The lowest point in the United States is the Sierra Nevada in California. Its altitude is 300 feet below the sea level. Identify the absolute value of the point. (Sierra Nevada).

The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)

1) We want to differentiate the function;

[tex]\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }[/tex]

Differentiating this gives;

dy/dx = [tex]\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }[/tex]

That can be simplified to get;

dy/dx = [tex]\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}[/tex]

2) We want to differentiate the function;

y = sin(2 sin⁻¹x)

Differentiating the function gives;

dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)

We know from trigonometric identity that;

cos²x = 1 - sin²x

Thus;

1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)

But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)

Thus; √(1 - y²) = cos(2 sin⁻¹x)

dy/dx = d√(1 - y²)]/(√1 - x²)

Read more about Differentiation of Functions at; https://brainly.com/question/5313449

#SPJ1

Answer:

Since both of the coordinates are positive, we have:

Find the hypotenuse of the right triangle using values of both legs:

Find sine:

Find cosine:

Answer:

Answer x=2/3, -1
Option B

Step-by-step explanation:

Answer:

B) x =( 2/3, -1)

Step-by-step explanation:

Equation:

[tex]6x {}^{2} + 2x = 4[/tex]

Solution:

We know that,

[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

According to the problem,

Plugging them on the formulae,we obtain,

Choice B is accurate.

Answer:

Yes

Step-by-step explanation:

Yes; points X and Y are fixed under the reflection, so they must lie on the line of reflection. Since two points determine a line, the line of reflection is XY.

https://www.rcboe.org/cms/lib010/GA01903614/Centricity/Domain/1030/Reflections.pdf

.

Answer:

C, D and E

Step-by-step explanation:

The numbers which are greater than given number are : -2, -1.5, and 1.25.

A fraction represents a part of a whole or, more generally, any number of equal parts.

Here, given number: -7/3

or we can write this as -2.33

Now, Converting option fraction value into decimal

A). -3

B) -5.5

C). -2

D). -1.5

E). 1.25

On comparing options from the given value we get

the number which are greater than -2.33;   -2, -1.5, and 1.25

Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.

Learn more about Fraction from:

https://brainly.com/question/10354322

#SPJ1

Answer:

x² - 10x + 25

Step-by-step explanation:

The formula for squaring any binomial (an expression with two terms) is:

(a ± b)² = a² ± 2ab + b²

Let a = x and b = 5.

∴ Substituting:

   (x - 5)² = x² - 2(x)(5) + (-5)²

               = x² - 10x + 25

The simplest form of the square root of 48 is 4√3

Given the following rational function √48

The correct prime factorization is given as;

√48 = √3×16

√48  = √16 × √3

Since the square root of 16 is 4, hence;

√48 = 4√3

Hence the simplest form of the square root of 48 is 4√3

Learn more on prime factorization here: https://brainly.com/question/92257

#SPJ1

There are 315 number of different pairs

The given parameters are:

Men = 15

Women = 21

The number of different pairs is calculated as:

Pair = Men * Women

So,we have:

Pair = 15 * 21

Evaluate

Pair = 315

Hence, there are 315 different pairs

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

Answer:

See below ~

Step-by-step explanation:

a) Forming the equation :

⇒ We start with a number, x

⇒ Now we double it so : 2(x) = 2x

⇒ Then we add 11 to it : 2x + (11) = 2x + 11

⇒ It is equal to 25 : 2x + 11 = 25

b) Solving the equation :

Subtract 11 from both sides :

⇒ 2x + 11 - 11 = 25 - 11

⇒ 2x = 14

Divide 2 on both sides :

⇒ 2x/2 = 14/2

⇒ x = 7

Let unknown number be x

Double it

Add eleven

You got 25

Lets solve the equation

Answer:

look at the picture .

Step-by-step explanation:

look at the picture .

Answer:

To order decimals, you first need a range of values.

Step-by-step explanation:

For example, if there are 5 values: 0.25, 0.87,0.19,0.89 and 0.98

First, look at the first digit after the decimal. The smallest digit is the smallest so far. In this case, it is 0.19 as '1' was the smallest digit. Second would be 0.25 because 2 is the second smallest digit here.

Now, we have 3 remaining numbers: 0.87, 0.89 and 0.98

You can notice that both 0.87 and 0.89 have the same first digit after the decimal.

Do fix this problem, look at the second digit and decide the smallest one. In this case, it is 0.87.

This means the order will go like this if it is smallest to largest: 0.19, 0.25, 0.87, 0.89, 0.98.

If it is largest to smallest, do it the other way around.

Hope this helped!

