Can you help me with this

The derivative function for equations 1 and 2 will be

y' = -1/ [2√(1-x²)] and y' = 3/[2(1 + x²)] respectively

Here we need to find the derivative of

[tex]y = tan^{-1}\sqrt{\frac{1-x}{1+x} }[/tex]

Let x = cos2z

Hence we get

[tex]y = tan^{-1}\sqrt{\frac{1-cos2z}{1+cos2z} }[/tex]

[tex]or, y = tan^{-1}\sqrt{\frac{2sin^{2}z}{2cos^{2}z} }[/tex]

[tex]or, y = tan^{-1}(tanz)[/tex]

or, y = z

Hence dy/dx = dz/dx

We know that

x = cos2z

or, 2z = cos⁻¹x

or, 2 dz/dx = -1/√(1-x²)

Hence dy/dx = -1/ [2√(1-x²)]

The second equation is

[tex]y = 3tan^{-1}[x-\sqrt{1+x^{2}} ][/tex]

Let x = cotz

Hence we get

[tex]y = 3tan^{-1}[cotz-\sqrt{1+cot^{2}z} ][/tex]

[tex]y = 3tan^{-1}[cotz-\sqrt{cosec^{2}z} ][/tex]

or, y = 3tan⁻¹ [cotz - cosecz]

or, y = 3tan⁻¹ [cosz/sinx - 1/sinz]

or, y = 3tan⁻¹ [(cosz - 1)/sinz]

or, y = 3tan⁻¹ [-2sin²(z/2)/{2sin(z/2) cos(z/2)}]

or, y = 3tan⁻¹ [-sin(z/2)/cos(z/2)]

or, y = 3tan⁻¹ [-tan{z/2)]

or, y = 3tan⁻¹ [tan{-z/2)]

or, y = -3z/2

or, dy/dz = -3/2 dz/dx

We have

x = cotz

or, z = cot⁻¹z

or, dz/dx = -1/(1 + x²)

Hence we get

dy/dx = 3/[2(1 + x²)]

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Answer:

After 2 years, there will be £ 2,121.80 in the account.

Step-by-step explanation:

Since £ 2000 was put into a bank account that pays 3% compound intrest per year, to determine how much will be in the account after 2 years the following calculation must be performed:

2000 x (1 + 0.03 / 1) ^ 1x2 = X

2000 x 1.03 ^ 2 = X

2,121.8 = X

Therefore, after 2 years, there will be £ 2,121.80 in the account.

EXPLANATION

2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.

Answer:

4

Step-by-step explanation:

Hypotenuse, on a 30 60 90 triangle, is equal to 2a. A being the shortest side.

That means 2(2) = 4

Yes, the order of the quantities in an inequality matters, and examples are given to show why.

The four inequality symbols, along with their meaning, are presented as follows:

It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:

5 > 3.

However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:

3 > 5.

Which is a false statement, as the number 3 is less than the number 5, and not more.

This shows that the order of the symbols in an inequality in fact does matter.

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Answer:

2

Step-by-step explanation:

0.2(x+50)-6=0.4(3x+20) multiply both sides by 10 to clear the decimals

2(x + 50) = 4(3x + 20) distribute across the terms in the parentheses

2x + 100 = 12x + 80 subtract 80, 2x from both sides

20 = 10x divide both sides by 10

x=2

Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of the smaller circle:

Equation of the greater circle:

The scale factor is the ratio of radiuses:

So the rule is:

Correct choice is A

Answer:

[tex]\sf A. \quad (x, y) \rightarrow \left(\dfrac{7}{2}x, \dfrac{7}{2}y \right)[/tex]

Step-by-step explanation:

The distance from the center of the circle to any point on the circumference is the radius.

From inspection of the given graph:

To find the scale factor of the dilation from the small circle C to the large circle C', divide the radius of the large circle by the radius of the small circle.

Therefore, the dilation is an enlargement of scale factor ⁷/₂ about the origin.

