You find yourself in a strange undulating landscape given by the function z = f (x, y) = cos y − cos x, where z is the elevation.
1. Find all maxima, minima, and saddle points. What are the level curves for z = 0?
Graph this function.
You are now at the origin and wish to hike to the point (4π, 0, 0). You contemplate two rather different routes.
2. Your first route always keeps you at the same elevation. Determine such a route of minimal length. What is the length?
3. Your second route always moves along the gradient. Determine such a route of minimal length, assuming you start hiking in the positive x-direction. What is its length? If you cannot find an exact answer, determine an upper bound and a lower bound between which the actual length must lie.
4. Which route is the shorter—that of part (b), or (c)?
Appropriate pictures should be supplied throughout. Justify your answers.

0.9758 is the decay factor of the model

Given that:

The value of the U.S. dollar over time v(t) can be modeled by the following formula:

v(t) = 1.36(0.9758)^t , where t is the number of years since 2000

The form of the exponential decay models is f(t) = ab^t

where,

a is the initial value, b is the decay factor and t is the time

Comparing  f(t) = ab^t with v(t) = 1.36(0.9758)^t :

a = 1.36

b = 0.9758

Therefore, the decay factor is 0.9758

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Answer:

Step-by-step explanation:

x = 174

Answer: 1

Step-by-step explanation:

Answer:

1 or 3/3

Step-by-step explanation:

There is a common denominator (bottom number) so you add straight across.
1+2=3 so it is 3/3, which is a whole, making it 1.

The length of the PM is 6 if ABCD is congruent to MNOP.

When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.

More specifically, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions including translation, rotation, and reflection. This indicates that either object may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. If we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are then congruent. I'm allowed to turn the paper over.

Here  both the given figures are congruent figures. So, their shape and size must be equal.

Therefore from the two figures, PM=DA

So, PM=6

Therefore, the length of the PM is 6 if ABCD is congruent to MNOP.

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The value of x in the quadratic equation using mathematical operations is  4±√19

To solve this problem, we have to use some mathematical operations to find the value of x.

In this process, we have to remove the square root and solve for x. This will eventually result to a quadratic equation

In the equation given;

√(2x - 6) = x - 3

Square both sides

(√(2x - 6)² = (x - 3)²

This will eliminate the square root

2x - 6 = (x - 3)²

Open the bracket on the right hand side

2x - 6 = x² - 6x - 9

Collect like terms

x² - 6x - 9 - 2x + 6 = 0

x² - 8x - 3 = 0

Solving for x

x = 4±√19

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x = 7.26

1. Add 11.24 to both sides

-3.98 = x - 11.24

-3.98 + 11.24 = x - 11.24 + 11.24

2. Simplify

Add the numbers:

-3.98 + 11.24 = x - 11.24 + 11.24

7.26 = x - 11.24 + 11.24

Add the numbers:

7.26 = x - 11.24 + 11.24

7.26 = x

Move the variable to the left:

7.26 = x

x = 7.26

x = 7.26

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

x = 7.26

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

First, add 11.24 to both sides of the equation:

-3.98 = x - 11.24

-3.98 (+11.24) = x - 11.24 (+11.24)

Next, simplify.

11.24 - 3.98 = x

x = 7.26

x = 7.26 is your answer.

~

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By using the concept of probability, it can be calculated that-

1)   P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]

2)  P(Ace [tex]\cap[/tex] 5) = 0

3)  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4)   P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]

5)   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

1) Number of ace card = 4

  Number of '5' card = 4

  P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]

                    = [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)

 Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]

  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) Number of black coloured even numbered card = 10

   Number of even numbered card = 20

   Number of card of black colour = 26

  P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]

                              = [tex]\frac{36}{52}[/tex]

5) Number of face cards of diamond = 3

   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

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The percent of the original price was the price after markup will be 6.29%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

During a deal, a store offered a 25% rebate on a bed that initially sold for $890. After the deal, the limited cost of the bed was increased by 25%.

The marked-up price is given as,

⇒ $890 x (1 - 0.25) x (1 + 1.25)

⇒ $890 x 0.75 x 1.25

⇒ $834

The percentage is given as,

P = [(890 - 834) / 890] x 100

P = (56 / 890) x 100

P = 0.0629 x 100

P = 6.29%

The percent of the original price was the price after markup will be 6.29%.

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Answer: 94%

Step-by-step explanation:

Find what percent of the original price this represents:

$834.375 / $890 = 0.9375

0.9375 × 100 = 93.75%

93.75% ≈ 94%

Round to the nearest whole number

The price after markup was 94% of the original price.