Answer:

b = 81

Step-by-step explanation:

given a² and b are directly proportional then the equation relating them is

a² = kb ← k is the constant of proportionality

to find k use the condition a = 2 when b = 9 , then

2² = 9k

4 = 9k ( divide both sides by 9 )

[tex]\frac{4}{9}[/tex] = k

a² = [tex]\frac{4}{9}[/tex] b ← equation of proportion

when a = 6 , then

6² = [tex]\frac{4}{9}[/tex] b

36 = [tex]\frac{4}{9}[/tex] b ( multiply both sides by 9 to clear the fraction )

324 = 4b ( divide both sides by 4 )

81 = b

The value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

From the question, we are to determine the value of

2(5+34-67/45*43)^2

This can be written as

[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]

First, we will simplify the bracket

[tex]2 (\frac{-28}{1935 })^{2}[/tex]

Then, we get

[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]

= [tex]\frac{1568}{3744225}[/tex]

= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

Hence, the value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

Lear more on Evaluating an expression here: https://brainly.com/question/23133222

#SPJ1

The measure of angle D to the nearest tenth of a degree is 47 degrees

This theorem is used to determine the measure of sides and angles of a triangle.

According to the theorem

tan theta = opp/adj = 1.055

theta = arctan(1.055)

theta = 46.53 degrees

Hence the measure of angle D to the nearest tenth of a degree is 47 degrees

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

#SPJ1

Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:

(x,y) -> (x, -y)

Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

The answer should be 3.3/4

Step-by-step explanation:

The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]

What are indices?

An index is a small number that tells us how many times a term has been multiplied by itself.

The plural of index is indices.

Below is an example of a term written in index form :[tex]4^{3}[/tex]

4 is the base and 3 is the index.

We can read this as ‘4 to the power 3’

Another way of expressing [tex]4^{3}[/tex] is

4 x 4 x 4 = 64

Indices can be positive or negative numbers.

Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]

=   [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex]                    By using the property of exponents is given by:

                                    [tex](a^{m})^{n}=a^{m n}[/tex]

=[tex]\frac{p^{7}q}{10 .16}[/tex]                              By using the property of exponents given by

                                       [tex]a^{m}a^{n}=a^{m + n}[/tex]  and  [tex]a^{-m}= \frac{1}{a^{m}}[/tex]

= [tex]\frac{p^{7}q}{160}[/tex]

Learn about indices here :

https://brainly.com/question/27327380

#SPJ4

The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]

The products can be simplified as follows;

Multiplying fraction,

[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]

Hence,

Let's reduce the fraction by dividing

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]

Therefore,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]

Hence,

[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]

learn more on simplification here: https://brainly.com/question/3306438

#SPJ1

Answer:

A, b+3/2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

multiply -4 and 3 to get -12

multiply -12 and -2 to get 24

multiply 2 and 7 to get 14

multiply 14 and 1 to get 14

subtract 14 from 24 to get 10

Answer:

second branch..................

Step-by-step explanation:

here I have done you can check it out

Answer:

[tex]\fbox {Perimeter = 37.92}[/tex]

Step-by-step explanation:

Finding the missing side :

⇒ Take the tan value of the listed angle

⇒ tan 60° = √3 = 6/x

⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46

Solving :

⇒ Perimeter = 10 + 2(6 + 3.46)

⇒ Perimeter = 10 + 2(9.46)

⇒ Perimeter = 19 + 18.92

⇒ Perimeter = 37.92

Answer:

b

Step-by-step explanation:

eq y=x+4 is for x>=2 inclusive

Answer:

As the sample size increases, the variability decreases.

Step-by-step explanation:

The actual departures from the mean are used to quantify variability. The variance would be lower the fewer the deviations.

By using the central limit theorem, we can determine that the sample mean for random samples of size n follows a normal distribution.

The standard deviation of the X bar will be [tex]\frac{s}{\sqrt{n} }[/tex].

where s is the sample's variance's square root.

As a result, we discover that the standard deviation, or variability, is inversely proportional to the square root of the sample size. Therefore, standard error lowers as sample size grows. The variability falls off as sample size rises.

Answer:

D

Step-by-step explanation:

The vertex is at (-2,4), so substituting into vertex form, only C and D match.

Also, the graph opens down, so the coefficient of x² is negative.

This eliminates C, leaving us with D

[tex] \frac{ {3}^{6} \times {5}^{3} }{ {9}^{2} \times {5}^{2} } \\ \\ \frac{ {3}^{6} \times {5}^{3 - 2} }{ {3}^{4} } \\ \\ {3}^{6 - 4} \times {5}^{1} \\ \\ {3}^{2} \times 5 \\ \\ 9 \times 5 \\ \\ 45.[/tex]

Answer:

⇒   Let marked price be Rs.x.

⇒  Discount = 20% of marked price.

⇒  Discount=  

100

20

​  

×x=  

100

20x

​

⇒  Selling price = Marked price - Discount.

⇒  192=x−  

100

20x

⇒  192=  

100

80x

⇒  x=  

80

19200

=Rs.240

Answer:

S.p = 992

discount = 20%

marked price = S. p + discount

= 992 + 20/100*992

= 992 + 198.4

= 1190.4

The geometry is that the number of sides for a 15- gon is 15 sides and the angles are 156° each.

The total angles in a 15 gon will be calculated as:

= (n - 2) × 180

= (15 - 2) × 180

= 2340

The value of each angle will be:

= 2340/15

= 156°

The total angles in a 16 gon will be calculated as:

= (n - 2) × 180

= (16 - 2) × 180

= 2520

The value of each angle will be:

= 2520/16

= 157.5°

Learn more about geometry on:

brainly.com/question/24375372

#SPJ1