So the rule that represents the transformation is:

[tex]\sf (x, y) \rightarrow \left(\dfrac{7}{2}x, \dfrac{7}{2}y \right)[/tex]

Check (see attached):

Point (0, 2) is on circle C.

[tex]\implies \sf (0, 2) \rightarrow \left(\dfrac{7}{2}(0), \dfrac{7}{2}(2) \right)=(0,7)[/tex]

Point (1, √3) is on Circle C:

[tex]\implies \sf (1, \sqrt{3}) \rightarrow \left(\dfrac{7}{2}(1), \dfrac{7}{2}(\sqrt{3}) \right)=\left(3.5,6.06)[/tex]

Answer:

x = 65

Step-by-step explanation:

180 - 115 = x

x = 65

Have a nice day!

The answer will start with 500 USD. For every hour, 75 USD is charged. We can multiply 'x' to 75 USD which will represent the amount of hours. The equation will now become, 'y = 75x + 500'. In most cases, like this one, y will represent the total cost. Here are the answers.

a. 75USD

b. x (amount of hours)

c. y (total cost)

d. y = 75x + 500

Hope I understood what you were asking and if not I'm really sorry <3

The value of x in the triangle LMO is 38°

An equation shows how two or more numbers and variables are related to each other.

∠KLO + ∠OLM = 180° (sum of angle in straight line)

134 + ∠OLM = 180°

∠OLM = 46°

∠OML + ∠OMN = 180° (sum of angle in straight line)

∠OML + 84 = 180°

∠OML = 96°

∠OLM + ∠OML + ∠LOM = 180° (angle in a triangle)

46 + 96 + x = 180

x = 38°

The value of x is 38°

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Answer:

x+7+3y

Step-by-step explanation:

You just remove the parentheses in this case since you don't have to change any of the operations.  

Answer:

Step-by-step explanation:

x+7+3y simplifed

After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Let, assume miles be m.

and, Let the total cost be x.

According to the question,

0.25m + 50 = x ........(i)

0.41m + 25 = x ........ (ii)

By solving equation (ii) by (i) we get -

0.16 m - 25 = 0

or, 0.16m = 25

or, m = 25 /0.16

or, m = 156.25

Thus, number of miles = 156.25 miles.

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Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

The initial pressure is 70 N / 0.2 m^2 = 350 Pa (Pascals). If the force is increased by 10 N and the area is increased by 10 cm^2, the new pressure is 80 N / 0.3 m^2 = 266.67 Pa

To calculate the percentage change in pressure, we divide the change in pressure by the initial pressure and multiply by 100:

So Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

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The height of an isosceles triangle can be found by using the Pythagorean Theorem to calculate the length of the hypotenuse, subtracting the lengths of the other two sides, and taking the square root of the difference.

To find the height of an isosceles triangle given three sides, you can use the Pythagorean Theorem. Begin by calculating the length of the hypotenuse (the longest side of the triangle). To do this, square the lengths of the two other sides and add them together. Then, take the square root of that sum. This is the length of the hypotenuse. Next, subtract the lengths of the other two sides from the hypotenuse and take the square root of the difference. The result is the length of the altitude, which is also the height of the triangle.

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Answer:

Option b.  -2x + 3y - 6 = 0

Step-by-step explanation:

Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Calculate the slope first.  Slope is the Rise/Run of any two points on a straight line.   Using the given points, (0,2) and (3,4) we find:

  Rise = 4 - 2 = 2

  Run = 3 - 0 = 3

Slope, m, Rise/Run = (2/3)

The equation becomes y = (2/3)x + b

To find b, enter either of the two given points.  

y = (2/3)x + b

2 = (2/3)(0) + b  :  for point (0,2)

b = 2

The equation becomes:  y = (2/3)x + 2

Reformat this to match the format of the answer options.  

y = (2/3)x + 2    

3y = 2x + 6      [Multiplied by 3]

3y - 2x - 6 = 0

-2x + 3y - 6 = 0     [rearrange]

This matches option b.

