You are given the functions f(x) and g(x) = sin^-1(fx). Which of the following expressions represents the ratio of the derivatives of these two functions, f'(x)/g'(x)? Assume that the domain of g(x) is -pi/2 < f(x) < pi/2.

A. f'(x)/g'(x) = 1/(sqrt( 1 - (f(x))^2 )
B. f'(x)/g'(x) = 1/(sqrt( 1 + f(x) )
C. f'(x)/g'(x) = (sqrt( 1 - (f(x))^2 )
D. f'(x)/g'(x) = (sqrt( 1 - f(x) )
E. f'(x)/g'(x) = (sqrt( 1 + f^2(x) )

Answers

Answer 1

Answer:

C

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle f(x) \text{ and } g(x)=\sin^{-1}(f(x))[/tex]

And we want to find the ratio that represents:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}[/tex]

To do so, we will compute the derivatives of both functions.

For f,  we can simply write that:

[tex]f^\prime(x)=f^\prime(x)[/tex]

For g, we will use the chain rule:

[tex]\displaystyle (u(v(x))^\prime=u^\prime(v(x))\cdot v'(x)[/tex]

We can let:

[tex]u(x)=\sin^{-1}(x)\text{ and } v(x)=f(x)[/tex]

We can double check this by doing the composition:

[tex]g(x)=u(v(x))=\sin^{-1}(f(x))[/tex]

Therefore, by the chain rule, we acquire that:

[tex]\displaystyle g^\prime(x)=\frac{1}{\sqrt{1-(v(x))^2}}\cdot v'(x)[/tex]

By substitution:

[tex]\displaystyle g^\prime(x)=\frac{f^\prime(x)}{\sqrt{1-(f(x))^2}}[/tex]

Hence, our ratio is:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\frac{f^\prime(x)}{\dfrac{f^\prime(x)}{\sqrt{1-(f(x))^2}}}[/tex]

Simplify:

[tex]\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\sqrt{1-(f(x))^2}[/tex]

Hence, our answer is C

Answer 2

Answer:

This isn't the answer as you can see it above, but do you have the rest of the questions?

Step-by-step explanation:

Thank you in advance.


Related Questions

Consider the following equations:
y = X-2
y = 2x-2
y = x-2
y = -2

Discuss the similarities and difference in the graphs of these equations. (Use a graphing calculator if needed.)

a. Same slopes; different y-intercepts
b. Same slopes; same y-intercepts
c. d. different slopes; same y-intercepts
d. different slopes, different y-intercepts

Please select the best answer from the choices provided​

Answers

Answer:

c number is the correct one i think

Answer:

c. d. different slopes; same y-intercept

for all the equations, when x = 0, y = -2

apart from the last equation which has no x-intercept.

They have different slopes i.e

y=x-2 has a slope of 1

y=2x-2 has a slope of 2

y=x-2 has a slope of 1

y=-2 has no slope

There are 3 times as many children as adults at the zoo. Complete the table with possible combinations of adults and children and write an equation that represents all the possible combinations

Answers

Answer:

Step-by-step explanation:

Adults = x, Children =y

3y=x

Multiply any number by three and you get all of your answers

Estimate the number of words in your textbook, without using a calculator.(The book has about 500 pages, with an average of 38 lines on a page, 12 words on a line.)

Answers

Answer:

[tex]500\ Pages = 228000[/tex]

Step-by-step explanation:

Given

[tex]Pages = 500[/tex]

[tex]Lines = 38[/tex]

[tex]Words = 12[/tex]

Required

Determine the number of words in the book

First, we need to calculate the number of words in a page.

[tex]1\ Page = Words * Lines[/tex]

[tex]!\ Page = 12 * 38[/tex]

[tex]1\ Page = 456[/tex]

Next, we calculate number of words in 500 pages

Multiply both sides by 500

[tex]500 * 1\ Page = 456 * 500[/tex]

[tex]500\ Pages = 228000[/tex]

Hence, there are 228000 words in the book

The larger of two numbers is 4 less than four times the smaller number. The sum of the two numbers is 51. Find the two numbers
What are the numbers?

Answers

Answer: 40,11

Step-by-step explanation:

larger number=a

smaller number =b

a+b=51

a=4b-4

4b-4+b=51

5b=51+4

5b=55

b=11

a=4*11-4=44-4=40

A speed skater travels how many meters per second?

Answers

Answer:

In skating, one skate pushes and the other skate glides--there is very little friction to slow you down. Speed skater Hiroyasu Shimizu of Japan can travel 500 meters in just 35.39 seconds, an average speed of 14.13 meters per second or 31.6 miles per hour.

Step-by-step explanation:

Answer:

Answer :

In skating, one skate pushes and the other skate glides--there is very little friction to slow you down. Speed skater Hiroyasu Shimizu of Japan can travel 500 meters in just 35.39 seconds, an average speed of 14.13 meters per second or 31.6 miles per hour.

have a nice day <3

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What term best describes the expression x + 3?


Binomial


Not a polynomial


Monomial


Trinomial

Answers

binomial since there are two elements in the equation

Solve for x. 7x−9<12

Answers

Answer:

x < 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Equality Properties

Step-by-step explanation:

Step 1: Define

7x - 9 < 12

Step 2: Solve for x

Add 9 to both sides:                    7x < 21Divide 7 on both sides:                x < 3

Here we see that any value x smaller than 3 would work as a solution to the inequality.

