If a-1/a=7 what find the value of a4+1/a4

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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The number of element sample space for the experiment is n(T) = 8.

Determine the probability for the number 5.

The possible number greater than 3 are 4, 5, 6, 7, and 8. So number of possible outcome for greater than 3 are 5.

Determine the probaility for the number greater than 3.

Both events are independent. So probability for number 5, and greater than 3 is,

Answer: 5/64

Answer:

I believe your answer should be B.) I hope this helps! :D

The number of hours to work to cover the medical bill is 146 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount earned per hour = $10

Amount after tax.

= 10 - 18/100 x 10

= 10 - 1.8

= $8.2

Now,

The number of hours to work to cover $1,200.

8.2x = 1,200

x is the number of hours.

x = 1,200 / 8.2

x = 146

Thus,

The number of hours to work is 146 hours.

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Solution

For this case we have the following roots:

4 (multiplicity 2) and i

Therefore we can create the following expression

Solving we have:

Simplifying we got:

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

The work that gravity does;

W = F.S = mgΔh

In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.

W = mgΔh

g = 9.8 m/s²

Δh  = 4.6 m

m = 0.60 kg

W = 0.60 x 9.80 x 4.6

W = 2.7 J

The source of gravitational potential energy in relation to the ground is;

U = mgh

The release point therefore

Ug = mgh(0)

U0 = 0.60 x 9.8 x 6.1

U0 = 35.87 J

At the point of release

U(gf) = mgh(f)

U(gf) = 0.60 x 9.80 x 1.5

U(gf) = 8.820 J

Gravitational potential energy changes are;

ΔU(g) = U(gf) - U0

ΔU(g) =  8.820 J - 35.87 J

ΔU(g) = -27.05 J

Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.

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Answer:

42 minutes.

Step-by-step explanation:

7/10 × 1 hour

1 hour is equal to 60 minutes.

7/10 × 60

420/10

= 42

7/10 of an hour is equal to 42 minutes.

Answer:

He had 3 and she gave 2 to John, Then he has 1 apple left here

Answer:

9% increase

Step-by-step explanation:

The calculated areas are the same for regular polygon and equal to 43.5 units squared.

The area of polygon is given by the formula:

A = (1/2)ap,

where A is the area, an is the apothem (the distance from the centre of the polygon to the midpoint of any side), and p is the polygon's perimeter, is the formula for calculating the area of a regular polygon.

The apothem of the equilateral triangle can be found using the formula:

a = s / (2 tan(π/n))

Substituting the value of s = 10 we have, and n = 3 side.

a = 10/ / (2 tan(π/3))

a ≈ 2.9 units

The perimeter of the triangle is given as:

p = 3 x 10 = 30 units

Now, the area of the triangle is given as:

A = (1/2)ap

A = (1/2)(2.9)(30) = 43.5 sq. units.

Hence, the calculated areas are the same and equal to 43.5 units squared.

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Answer:

Step-by-step explanation:

Bianca’s answer.

The apothem, rounded to the nearest tenth, is

✔ 2.9 units.

The perimeter of the equilateral triangle is

✔ 30 units.

Therefore, the area of the equilateral triangle is

✔ 1/2(2.9)(30) , or approximately 43.5 units2.

The calculated areas are

✔ the same, despite using different formulas

.

There are 12 students that know all of the language .

Given : Total U = 80

Let A be the set of students  that know English

A = 50

Let A be the set of students  that know French

B = 55

Let A be the set of students  that know German

C =46

Since , 7 students know none of the language

Therefore , |A?B?C| = 7

Also ,

|A∩B| = 37

|B∩C| =28

|C∩A| = 25

Now ,

U - (A∪B∪C) = (A?B?C)

80 - (A∪B∪C) = 7

(A∪B∪C) = 73

Number of students that know all three languages

(A∪B∪C) = A + B + C - [(A∩B) + (B∩C) + (A∩C)] + (A∩B∩C)

73 = 50 + 55 + 46 - 37 -28 -25 + (A∩B∩C)

Therefore , (A∩B∩C) = 12

Hence , there are 12 students that know all of the language .

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Answer:

(a+3)(5a+14)

Step-by-step explanation:

Hope this helps

Answers:

There are infinitely many possible ways to answer the third part.

===========================================================

Explanation:

The midline is the horizontal line that goes through the center of the sine curve. Visually we can see that is y = 0. Another way we can see this is to note how y = 0 is the midpoint of y = 1.5 and y = -1.5, which are the max and min respectively.

---------

The amplitude is the vertical distance from y = 0 to y = 1.5, and it's also the vertical distance from y = 0 to y = -1.5; in short, it's the vertical distance from center to either the peak or valley.

---------

The general format of a sine curve is

y = A*sin(B(x-C)) + D

where,

In this case, we found so far that

The only thing we're missing is the value of C, which is the phase shift.

