Use the method of Lagrange Multipliers to find any maximum or minimum values of the function f(x,y)=x2+y2 subject to the constraint xy=1.

Answer: 4

Step-by-step explanation:

The standard equation of a circle is (x−h)^2 + (y−k)^2 = r^2, with (h,k) being the center and r being the radius. In the equation you provided, r = 4.

Answer:

Step-by-step explanation:

(x-h)²+(y-k)²=r²

radius=r

Answer:

[tex] x = 11 [/tex]

Step-by-step explanation:

Given that ∆CDE ~ ∆FGH

CD = 25

DE = 35

FG = 65

GH = 8x + 3

Therefore,

[tex] \frac{CD}{FG} = \frac{DE}{GH} [/tex]

(Similarity Theorem)

[tex] \frac{25}{65} = \frac{35}{8x + 3} [/tex]

Cross multiply

[tex] 25(8x + 3) = 35*65 [/tex]

[tex] 200x + 75 = 2275 [/tex]

[tex] 200x + 75 - 75 = 2275 - 75 [/tex]

[tex] 200x = 2200 [/tex]

[tex] \frac{200x}{200} = \frac{2200}{200} [/tex]

[tex] x = 11 [/tex]

Answer:

C. 11

Step-by-step explanation:

x = 11

Answer: 10,000

Step-by-step explanation: 10 to the 2nd power or 10^2 is 100 so you multiply 100x100 which is 10,000

Answer:

10,000

Step-by-step explanation:

10^2*10^2

10^4=10,000

Answer:

Hey there!

3x-9=114

3x=123

x=41

Let me know if this helps :)

Answer:

at N ≥ 6

Step-by-step explanation:

Error permissible = 0.001

The series = infinity  

at ( N + 1 ) ! > 1000  the inequality N ≥ 6 is valid and holds

attached below is the detailed solution using alternating series remainder

Answer:

x^2 -81

Step-by-step explanation:

(x+9)(x-9)

FOIL

first x*x = x^2

outer -9x

inner 9x

last -9*9 = -81

Add them together

x^2 -9x+9x -81

Combine like terms

x^2 -81

Answer: B

Step-by-step explanation:

Simply using (a-b)(a+b)=a^2-b^2.

Evaluate the power (9^2).

x^2 - 81

Answer:

the answer is 4) 10π/9 inches

Step-by-step explanation:

all answers have π on the nominator but i could not insert it for some reason

[tex]Question 7 options:\\1) \frac{40}{3}inches \\2) \frac{5}{3} inches\\3) \frac{100}{3} inches \\4) \frac{10}{9} inches[/tex]

A circle is a curve sketched out by a point moving in a plane. The length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the radius of the circle is 2 inches, while the angle made by the arc at the centre of the circle is 100°. Therefore, the length of the arc can be written as,

Length of the arc = 2 × π × R × (θ/360°)

                              = 2 × π × 2 inches × (100°/360°)

                              = 10π / 9  inches

                              = 3.49 inches

Hence, the length of the arc with a central angle of 100° and a radius of 2 inches is 3.49 inches.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ2

Answer:

Step-by-step explanation:

a) Revenue function us derives by taking the product of the number of yachts and the demand function p given. Mathematically,

R(x) = xp(x)

Given p(x) = 700 − 0.01x ln(x)

R(x) = x{700 − 0.01x ln(x)}

R(x) = 700x - x(0.01x ln(x))

R(x) = 700x - 0.01x²lnx

Hence the revenue function R(x) is expressed as R(x) = 700x - 0.01x²lnx

Marginal revenue function is derived by finding the derivative of the revenue function R(x). On differentiating;

d{R(x)}/dx = 700 - 0.01{x²(1/x)+2xlnx} (note that product rule was used to differentiate the function in parenthesis).

d{R(x)}/dx = 700 - 0.01{x+2xlnx}

Open the parenthesis

d{R(x)}/dx = 700 - 0.01x-0.02xlnx

Hence the marginal revenue function R'(x) is expressed as 700 - 0.01x-0.02xlnx.

b) In order to estimate the revenue to be realized from the sale of the 375th 34 ft Sundancer yacht, we will simply substitute the variable x = 375 into the revenue function R(x)

Given R(x) = 700x - 0.01x²lnx

R(375) = 700(375) - 0.01(375)²ln(375)

R(375) = 262500-1406.25ln(375)

R(375) = 262500-8334.74

R(375) = 254,165.26

Hence the revenue realized from the sale is approximately $254,165

For the Marginal revenue Function,

R'(x) = 700−0.01x−0.02xln(x)

R'(375) = 700−0.01(375)−0.02(375)ln(375)

R'(375) = 700−3.75−0.02(375)ln(375)