Answer:

Step-by-step explanation: Q13 Find the perimeter of the shape

42x *2=84x

72x*2=72x

Perimeter=84x+72x=156x

Q14 Find the perimeter of the shape just add up 3x +(4x+8)+3(x-2)

=3x+4x+8+3*x+3 *-2

=3x+4x+8+3x-6

=3x+4x+3x+8-6......add together like terms and number terms

=10x+2

Answer:

13.) 156x

14.) 10x + 2 or 2( 5x + 1)

Step-by-step explanation:

13.)perimeter of a parallelogram is

p = 2(a + b)

P = 2( 36x + 42x)

P = 2( 78x )

P = 156x

14.) perimeter of a scalene triangle

P = a + b + c

P = 3x + 3(x – 2) + 4x + 8

P = 3x + 3x –6 + 4x +8

P = 6x + 4x –6 + 8

P = 10x + 2

in factorise form

P = 2(5x + 1)

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The expression for the discount will be written as d = 0.5L.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the discount d is 50% of the list price L. The expression for the discount will be written as below,

Discount = 50% of the list price

d = ( 50 / 100) x L

d = 0.5L

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The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth

What are exponential growth and exponential decay?

Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.

From question,

1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500

This means it is decaying. The difference between the initial price and after 2 years price is $7500.

To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.

Thus exponential decay.

2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.

After 4 hours, the loss is (60 -20) = 40%

As the loss is the same in equal intervals of time, the decay is linear.

3) In the third one, A tiger reserve had an initial population of 20 tigers.

After 5 years the population was 30 tigers, thus the growth is (30-20) =10.

After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.

Thus the increase is non-linear, and so is exponential growth.

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Answer:

Yes it is

Step-by-step explanation:

It will take 12.91 years to earn $ 500 in interest  

Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest. 

The formula used for

P = Principal amount

r = Rate of interest  

n = Number of compounds in a year  

t = Time period in years

And the formula for

Here we have

Principal amount = 1700,

Rate of interest = 2% = 2/100  = 0.02 on decimals  

Given that compound interest gained = $ 500

Number of compounds = 4 times

Let a be the time period

By the given formula,

Amount, A = 1700(1+0.02/4)^4t  

= 1700(1+0.005)^4t    

= 1700 (1.005)^4t  

Compound interest = 1700 (1.005)^4t - 1700

From the given data,

Compound interest = $ 500

=> 1700 (1.005)^4t - 1700 = 500

=> 1700 (1.005)^4t = 2200

=> (1.005)^4t = 1.294

Take logs on both sides

=> log (1.005)^4t = log 1.294

=> 4t log (1.005) = log (1.294)

=> 4t = log(1.294)/log(1.005)

=> 4t = 0.111934276/ 0.00216606176      

[ Use calculator for log(1.294) and log(1.005) ]

=> 4t = 51.6764012

=>  t = 12.9191003  

=>  t = 12.91  

Therefore,

It will take 12.91 years to earn $ 500 in interest

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The monomial that completes the expression 0.01 b²+.....+100 c² is 2bc

From the question, we have the following parameters that can be used in our computation:

0.01 b²+.....+100 c²

Complete the expression with a variable

So, we have

0.01 b² + x + 100 c²

The given terms of the expression are factors/multiples of 10

By trial and error, we make use the following representation

0.01 b² + x + 100 c² = (0.1b + 10c)²

Expand the expression

0.01 b² + x + 100 c² = 0.01 b² + 2bc + 100 c²

Evaluate the like terms

x = 2bc

Hence, the monomial is 2bc

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The mapping diagram above is a function since there are no two values in set B where there is only one mapping from  Set A.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

In the example provided, each element in Set A is mapped to one specific element in Set B.

Set A stands for the domain, whereas Set B stands for the range. There would be exactly one value in the range for each value in the domain as a result.

Hence, the mapping diagram above is a function since there are no two values in set B where there is only one mapping from  Set A.

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Step-by-step explanation:

[tex]x + \frac{75}{4} (x) = 0[/tex]

[tex] \frac{79x}{4} = 0[/tex]

[tex]x = 0[/tex]

Answer:

:)

Step-by-step explanation:

-5a + 6 + 3a + 2

Combine like terms:
-5a + 3a + 6 + 2

2a + 8 is your answer, you can't simplify it further

----------------------------------------------------------------------------------------------------------

If you want to solve for the a value:

-5a + 6 = 3a + 2

Subtract 2 from both sides

-5a + 6 = 3a + 2

      - 2          - 2

-5a + 4 = 3a

(The +2 and -2 cancel each other out, it makes 0)

Add +5a to both sides

-5a + 4 = 3a

+5a        +5a

(The -5a and +5a cancel each other out, it makes 0)

4 = 8a

Divide by 8 on both sides

4/8 (OR 1/2 OR 0.5) = a

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The long term behavior of the rational function f(x) = (x² - 3) / (x³ + 2) is 0, for the rational function g(x) = (x³ - 3) / (x³ + 2) is 1 and for the rational function h(x) = (x⁴ - 3) / (x³ + 2) does not exist.