Note the point (pi/2, 1.5) is one of the max points on this curve. Also, recall that sin(x) maxes out at 1 when x = pi/2

This must mean that the stuff inside the sine, the B(x-C) portion, must be equal to pi/2 in order to lead sin(B(x-C)) = 1.

So,

B(x-C) = pi/2

0.5(pi/2-C) = pi/2

pi/4 - C/2 = pi/2

4*( pi/4 - C/2 ) = 4*(pi/2)

pi - 2C = 2pi

-2C = 2pi - pi

-2C = pi

C = pi/(-2)

C = -pi/2

This allows us to update the function to get g(x) = 1.5*sin(0.5(x+pi/2)) which is the same as g(x) = 1.5sin(0.5x + pi/4)

This is one possible answer because we could have infinitely many possible values for C, due to sin(x) = 1 having infinitely many solutions.

Also, you could use cosine instead of sine. Cosine is just a phase shifted version and of sine, and vice versa.

There were approximately 6056 no votes.

Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.

Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.

The total number of votes is given as 9854, so we can set up the following equation:

\(5x + 8x = 9854\)

Combining like terms, we have:

\(13x = 9854\)

To solve for x, we divide both sides of the equation by 13:

\(x = \frac{9854 }{13}\)

\(x \approx 757.23\)

Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.

Now, we can find the number of no votes by multiplying x by the ratio of no votes:

No votes \(= 8x\)

\(= 8 \times 757\)

\(= 6056\)

Therefore, there were approximately 6056 no votes.

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Step-by-step explanation:

A=2πr(r+h)

A=6.28×14mm(+29mm)

A=77.92(14mm+29mm)

A=77.92×43

A=3350.56 mm

Hope it helps

KC

The amount that would be reported as ending Merchandise Inventory on the balance sheet using the lower-of-cost-or-market rule is $102,000.

Using this formula

Ending Merchandise Inventory= Units of ending inventory× Current replacement cost per units

Let plug in the formula

Units of ending inventory=24,000 units

Current replacement cost per units=$4.25 per units

Let plug in the formula

Ending Merchandise Inventory= 24,000 units ×$4.25 per units

Ending Merchandise Inventory= $102,000

Inconclusion the amount that would be reported as ending Merchandise Inventory on the balance sheet using the lower-of-cost-or-market rule is $102,000.

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Answer:

4/9, 11/13, 6/5

Step-by-step explanation:

We know that:

Given ratio can be simolified as,

The expression that What formula(s) below represents the frequency of

that E are Option A, C and E.

A stored expression that can be invoked from other expressions is known as an expression rule. You can use rule inputs in your expression rules to allow you to dynamically alter the data your expression returns.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is called an expression or a mathematical expression.

From the option A, we have \(440. 2^{\frac{7}{12} } \\\\\)

Then  this can be written as ; \(440 ^{\sqrt[12]{2} }\)

which can be written as \(440 .10597^7}\)

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Answer:

Step-by-step explanation:

The answer is B

Answer:

\(f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$\)

Step-by-step explanation:

The permissible values of x for a function is called the domain of the function. Permissible values mean that the function is real and defined.

The range of a function is the set of all y values for the domain

If a point on a graph is a filled circle, that point is included in the domain(x-value) and represents a ≤ or a ≥ inequality

If a point on a graph is an unfilled or hollow circle, that point is not included in the domain(x-value) and represents a < or a >inequality

Let's look at the three parts of the given piecewise graph

Piecewise part A

We see that the minimum and maximum values of x for this function are x = -2 and x = 1 respectively. The point corresponding to x= 1 is a hollow circle so it is not included in the domain whereas the point corresponding to x = -2 is included

Let's find the equation of this line:
Take 2 points on the line. We choose points (0, -4) and (1, -1)

Slope of this line is -1 -(-4)/(1-0) = (-1 + 4)/1 = 3
The y-intercept is -4

So equation of the line is y = 3x -4  for -2 ≤ x < 1

Proceeding in a similar manner we can determine the domain and function equation for the other two pieces, B and C

Piecewise part B

Domain of x : 1 ≤ x ≤5
Slope = (8-4)/(5-1) = 4/4 = 1

Equation is of the form y = 1x + b
To calculate b, plug in values of x = 1, y = 4 to get
4 = 1(1) + b

b = 3

Equation of this piecewise function is
y = x + 3    for 1 ≤ x ≤ 5

Piecewise Part C

This is a flat horizontal line at y = 8
So that is the equation of the line
The domain of this piece is 5 ≤ x ≤ 8  
So we get y = 8 for \($\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$\)

Normally, instead of using y we use f(x)

Putting all this together we get the piecewise function defined as

\(f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$\)

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

Answer:

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

There are various combinations of coins.

In total there are: