number of coins = number of nickels + number of dimes +number of quarters

total number of coins =n+1.5n+3.75

there are 500 coins

so, we get

$n+1.5n+3.75n=500$

now, we can solve for n

$6.25n=500$

divide both sides by 6.25

so, we get

$n=80$

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$=1.5\times 80$

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number of quarters is 3.75n

$=3.75\times 80$

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so,

Number of nickels =80

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2 years ago

Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be

makkiz [27]

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

Lets get Jorge's time :

As the rate is constant, we can find the slope to know the number of cups he is filling per minute.

Slope is found using: $\frac{y2-y1}{x2-x1}$

= $\frac{53-25}{5-3}$

= $\frac{28}{2}=14$

From the table lets get Mary's time:

$\frac{99-81}{1-0.5}$

= $\frac{18}{0.5}=36$

Another data: $\frac{63-45}{2-1.5}$

= $\frac{18}{0.5}=36$

Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.

Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.

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2 years ago

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Answer:

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Thank you.

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