In this case we find three rational functions, that is, functions of the form:

m(x) = p(x) / q(x)

Where:

Please notice that both numerator and denominator are polynomic functions, the long run behavior of the function depends on the grades of numerator and denominator according to these rules:

Now we proceed to analyze the long run behavior of each rational function:

Case 1: f(x) = (x² - 3) / (x³ + 2)

Grade of numerator: 2, grade of denominator: 3

Result: 0

Case 2: g(x) = (x³ - 3) / (x³ + 2)

Grade of numerator: 3, grade of denominator: 3

Result: 1

Case 3: h(x) = (x⁴ - 3) / (x³ + 2)

Grade of numerator: 4, grade of denominator: 3

Result: N / A

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If the expression  (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2

The expression is (4k + 8) / 4

The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.

The given expression is (4k + 8)/ 4

Solve the expression

(4k + 8) / 4 = 4k/4 + 8/4

Divide the terms

=k + 2

The result is in the form of ak + b

The value of a = 1

The value of b = 2

The value of a/b = 1/2

Therefore, the value of the expression a/b is 1/2

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Answer:

[tex]y=x^2-8x+16[/tex]

Step-by-step explanation:

[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]

The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

At a specific zoo, the typical mass of one blue whale is estimated to be 190000 kilograms. Utilize logical documentation to communicate the mass of 125 blue whales.

⇒ 190,000 × 125

Simplify the expression in the scientific notation, then we have

⇒ 190,000 × 125

⇒ 23,750,000

⇒ 23.75 × 10⁶ kilograms

The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.

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The difference between book value and the amount received is $2000

What was the difference between the book value and the amount received ?

van cost = $16000

Estimated life= 4 years

Residual value= $4000

using straight line method of depreciation

Depreciation per year= 16000-4000/4= 3000

Therefore book value after two years = $16000- 2*3000= $10000

Selling price of book after 2 years= $8000

hence the difference between book value and the amount received

10000-8000= $2000

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The risk-free rate of return on Hilo stock is 1.58%

What is the market risk premium?

Expected return on the stock=risk free rate beta x (expected market return-risk free rate)

14.08%=risk free rate+1.26 x (11.5%-risk free rate)

14.08%=risk free rate+14.49%-1.26 x risk free rate

0.41=0.26 x risk-free rate

risk-free rate=[tex]\frac{0.41}{0.26} %=1.58%[/tex]%=1.58%

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Answer:

10z + 2

Step-by-step explanation:

combine the like terms

3z + 7z = 10z

1 + 1 = 2

10z + 2

The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵

From the question, we have the following parameters that can be used in our computation:

1/7log(x - 1) = 3log(2)

3 ln(w + 6) = 5 ln(6)

Solving the equation (1), we have the following equation

1/7log(x - 1) = 3log(2)

Multiply both sides of the equation by 7

So, we have the following representation

log(x - 1) = 21log(2)

Apply the power rule of logarithm

log(x - 1) = log(2)²¹

By comparison, we have

x - 1 = (2)²¹

Evaluate the exponent

x - 1 = 2097152

So, we have

x = 2097153

Solving the equation (2), we have the following equation

3 ln(w + 6) = 5 ln(6)

Multiply both sides of the equation by 1/3

So, we have the following representation

ln(w + 6) = 5/3 ln(6)

Apply the power rule of logarithm

ln(w + 6) = ln(6)³/⁵

By comparison, we have

w + 6 = (6)³/⁵

So, we have

w = (6)⁻²/⁵

Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵

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Answer

The first equation is the same (4x+2y=26), so we only need to compare the second equation. Just by looking at the second equation, you can see that x+y=8 and -2x - 2y = -16 are the same equation because -2 is multiplied to both sides of the equation x+y=8.

Answer:

Step-by-step explanation:

Triangle Area = 1/2bxh

Base (b) = 12 units

Height (h) = 5 units

1/2 × 12 × 5 =

6 × 5 =

30 units²

Answer:

1 divided by 7 raised to the third power

Step-by-step explanation:

To find the equivalent expression, we can start by applying the rule for multiplying powers with the same base:

(7^(-2)) * (7^3) = 7^(-2+3) = 7^1 = 7

Then, we can apply the rule for raising a power to a power:

7^1 = (7^1)^(-3) = 7^(-3)

Finally, we can apply the rule for raising a number to a negative power:

7^(-3) = 1 / (7^3) = 1 / 343 = 1/7^3

Therefore, the equivalent expression is 1 divided by 7 raised to the third power.