The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

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Answer:

c maybe

Step-by-step explanation:

Answer:

i cant see it very well but i wanna say its A but im not 100% sure

Step-by-step explanation:

Answer:

306 toy cars

Step-by-step explanation:

since he has a total of 360 toy cars, and he keeps 85% on the wall, to find how many toy cars he keeps on his wall we have to find 85% of 360:

360*0.85=306

therefore, he keeps 306 toy cars on his wall

The number of toy cars does that Deion keeps on his wall is 306 cars.

Number of cars = 360

Percentage of the toy cars on his wall = 85%

Then, the number of toy cars that is kept in his wall will be:

= 85% × 360

= 0.85 × 360

= 306

In conclusion, 306 toy cars are kept on the wall.

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The money invested by Phyllis with simple interest rate 3 1/2% and 3% per year is given by $7500 , and $3,000 respectively.

As given in the question,

Total amount with Phyllis is equal to $10,500

Let 'x' be the portion of Phyllis earning invested with 3 1/2% per year simple interest rate

Then $( 10,500 - x ) invested by Phyllis with simple interest rate 3% per year

Total interest earned by the investment = $352.50

0.035x + 0.03( 10,500 - x ) = $352.50

⇒0.035x + 315 - 0.03x = 352.50

⇒0.005x = 352.50 - 315

⇒0.005x = 37.5

⇒x = $7500

and $( 10,500 - x ) = $( 10,500 - 7500 )

                              = $ 3,000

Therefore, the amount of invested with simple interest rate 3 1/2% per year and 3% is equal to $7500 and $3,000 respectively.

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Answer:

21 meters

Step-by-step explanation:

First find the circumference of the tire:

c = πd

c = 3.14(670)

c = 2103.8

Multiply by 10 to find the distance the bike has travelled:

2103.8*10 = 21,038

Convert millimeters to meters:

21,038 millimeters ≈ 21 meters

Answer:

NEEEEEEGAARRRRR

Step-by-step explanation:

Answer: look at the picture

Step-by-step explanation: Hope this help :D

Answer: x = 3

Step-by-step explanation:

Simplifying

17x + -3 = 48

Reorder the terms:

-3 + 17x = 48

Solving

-3 + 17x = 48

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + 17x = 48 + 3

Combine like terms: -3 + 3 = 0

0 + 17x = 48 + 3

17x = 48 + 3

Combine like terms: 48 + 3 = 51

17x = 51

Divide each side by '17'.

x = 3

Simplifying

x = 3

Answer:

1/2

Step-by-step explanation:

So lets go over what slope is.

The formula for slope is y/x

To find this, we can just count the change in y, and put it over x.

So lets see.

On the graph, we can count that y goes up by one, and that x goes to the right by 2.

So this means our slope is y/x, or 1/2.

This is our answer.

I hope this helps! :)

I included a visual of this as well!

Answer: Are you talking about Circumference?

If it is then the Formula is 2πr or the easy way ... πd

1st use of formula: you would multiply 7.5 twice then multiplying by Pi or 3.14

2nd use of formula: You would get the diameter then multiply it by Pi or 3.14

Hope this helps :)

Using multiplication we know that the product of 3 * - 4 is -12.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

The addition method, lengthy multiplication, grid method, and drawing lines are four different ways to multiply.

So, we have:

3 * -4

Here, we know that 3 is a positive number and -4 is a negative number.

And so the product will be a negative number.

Now, calculate the product as follows:

3 * -4

-12

Therefore, using multiplication we know that the product of 3 * - 4 is -12.

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Short term memory is a response variable as it is dependent. Hence Option C is the answer.

A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.

Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.

The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.

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Answer:

$6.51

Step-by-step explanation:

To make a percent a decimal, divide by 100

62% = .62

.62 x 10.50 = 6.51

We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.

Answer:

dude... I have fallen in love with your profile picture