4 - 3x = 7 - 4x what is x?

40=4(3d-5)

40=12d-20

60=12d

5=d

d=5

Derivative of six inverse trigonometric functions are as follow:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

As given in the question,

Explanation of the derivative of six inverse trigonometric functions are as follow:

1. y = sin⁻¹x

⇒ x = siny

⇒d/dx(x) = d/dx(siny)

⇒ 1 = cosy dy/dx

⇒dy/dx = 1/cosy

⇒dy/dx = 1/√1-sin²y

⇒dy/dx = 1/√1-x²

⇒d/dx( sin⁻¹x) = 1/√1-x²

2. y = cos⁻¹x

⇒ x = cosy

⇒d/dx(x) = d/dx(cosy)

⇒ 1 =-siny dy/dx

⇒dy/dx = -1/siny

⇒dy/dx = -1/√1-cos²y

⇒dy/dx = -1/√1-x²

⇒d/dx( cos⁻¹x) = -1/√1-x²

3. y = tan⁻¹x

⇒ x = tany

⇒d/dx(x) = d/dx(tany)

⇒ 1 =sec²y dy/dx

⇒dy/dx = 1/sec²y

⇒dy/dx = 1/√1+ tan²y

⇒dy/dx = 1/√1 + x²

⇒d/dx( tan⁻¹x) = 1/√1+x²

4. y = cosec⁻¹x

⇒ x = cosecy

⇒d/dx(x) = d/dx(cosecy)

⇒ 1 =-cosecy coty dy/dx

⇒dy/dx = -1/cosecy coty

⇒dy/dx = -1/cosecy√cosec²y-1

⇒dy/dx = -1/|x|√x²-1

⇒d/dx( cosec⁻¹x) = -1/|x|√x²-1

5.   y = sec⁻¹x

⇒ x = secy

⇒d/dx(x) = d/dx(secy)

⇒ 1 =secy tany dy/dx

⇒dy/dx = 1/secy tany

⇒dy/dx = 1/secy√sec²y-1

⇒dy/dx = 1/|x|√x²-1

⇒d/dx( sec⁻¹x) = 1/|x|√x²-1

6. y = cot⁻¹x

⇒ x =coty

⇒d/dx(x) = d/dx(coty)

⇒ 1 =-cosec²y dy/dx

⇒dy/dx = -1/cosec²y

⇒dy/dx = -1/√1+ cot²y

⇒dy/dx = -1/√1 + x²

⇒d/dx( cot⁻¹x) = -1/√1+x²

Therefore, the derivative of the six inverse trigonometric functions are given below:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

Learn more about inverse trigonometric functions here

brainly.com/question/1143565

#SPJ4

Which graph?

___________

Answer:

A is correct

Step-by-step explanation:

A has no solution because since the slopes are the same, setting both equations equal to each other will cancel out the slopes and result in 8=16, meaning no solution will make both sides equal to each other.

B does have a solution because of different slopes

C does have a solution because of different slopes

D does have a solution because of different slopes

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

Learn more about percentage here:

https://brainly.com/question/29763752

#SPJ11

The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.

To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.

Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.

to learn more about Cartesian equation click here:

brainly.com/question/27927590

#SPJ11

Answer:

28 or 24

Step-by-step explanation:

Answer:

32 +x+x=180(Sum of angles of a triangle)

32+2x=180

2x=180-32

2x=148

x=148/2

Therefore,X=74

Answer:

the answer for x is 74°

Step-by-step explanation:

\(32 + x + x = 180 \\ 2x + 32 = 180 \\ 2x = 180 - 32 \\ 2x = 148 \\ x = 74 \: degrees\)

Answer:

156

Step-by-step explanation:

its perimeter i think

The probability that only one phone call passes through a given minute, provided that the relay follows a Poisson distribution with a mean of 5 is 0.033689.

Here it is given that the number of phone calls that pass through a particular cell phone relay system follows a Poisson distribution. The time interval given here is of a minute.

For any Poisson distribution

P(X = x) = λˣ X e^(-λ) / x!

where λ = mean of the distribution.

x = the no. of times the event occurs in the time interval.

It is given that

λ = 5 calls per minute.

We need to find the probability that only n a given minute, the relay receives only one phone call.

Hence, x = 1

Therefore, the probability that only one phone call passes through in a given minute is

P(X = 1) = 5¹ X e^(-5) / 1!

= 0.033689

To learn more about Poisson distribution visit

https://brainly.com/question/17280826

#SPJ4

Answer:

Step-by-step explanation:

Circumference formula:

Substitute and solve for d:

A rose garden is formed by rectangular and semi-circular parts. If the gardener wants to build a fence around the garden, then total 134.95 feet of fence are required.

The perimeter is defined as calculating the outer length of boundaries of shape.

We have a rose garden is formed by joining a rectangle and a semicircle, as present in above figure. We have to determine the feet of fence are required to build a fence around the garden.

From the above figure, length of rectangular part, l = 34 ft

Width of rectangular part, w = 26 ft.

Also, diameter of semi-circular part, d

= 26 ft

Radius of of semi-circular part, r = d/2

= 26/2 ft = 13 ft

So, the perimeter of semi-circular part, Pₛ= π× r = π× 13 ft

= 40.95 ft.