R'(375) = 700-3.75-44.45

R'(375) = 651.8

The marginal revenue is approximately $652

Answer:

[tex]\sqrt[3]{x^2}[/tex]

x ^( 1/8)

Step-by-step explanation:

x ^ (5/6)  ÷ x ^ (1/6)

We know that a^ b ÷ a ^c = a^ ( b-c)

x^ ( 5/6 - 1/6)

x^ (4/6)

x ^ 2/3

[tex]\sqrt[3]{x^2}[/tex]

[tex]\sqrt{x}[/tex][tex]\sqrt[\\4]{x}[/tex]

x ^ 1/2 * x ^ 1/4

We know that a^ b * a ^ c = a^ (b*c)

x ^ (1/2 * 1/4)

x ^( 1/8)

Answer:

[tex]\huge \boxed{\sqrt[3]{x^{2} } } \\ \\ \huge \boxed{x^{\frac{3}{4} } }[/tex]

Step-by-step explanation:

Part 1:

x^(5/6) ÷ x^(1/6)

Applying exponent rule : a^b ÷ a^c = a^(b-c)

x^(5/6-1/6)

x^(4/6)

Simplifying the exponent.

x^(2/3)

Converting to simplest radical form.

(x^2)^(1/3)

[tex]\sqrt[3]{x^{2} }[/tex]

Part 2:

[tex]\sqrt{x} \times \sqrt[4]{x}[/tex]

Converting to exponent form.

x^(1/2) × x^(1/4)

Applying exponent rule : a^b × a^c = a^(b+c)

x^(1/2+1/4)

x^(2/4+1/4)

x^(3/4)

Answer: No solution. 27=9

Answer:  14) 44°    15) 6.5

Step-by-step explanation:

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped

14) Given: a = 7,  b = 6,  c = 10, A = ???

7² = 6² + 10² - 2(6)(10) · cos A

49 = 36 + 100 - 120 cos A

49 = 136 - 120 cos A

-87 =  - 120 cos A

0.725 = cos A

43.5° = A

15) Given: A = 21°,  b = 18,  c = 16

a² = 18² + 16² - 2(18)(16) · cos 21°

   = 324 + 256 - 576 cos 21°

   = 580 - 576 cos 21°

   = 42.26

[tex]a=\sqrt{42.26}[/tex]

   = 6.5

Answer:

Assuming you mean (6^2/3)^6, the exponent 6 2/3 in the simplification should be replaced with 4

Step-by-step explanation:

Apply the power rule and multiply exponents.

6 ^2 /3  * 6

Cancel the common factor of  3

6 ^2 *2

Multiply  2  by  2 .

6 ^4

Answer: B. a savings account earns interest

Step-by-step explanation: Money loses value over time as the rate of inflation increases. In this scenario, when you have some money to spare, the ideal is to seek some kind of investment that earns interest.

Saving is one such option. The money in savings earns interest and is highly liquid, meaning it can be used at any time. In addition, saving is a very...

Answer:

B

Step-by-step explanation:

Answer:

Wyatt played 3 games and went on 6 Rides

Step-by-step explanation:

Let games be represented as x

Let ride be represented as y

Each game cost $1.25

Each ride cost $2.75

Total money spent by Wyatt= $20.25

x1.25 + y2.75 = 20.25 ..... Equation 1

the number of rides he went on is twice the number of games he played

Y= 2x ... Equation 2

Substituting the value of y into equation 1

x1.25 + y2.75 = 20.25

x1.25 + 2(x)2.75 = 20.25

x1.25 + x5.5 = 20.25

x6.75= 20.25

x= 20.25/6.75

X= 3

Y= 2x

Y= 2(3)

Y= 6

Wyatt played 3 games and went on 6 Rides

Answer:

Wyatt played 3 games and went on 6 rides.

Step-by-step explanation:

Answer:

Sample mean = 6

Sample standard deviation = 3

Range = 3 to 9

Step-by-step explanation:

Given data:

Rankings (x)

9

6

1

7

7

sample size = n = 5

(a)

Sample Mean: [tex]\frac{}{x}[/tex] = ∑x/n

                            = 9+6+1+7+7 / 5

                            = 30 / 5

                    [tex]\frac{}{x}[/tex]      = 6

Sample Standard Deviation = s = √(x- [tex]\frac{}{x}[/tex] )²/n-1

= √((9-6)² + (6-6)² + (1-6)² + (7-6)² + (7-6)²) / (5-1)

= √((3)² + (0)² + (-5)² + (1)² + (1)²) / 4

= √(9+0+25+1+1)/4

= √36 / 4

= √9

= 3

s = 3

b) In what range does the empirical rule predict that approximately 68% of the class will rank you?

As per the empirical rule, 68% of data falls within first standard deviation  from the mean μ ± 1σ

[tex]\frac{}{x}[/tex]  = 6

s = 3

So

6 - 3 = 3

6 + 3 = 9

Hence the range is from 3 to 9

Answer:

-2, 2 and 3.

Step-by-step explanation:

each of the brackets could be zero.

So for example x + 2 = 0 gives x = -2.

Answer:

x=-2   x=2   x=3

Step-by-step explanation:

g(x) = (x + 2)(x − 2)(x − 3)

Set the function equal to 0

(x + 2)(x − 2)(x − 3) =0

Using the zero product property

x+2 =0  x-2 =0  x-3 =0

Solve each equation

x=-2   x=2   x=3

These are the zeros

Answer:

n = 10

Step-by-step explanation:

3n1!/(n-4)! = (n-1)!/( n-1-5)

3n(n-1)(n-2)(n-3)(n-4) / N-4 -------- case1 ( cancel ( n-4) from top and bottom)

= (n-1)(n-2)(n-3)(n-4)(n-5)(n-6) / n-6 --------- case 2 ( Cancel n-6 from top and

                                                                                 bottom and also cancel n-1,

                                                                                  n-2, n-3 with case 1)

3n = ( n-4)(n-5)

3n = n² - 5n - 4n + 20

3n =  n² - 9n + 20

0 = n² - 9n - 3n + 20

0 = n² - 12n + 20

0 = (n-2)(n-10)

n = 2  ( not valid)       n = 10

Therefore n = 10

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}}}}[/tex]

Step-by-step explanation:

[tex] \sf{( {x}^{5} + {x}^{3} ) - (6x - {x}^{3} + 6 {x}^{5}) }[/tex]

When there is a ( - ) in front of an expression in parentheses , change the sign of each term.

Also, remove the parentheses

⇒[tex] \sf{ {x}^{5} + {x}^{3} - 6x + {x}^{3} - 6 {x}^{5} }[/tex]

Collect like terms

⇒[tex] \sf{ {x}^{5} - 6 {x}^{5} + {x}^{3} + {x}^{3} - 6x}[/tex]

⇒[tex] \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}[/tex]

Hope I helped!

Best regards!!

Answer:

1/8

Step-by-step explanation:

1/4 ÷ 2

copy dot flip

1/4 * 1/2

1/8

Answer:

Step-by-step explanation:

(r/s)(x) is the quotien of r(x) = 3x - 1 and s(x) = 2x + 1:

  r            3x - 1

(-----)(x) = ----------

  s            2x + 1

Answer:

Hello The data set is missing below is the missing data set

507,389,305,291,336,310,514,442,373,428,387,454,323,441,388,426,411,382,320,450,309,416,359,388,307,337,469,351,422,413

Step-by-step explanation:

Data set:

507,389,305,291,336,310,514,442,373,428,387,454,323,441,388,426,411,382,320,450,309,416,359,388,307,337,469,351,422,413

To CONSTRUCT a Frequency Distribution do the following

attached is the frequency table and histogram representation

Answer:

  b.  3 = 3/1

  c.  -4 = -4/1

Step-by-step explanation:

An integer can be written as a rational number with a denominator of 1. The denominator can be anything else, too, in which case the numerator must be multiplied by that same value.

__

b. 3 = 3/1 = 6/2 = 27/9

__

c. -4 = -4/1 = 8/-2 = -12/3

Answer:

The question is not clear

Answer:

x=2

Step-by-step explanation:

-7/2x + 3/2 + 2 =-7/2

Add the numbers

3/2+2

2=2/1=4/2

3/2+4/2=7/2

-7/2x+7/2=-7/2

Subtract 7/2 from both sides

-7/2x=-14/2

Multiply both sides by 2

-7x=-14

Divide both sides by -7

x=2

Answer:Variable expressions are expressions that involve variables, which are symbols that represent changing quantities. The value of the expression will change as the value of the variable changes.

For example, let's say with have the equation

x

+

5

When

x

=

1

, then

x

+

5

=

6

When

x

=

2

then

x

+

5

=

7

Hope that was helpful.

Answer:

Place Value

Step-by-step explanation:

To Find:in a multi-digit number, the number place that a digit is in determines it's?

Solution :

The number place that a digit is in determines it's PLACE VALUE

Definition of place value : Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Thus in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

Eg . 389

Since the digit 8 is on tens place

So, it makes us to determine its place value

Place value of 8 is 80

Hence in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

Answer:

1245 is the answer of this question

Answer:

$450

Step-by-step explanation:

Let R be the hourly pay rate in dollars per hour. Hannah worked 10 hours and Zach worked 9 hours for a total of $950, so we get the equation:

10R + 9R = 950

Solve for R:

19R = 950

R = 50

Zach worked for 9 hours, so the total he earned is:

9 hours * 50 dollars/hour = $450