Using Euler's relation, derive the following relationships:a. Cosθ=½(e^jθ+e^−jθ)b. Sinθ=½(e^jθ−e(^−jθ)

Answer:

k =  z/4 + 3

Step-by-step explanation:

8k-2z = 24

8k = 24 + 2z

k = (24 + 2z)/8

k = (24 + 2z) / (4*2)

k = (12 + z) / 4

k = 3 + z/4

Answer:

A. 6 = 36

8 = 64

10 = 100

12 = 144

14 = 196

B. 340

C. 582

D.6= 36

7 =49

8 = 64

9= 81

10= 100

no just do the stuff in the parentheses then multiply by 5

Answer:

[tex]6+2.5r\leq 50[/tex]

Step-by-step explanation:

Hi!

The options regarding the inequalities are not listed, though we can still proceed to write the inequality.

From the problem statement you cannot spend more than $50

and you are charged admission fee of $6 flat

a ride cost $2.50 per ride

the number of rides is given as r

yet in all you must not go beyond your limit

Therefore the inequalities can be presented as

[tex]6+2.5r\leq 50[/tex]

Answer:

2.5r + 6 ≤ 50

Step-by-step explanation:

Answer:

(14, 6 )

Step-by-step explanation:

Given

[tex]\frac{1}{7}[/tex] x + [tex]\frac{1}{6}[/tex] y = 3 ( multiply through by 42 to clear the fractions )

6x + 7y = 126 → (1)

[tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{3}[/tex] y = 5 ( multiply through by 6 to clear the fractions )

3x - 2y = 30 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 6x + 4y = - 60 → (3)

Add (1) and (3)term by term to eliminate x

11y = 66 ( divide both sides by 11 )

y = 6

Substitute y = 6 into either of the 2 equations and evaluate for x

Substituting into (1)

6x + 7(6) = 126

6x + 42 = 126 ( subtract 42 from both sides )

6x = 84 ( divide both sides by 6 )

x = 14

Solution is (14, 6 )

Answer:

7 is not a solution for x.

Step-by-step explanation:

To see if 7 is a solution for x, we will simply plug in the value for x and see if the left hand side is equal to the right hand side.

3x + 8 - x = 57 - 4

3(7) + 8 - (7) ?= 57 - 4

21 + 8 - 7 ?= 53

29 - 7 ?= 53

22 ?= 53  (( NO ))

Since 22 does not equal 53, 7 is not a solution for x.

Let's find the solution for x:

3x + 8 - x = 57 - 4

2x + 8 = 53

2x = 45

x = 22.5

Let's validate this solution for x:

3x + 8 - (x) = 57 - 4

3(22.5) + 8 - (22.5) ?= 57 - 4

67.5 + 8 - 22.5 ?= 53

45 + 8 ?= 53

53 == 53  (( YES ))

Since 53 is indeed equal to 53, then 22.5 is a solution for x.

Cheers.

Answer:

No, 7 is not a solution. x=11.25

Step-by-step explanation:

To find whether 7 is a solution, we can plug it in as x.

3(7)+8-7=57-4

21+15=53

36=53

No, 7 is not a solution.

We can find the solution by solving out the equation normally

3x+8+x=57-4

2x+8=53

2x=45

x=22.25

Answer:

(5,4)

Step-by-step explanation:

Moving right, so moving along the x- axis in the positive direction. So add 4 to the x value of the ordered pair.

Answer:

16x^2 - 8x - 3

Step-by-step explanation:

f(x) = 4x + 1

g(x) = 4x -3

f(x) * g(x) = (4x+1) * (4x-3)

(16x^2 - 12x + 4x -3)

Combine like terms

16x^2 - 8x - 3

that's your answer

The value of f (x) × g (x) will be;

⇒ 16x² - 8x - 3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The value of function are,

⇒ f(x) = 4x + 1

⇒ g (x) = 4x - 3

Now.