Here, the fence required for the rectangle shape is three sides that two long sides and one wide side. The fourth side of the width is already covered by the semi-circular part. So, the perimeter formula for the rectangle shape, Pᵣ = 2l + w. Therefore, perimeter of garden

= Pₛ + Pᵣ

= 40.95 ft + 2×34 ft + 26 ft

= 68 ft + 26 ft + 40.95 ft

= 134.95 ft.

Hence, required value is 134.95 feet.

For more information about perimeter, refer:

https://brainly.com/question/19819849

#SPJ4

Complete question:

The above figure complete the question. a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 34 feet long and 26 feet wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? (use the value for , and do not round your answer. be sure to include the correct unit in your answer.)

Answer:

alr pal

Step-by-step explanation:

take a better picture and i got you

Answer:

[3/3+5](2-(-14))+(-14)

Step-by-step explanation:

3:5 Ratio means that the m/m+n would be 3/3+5.

Then X2 is 2 and X1 is -14.

X2-X1 is 2-(-14)

False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

Know more about frequency polygon here:

https://brainly.com/question/1581651

#SPJ11

Answer:

2:3

Step-by-step explanation:

You can simplify 12/18 to 2:3 also if michel is that good at basketball he should go to the NBA

Answer:

w = 5

Step-by-step explanation:

Given

- 4(w + 1) = - 24 ( divide both sides by - 4 to isolate w + 1 )

w + 1 = 6 ( subtract 1 from both sides )

w = 5

Answer:

#: Solve the equation. Round to the nearest tenth if necessary.

6y - 6 = 4y + 16

1. y = 2.2

2. y = -2.2

3. y = 11

4. y = 5

_______________________________Step-by-step explanation:

The monthly payment is $130.50. Therefore, option C is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$2700, rate of interest =8% and time =2 years

Here, SI=(2700×8×2)/100

= 43200/100

= $432

Amount =Principal+Interest

= 2700+432

= $3132

We know that 2 years =24 months

Now, the monthly payment = 3132/24

= $130.50

Therefore, option C is the correct answer.

To learn more about the simple interest visit:

https://brainly.com/question/25845758.

#SPJ1

Answer:

a k= and y=15

B . k=1 and y=5

Answer:

\(n(x)=x-2\)

Step-by-step explanation:

You can notice that between each of the arithmetic sequence there is a addition of 2. So we know that to add a 2 to get the next value. We can write it as n(x) where n is a function where x is the number:

Answer: kindly check explanation

Step-by-step explanation:

Given the following :

Amount saved by Jacob = $50

Amount spent at the movies = $15

Amount left after paying for bike repair = $0

Cost of bike repair :

$50 - $15 = $35

What integer represents Jacob’s savings?

Initial amount before any spending

Jacob's saving = +$50

2.What integer represents the change in Jacob’s savings after he spends money at the movies?

Saved amount - amount spent at the movies

$50 - $15 = $35

No number line is given

Answer:

18%

Step-by-step explanation:

To find percent change subtract.

big number - small number

then divide by the original number.

350 - 287 = 63

63/350 = 0.18

change to a percent by moving the decimal two place right.

0.18 = 18%

Using the Fundamental Counting Theorem, it is found that there is 1 rose tree at the garden center.

States that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem:

Hence:

\(N = n_1 \times n_2\)

\(266 = 266n_2\)

\(n_2 = \frac{266}{266}\)

\(n_2 = 1\)

Hence, there is 1 rose tree at the garden center.

To learn more about the Fundamental Counting Theorem, you can take a look at

The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26

To solve the quadratic equation f(x) = x² + 10x - 1

we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 1, b = 10, and c = -1.

Substituting these values into the quadratic formula:

x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))

= (-10 ± √(100 + 4)) / 2

= (-10 ± √104) / 2

Simplifying further:

x = (-10 ± 2√26) / 2

= -5 ± √26

Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:

x = -5 + √26 and x = -5 - √26

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

The optimal solution for the given problem is x ≈ 1.083, y ≈ 0.917, and the maximum value of C is approximately 15.225.

Objective function: C = 9x + 7y

The constraints are:

1) 8x + 10y ≤ 17

2) 11x + 12y ≤ 25

Let's graph the feasible region:

First, we'll find the intersection points of the two constraint lines:

Solving the system of equations:

8x + 10y = 17

11x + 12y = 25

We find x ≈ 1.083 and y ≈ 0.917 as the intersection point.

Next, we'll plot the constraint lines and shade the feasible region:

The feasible region is bounded by the lines 8x + 10y = 17, 11x + 12y = 25, and the coordinate axes.

Now, we'll evaluate the objective function C = 9x + 7y at each corner point of the feasible region:

Corner points:

1) (0, 0) - Origin

  C = 9(0) + 7(0) = 0

2) (0, 1.7)

  C = 9(0) + 7(1.7) ≈ 11.9

3) (1.083, 0.917)

  C = 9(1.083) + 7(0.917) ≈ 15.225

The maximum value of C is approximately 15.225 at the corner point (1.083, 0.917).

Therefore, the optimal solution for the given problem is x ≈ 1.083 and y ≈ 0.917, with a maximum value of C ≈ 15.225.

To know more about optimal solution, refer here:

https://brainly.com/question/14914110

#SPJ4