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2 years ago

Perform the indicated operation. (y4 - 1) ÷ (y + 1)

2 answers:

7 0

$The\ domain:\\D:y\neq-1\\\\(y^4-1)\div(y+1)=\dfrac{(y^2)^2-1^2}{y+1}=\dfrac{(y^2-1)(y^2+1)}{y+1}\\\\=\dfrac{(y-1)(y+1)(y^2+1)}{y+1}=(y+1)(y^2+1)=y^3+y^2+y+1\\\\Used:\\(a^n)^m=a^{nm}\\\\a^2-b^2=(a-b)(a+b)$

Dmitry_Shevchenko [17]2 years ago

3 0

Answer: y^3 - y^2 + y - 1

Step-by-step explanation: Factor the numerator and denominator and cancel the common factors. This should leave you with y^3-y^2+y-1.

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

Strike441 [17]

(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 )

8 0

2 years ago

In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.5 mm. Someone says that th

Travka [436]

Answer:

This statement can be made with a level of confidence of 97.72%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8.1 mm

Standard Deviation, σ = 0.5 mm

Sample size, n = 100

We are given that the distribution of thickness is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling:

$=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.5}{\sqrt{100}} = 0.05$

P(mean thickness is less than 8.2 mm)

P(x < 8.2)

$P( x < 8.2)\\\\ = P( z < \displaystyle\frac{8.2 - 8.1}{0.05})\\\\ = P(z < 2)$

Calculation the value from standard normal z table, we have,

$P(x < 8.2) =0.9772 = 97.72\%$

This statement can be made with a level of confidence of 97.72%.

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2 years ago

At a track meet, the longest shot put throw by a boy is 25 feet and 8 inches. The longest shot put throw by a girl is 19 feet an

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Its 6 feet and 5 inches

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2 years ago

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Difference of 86.42 - 2.1.

densk [106]

Answer:

The first one

Step-by-step explanation:

The decimals line up when you subtract them

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Answer:

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2 years ago