Since, The value of function are,

⇒ f(x) = 4x + 1

⇒ g (x) = 4x - 3

Hence, We get;

⇒ f (x) × g (x) = (4x + 1) (4x - 3)

                    = 16x² - 12x + 4x - 3

                    = 16x² - 8x - 3

Thus, The value of f (x) × g (x)  = (16x² - 8x - 3)

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Answer:

Domain : (- ∞, - 5), and (3 / 2, ∞),

Range : (∞, 0.4437]

Step-by-step explanation:

Assuming that we want our answer in interval notation, let's start by determining the domain. Remember that the domain can be found where the function is undefined.

Given : f(x) = (2x - 7) / (2x² + 7x - 15)

Alternative Form : (2x - 7) / (x + 5)(2x - 3)

To receive this 'alternative form' we can simply factor the expression 2x² + 7x - 15. See the procedure below,

[tex]\mathrm{Given : 2x^2+7x-15} ,[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups : \left(2x^2-3x\right)+\left(10x-15\right)} ,[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right),\\\mathrm{Factor\:out\:}5\mathrm{\:from\:}10x-15\mathrm{:\quad }5\left(2x-3\right),[/tex]

[tex]x\left(2x-3\right)+5\left(2x-3\right) = \left(2x-3\right)\left(x+5\right) - \mathrm{Factored\:expression}[/tex]

Now let's find the domain using the expression '(x + 5)(2x - 3) = 0.' If the denominator equals 0, the function is considered undefined.

[tex]\mathrm{Given : \left(x+5\right)\left(2x-3\right)=0} ,\\x+5=0:\quad x=-5, 2x-3=0:\quad x=\frac{3}{2}\\\mathrm{The\:solutions\:are: x=-5,\:x=\frac{3}{2}}[/tex]

Knowing these solutions the domain has the intervals (- ∞, - 5), and (3 / 2, ∞). The range is the set of values that correspond to the domain, so in this case the range would be (∞, 42 + 8√17 / 169]. 42 + 8√17 / 169 = (About) 0.4437, so it lies on the interval (∞, 0.4437].

The images below represent the plotted function in two areas. There are 3 curves in this graph.

Answer:

work shown and pictured

Answer:

|60+3c|<2

That should be a less than or equal to sign

Also I’m sorry but I can’t explain it because I got this answer from someone else on here.

Step-by-step explanation:

Answer:

The answer is n = 31

Step-by-step explanation:

Equation:   2n + 13 = 75

2n = 75 - 13

2n = 62

n = 62/2

n = 31

check:

2*31 + 13 = 75

62 + 13 = 75

Answer: n = 31

Step-by-step explanation: Remember that the word sum mean addition.

So the sum of twice a number and 13 means 2n + 13 = 75.

So our equation is 2n + 13 = 75.

Now let's solve the equation.

Start by subtracting 13 from both sides to get 2n = 62.

Now, divide both sides by 2 and we have n = 31.

Answer:

SOHCAHTOA.

We are to use SOH in this question because we have the opposite which is 15 and the hypotenuse which is 17.

which will be Sin theta =15/17.

Sin theta =0.8823~1.

then Sin theta =1.

which is theta = (inverse of sin) sin^-1(1).

theta =90°.

Answer:x = theta =90°.

Step-by-step explanation:

Answer:

  both are positive even composite integers with a common factor of 8.

Step-by-step explanation:

Both are positive even composite integers with a common factor of 8. They are solutions to the quadratic equation (x-16)(x-24) = 0. Their cube roots (or any root of index greater than 2) are irrational. They are divisors of 48.

There are also many things that both numbers are not. They are not the lengths of sides of a right triangle with integer side lengths. They are not negative or irrational. They are not triangle numbers or elements of the Fibonacci sequence.

Answer:

2x + 2y = 24

Step-by-step explanation:

You have to isolate y and then use substitution.

x + y = 12       and         y = x - 1        

-x       -x          

y = -x + 12       and         y = x - 1

-x + 12 = x - 1

+x          +x

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

12 = 2x - 1

+1          +1

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

13 = 2x

2x = 13              [ divide both sides by 2]

x = 6.5

Now, you have to plug x (6.5) into y = x - 1.

y = x - 1

y = 6.5 - 1

y = 5.5

Finally, plug both x (6.5) and y (5.5) into 2x + 2y.

