Whats 8.398 x 10 ^-2 in standard notation

Y=4x-2tan(x), (-pi/2,pi/2) which are the relative min and max?

Jlenok [28]

relative max = pi -2

relative min = -2 pi

Step-by-step explanation:

y= 4x- 2tan(x), (-pi/2,pi/2)

To find relative max and min,

According to mathematical procedure to find relative max and relative min,

the following procedure should be carry out.

Derivating equation with respect to x,

$\frac{dy}{dx} =\frac{d}{dx} (4\times x -2 \times tan x)$ .....(1)

Equating equation (1) to Zero,

We get,

$0 =\frac{d}{dy} (4\times x -2 \times tan x)$

$0 = 4 -2 \times sec^{2} x$

$4 = 2 \times sec^{2} x$

$2 = sec^{2} x$

$x= \frac{\pi }{4}$ ....stationary point

There are total three points

1. -pi/2 2. pi/2 3. pi/4

checking local min and local max

first considering -pi/2;

$\frac{d^{2}y }{dx^{2} } =\frac{d^{2} }{dx^{2} } (4\times x -2 \times tan x)$ ...(2)

putting x= pi/4 in equation (2),

we get,

$\frac{d^{2}y }{dx^{2} } = -4$ <0

So, we have local max at x=pi/4

by putting value of x in equation (1);

we get,

$y = 4\times (\pi /4 ) -2 \times tan (\pi /4 )$

$y = \pi - 2$ .... is maximum point.

Similarly, at x= -pi/ 2,

$\frac{d^{2}y }{dx^{2} } = 1$ >0

So, we have local min at x=-pi/2

by putting value of x in equation (1);

we get,

$y = 4\times (-\pi /2 ) -2 \times tan (-\pi /2 )$

$y = -2 \times \pi$ .... is minimum point

3 0

3 years ago

Read 2 more answers

Leo invests $2,000 loses money at a rate of 4%. How much is the investment worth in total at the end of 3 years? Round to the ne

barxatty [35]

Answer:

Leo's investment is worth $1,760 at the end of 3 years

Step-by-step explanation:

Simple Interest

Leo invests $2,000 and loses money at a rate of 4% (yearly),

It's required to find the value of his money at the end of 3 years.

Since Leo losses 4% per year, the amount lost per year is:

$2,000*4/100=$80

For three years, he loses 3*$80 = $240

Thus, his money is worth:

$2,000 - $240 = $1,760

Leo's investment is worth $1,760 at the end of 3 years

5 0

3 years ago

A basketball coach keeps track of the points scored per game for all of the players . She gives a trophy to the player with the

Verdich [7]

Your Question was incomplete so I will solve a similar question that will help you to tackle this kind of questions.

Q)Two university female basketball players are being considered for an award to be given to the most consistent player with the highest scoring average for the season. The number of points scored per game for all games played during the season is given by the following table. ( Table Attached)

a) Calculate the population mean and population standard deviation of the number of points scored per game for each player.

(b) Using the results of part (a) which player should receive the award.

Answer:

<h3>Player B should receive the award.</h3><h3>Step-by-step explanation:</h3>

Points of player A:- 5,32,45,25,8,10,35,12,37,21

First we will calculate the mean for player A

∑x = 5 + 32 + 45 + 25 + 8 + 10 + 35 + 12 + 37 + 21

∑x = 230

N = 10

Mean = µ= ∑x/N = 230/10 = 23

Now we will calculate the standard deviation for Player A

x - µ = -18 , 9, 22, 2, -15, -13, 12, 11, 14, -2

(x - µ)^2 = 324, 81, 484, 4, 225, 169, 144, 121, 196, 4

∑(x - µ)^2 = 1752

σ = sqrt( ∑((x - µ)^2/N) )

σ = sqrt(1752/10)

σ = 13.236

Calculating mean for player B:

Points of player B = 18, 20, 22, 15, 35, 24, 29, 19, 25, 23

∑x = 18 + 20 + 22 + 15 + 35 + 24 + 29 + 19 + 25 + 23

N =10

µ = 230/10

µ = 23

Calculating standard deviation for player B:

(x - µ ) = -5, -3, -1, -8, 12, 1, 6, -4, 2, 0

(x -µ )^2 = 25, 9, 1, 64, 144, 1, 36, 16, 4, 0

∑(x - µ)^2 = 300

σ = sqrt(300/10)

σ = 5.48

Since both Player A and Player B have same mean we will calculated the coefficient of variation for both the players.

For player A:

σa/µa *100 = 13.24/23 *100 = 57.56

For Player B:

σb/µb *100 = 5.48/23 * 100 = 23.82

Since the coefficient of variation of Player B is less than Player A hence Player B should receive the award.

3 0

3 years ago

Read 2 more answers

Does (3,8) make the Equation y=x-5 true?

Setler79 [48]

Answer:

no

Step-by-step explanation:

3 0

3 years ago

Give a list of three rational numbers eat in a different form

alexira [117]

I guess you mean 'each'.
They could be:-
_
2 , 1/2 and 0.3

4 0

3 years ago