2x + 2y

= 2 (6.5) + 2 (5.5)

= 13 + 11

= 24

Answer:

c. Your liabilities exceed your assets.

Step-by-step explanation:

The negative net worth indicates option(C)  Your liabilities exceed your assets

This means you owe more money than assets that you own.

A liability is something a person or company owes, usually a sum of money

Here,

Negative net worth indicates option (C) Your liabilities exceeds your assets is negative net worth. Because this means you owe more money than assets that you own.

Other options are not indicating negative net worth

Hence,  the negative net worth indicates option(C)  Your liabilities exceed your assets

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Answer:

Step-by-step explanation:

[tex]10 + 5 - 6.10 + 6.5 \times 6 \\ [/tex]

Follow PEDMAS

[tex]10 + 5 - 6.10 + 39[/tex]

[tex]15 - 6.10 + 39 \\ 15 + 39 - 6.10 \\ 54 - 6.10 \\ = 47.9[/tex]

Answer:

x= 20

Step-by-step explanation:

The two smaller angles add to 90 degrees

x + 3x +10 = 90

4x+10 = 90

Subtract 10 from each side

4x+10-10 = 90-10

4x = 80

Divide each side by 4

4x/4 = 80/4

x = 20

Answer:

[tex]x=20\textdegree[/tex]

Step-by-step explanation:

The angle we have here is a right angle. Right angles have a total measure of 90°. Therefore, the two parts must equal 90°:

Thus, we have the equation:

[tex](x)+(3x+10)=90[/tex]

Combine like terms:

[tex]4x+10=90[/tex]

Subtract 10 from both sides. The left side cancels:

[tex](4x+10)-10=90-10\\4x=80[/tex]

Divide both sides by 4. The left side cancels:

[tex](4x)/4=(80)/4\\x=20[/tex]

Thus, x is 20°.

Answer:

The answer is 6.5

Step-by-step explanation:

(3.5/1)+3(1)^2

3.5/1=3.5

3(1)^2=3

3.5+3=6.5

To determine the 'intervals of increase' and 'intervals of decrease' we can refer to the graph with respect to the x - axis.

• Knowing that t = x - axis, the 'intervals of increase' as an inequality would be 1 < x < 3, and 4 < x < ∞. Therefore we have our intervals of increase as (1,3) and (4, ∞).

• Respectively our 'intervals of decrease' as inequalities would be - ∞ < x < 1, and 3 < x < 4. Our intervals of decrease would then be (- ∞, 1) and (3,4).

• We are left with our local extrema and absolute extrema. Now remember the absolute extrema is the absolute lowest point in the whole graph, while the local extrema is the lowest point in a restricted interval. In this case our local extrema is our maximum, (3,1). But this maximum is not greater than the starting point (0, 4) so it appears, and hence their is no absolute extrema.

Answer: -9 and up

Step-by-step explanation: An integer is any whole number. An integer can be zero, greater than zero or less than zero. The integers greater than zero are the natural numbers.

Answer:

-7 through -1

Step-by-step explanation:

its more than -8 and less than 0 i had this question in 7th yr

Answer:

B) Approximately 50%

Step-by-step explanation:

In any distribution of data, the data can be divided into 4 main quarters that are approximately equal in percentage.

Thus, the first quartile consists of approximately 25%, the second is 25%, third quartile about 25%, while the fourth is 25% also.

Therefore, in a data set distribution of students, approximately 50% of the distribution of students will fall within the first and third quartiles.

Answer:

(B) Approximately 50%

Step-by-step explanation:

First quartile is 1/4 and that is 25% of students in the distribution.

Third quartile is 3/4 and that is 75% of students in the distribution.

Between the first quartile and third quartile is automatically, 50% of the students in the distribution. The answer is (B) Approximately 50%.

Answer:

Infinite solutions.

Step-by-step explanation:

Use the elimination method:

15x - 5y = -20

-3x + y = 4              Multiply this equation by 5:

-15x + 5y = 20         Now add this to the first equation:

0 = 0

So the 2 equations are the same and there are infinite solutions.      

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

Answer:

0.75 inches is the correct answer

Answer:

0.75 inches

The coin is 0.75 inches (19.05 mm) in diameter and 0.0598 inches (1.52 mm) in thickness.

Answer:

a

   The  null hypothesis is  [tex]H_o : p = 0.75[/tex]

  The  alternative  hypothesis is  [tex]H_a : p \ne 0.75[/tex]

b

   [tex]t = 2.51[/tex]

c

   [tex]p-value = 0.01207[/tex]

d

 There no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns

Step-by-step explanation:

From the question we are told that

    The  sample  size is  [tex]n = 745[/tex]

     The  number that said it is morally wrong is  [tex]k = 589[/tex]

       The  level of significance is  [tex]\alpha = 0.01[/tex]

        The population proportion is [tex]p = 0.75[/tex]

Generally the sample  proportion is mathematically represented as

        [tex]\r p = \frac{k}{n}[/tex]

=>     [tex]\r p = \frac{589}{745}[/tex]

=>     [tex]\r p = 0.79[/tex]

 The  null hypothesis is  [tex]H_o : p = 0.75[/tex]

  The  alternative  hypothesis is  [tex]H_a : p \ne 0.75[/tex]

The  standard error is mathematically represented as

     [tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]

=>    [tex]SE = \sqrt{\frac{0.75(1-0.75)}{745} }[/tex]

=>    [tex]SE =0.0159[/tex]

Generally the test statistics is mathematically represented as

      [tex]t = \frac{\r p - p }{SE}[/tex]

=>   [tex]t = \frac{0.79 - 0.75 }{0.0159}[/tex]

=>    [tex]t = 2.51[/tex]

Generally the p-value is  mathematically represented as

        [tex]p-value = 2 * P(Z > 2.51)[/tex]

From the the z-table  

            [tex]P(Z > 2.51) = 0.0060366[/tex]

=>   [tex]p-value = 2 * 0.0060366[/tex]

=>   [tex]p-value = 0.01207[/tex]

From the calculation  [tex]p-value >\alpha[/tex]

    Hence we fail to reject the null hypothesis

Thus there no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns

Answer:

The  correct option is  false

Step-by-step explanation:

Generally the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size( i.e [tex]n \ge 30[/tex] ) regardless of the shape of the population distribution.

But the question states that the mean is normally distributed if the sample size is  5  or  more which is  false hence the statement is false

Answer:

1/4

Step-by-step explanation:

Hello, first of all we could say, let 's replace x by 1 and see if we can conclude.

numerator gives [tex]\sqrt{1+15}-4=\sqrt{16}-4=4-4=0[/tex]

denominator gives 1-1=0

So, this is 0/0 and this is not defined.

We need to ask a friend for help. Guillaume de l'Hôpital, French mathematician from the 1600s,  has a trick to solve this kind of stuff.

In short, he says that

[tex]\displaystyle \lim_{x\rightarrow c} \ {\dfrac{f(x)}{g(x)}}=\lim_{x\rightarrow c} \ {\dfrac{f'(x)}{g'(x)}}[/tex]

In our case here, we have c = 1

[tex]f(x)=\sqrt{x^2+15}-4\\\\g(x)=x-1[/tex]

[tex]f'(x)=\dfrac{1}{2}\dfrac{2x}{\sqrt{x^2+15}}=\dfrac{x}{\sqrt{x^2+15}}\\\\f'(1)=\dfrac{1}{4}\\\\g'(x)=1\\\\\dfrac{f'(1)}{g'(1)}=\dfrac{1}{4}[/tex]

So, we can conclude

[tex]\displaystyle \lim_{x\rightarrow1} \ {\dfrac{\sqrt{x^2+15}-4}{x-1}}=\lim_{x\rightarrow1} \ {\dfrac{1}{4}}=\boxed{\dfrac{1}{4}}[/tex]

Thanks