Answer:

x < 3

Step-by-step explanation:

7x-9 = 12

take -9 on the other side to get

7x =12+9

7x = 21

x=3

x < 3


What is the degree of the polynomial below?
2x^2 + 3x +1
A. 0
B. 2
C. 3
D. 1

Answers

Answer:

2

Step-by-step explanation:

The highest exponent of the variable is known as degree of the polynomial. The eqn. given in the question has exponents 2 & 1 out of which 2 is the highest exponent . So 2 is the degree of the polynomial.

I need to know the answer to this question.

Answers

Answer:

6

Step-by-step explanation:

Answer:

j + 9 = 15

j=6

Step-by-step explanation:

Which is a simplified form of the following expression?

Answers

Answer:

option C.

Step-by-step explanation:

X⁵y⁷ is the correct answer.

Answer:

[tex]x^5y^7[/tex]

Step-by-step explanation:

[tex](xy^3)(xy)^4[/tex]

Open up the parentheses

[tex]xy^3x^4y^4[/tex]

Combine x values and y values

[tex]x^5y^7[/tex]

I hope this helps!

7 decreased by n
The expression is

Answers

Answer:

7-n

Step-by-step explanation:

Answer:

The expression would just be 7-n

Give the slope and y-intercept of the
relationship shown in the table.

Answers

Find slope

25-50 divided by 100-0

Which is -1/4

When x is equal to 0, y is equal to 50

So, your answer is option b

Answer:

B

Step-by-step explanation:

Which method listed below would NOT be used to prove that two triangles are congruent?.
A. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle.

B. Prove that two angles and an included side of one triangle are congruent to two angles and an included side of the other triangle.

C. Prove all three sets of corresponding sides congruent.

D. Prove all three sets of corresponding angles congruent.

Answers

Answer:

C

Step-by-step explanation:

1
2
B
4
3
5
6
С
8
7
D
In this figure, AB | CD and m_1 = 105°
What is m25?
Enter your answer in the box.

Answers

Answer:

105°

Step-by-step explanation:

105°

If [tex]\sf a = log_92[/tex] and [tex]\sf b = log_54[/tex], find [tex]\sf log_615[/tex] in terms of a and b.​

Answers

Answer:

(4a + b)/(2ab + b)

Step-by-step explanation:

Givena = log9 2b = log5 4To findlog6 15 in terms of a and bSolution

Rewrite the given

log9 2 = a ⇒ log2/log9 = a ⇒ 1/2*log2/log3 = a ⇒  log3 = 1/2*log2/alog5 4 = b ⇒ log4/log5 = b ⇒ log5 = 2*log2/b

Rewriting the log6 15:

log6 15 = log15/log6= (log 5 + log3)/(log2 + log3)

Substitute as follows:

(log 5 + log3)/(log2 + log3) =(2*log2/b + 1/2*log2/a)/(log2 + 1/2*log2/a) =(2/b + 1/(2a))/(1 + 1/(2a)) =(4a + b)/2ab ÷ (2a + 1)/2a =(4a + b)/(2ab + b)

1. It is the capacity to direct and discipline one's
activities and the behavior using reason that is
cautious and, as much as possible, keeps
from any risks.​

Answers

Answer:

The answer is "Prudence".

Step-by-step explanation:

It is the capacity, through the use of justification, to regulate or control yourself. Although pragmatism does not perform any actions and seems to be concerned primarily with information, it would have to control certain values. It is also the desire, utilizing purpose, to direct the control from one's activities and behavior.

Please work n solve this problem out i will Mark brainlist !!
-
1 1/4 + 2 2/4 + 3 3/4 + 1/4 + 2 1/4 = ?

Answers

Answer:

The answer is 10.

Step-by-step explanation:

We need to solve 1 1/4 + 2 2/4 + 3 3/4 + 1/4 + 2 1/4.

Every fraction has a denominator as 4. So, the denominator of the whole fraction is 4.

[tex]\dfrac{5}{4}+\dfrac{10}{4}+\dfrac{15}{4}+\dfrac{1}{4}+\dfrac{9}{4}\\\\=\dfrac{5+10+15+1+9}{4}\\\\=\dfrac{40}{4}\\\\=10[/tex]

So, the value of the given expression is 10.

Rachel and David were shopping for holiday gifts when they noticed a Thanksgiving sweater on the discount rack. Rachel really wanted the sweater, even though she wouldn’t be wearing it until Thanksgiving of 2021! Part A: ​If the original price of the sweater was $24.00, and the sweater is on sale for 60% off, what is the sale price?

Answers

Answer:

[tex]Sales\ Price = \$9.60[/tex]

Step-by-step explanation:

Given

[tex]Price = \$24.00[/tex]

[tex]Discount = 60\%[/tex]

Required

Determine the sales price

First, we calculate the discount price

[tex]Discount\ Price = Price * Discount[/tex]

[tex]Discount\ Price = \$24.00 * 60\%[/tex]

[tex]Discount\ Price = \$14.4[/tex]

The sales price is then calculated by subtracting the discount price from the original price of the item

[tex]Sales\ Price = Price - Discount\ Price[/tex]

[tex]Sales\ Price = \$24.00 - \$14.40[/tex]

[tex]Sales\ Price = \$9.60[/tex]

what is the equation of the line that passes through the point (-3,4) and has a slope of 1/3?​

Answers

Answer: Y= mx+c

So m= the gradient (slope)

And c=the y intercept (x,y= -3,4)

So it should be

Y=1/3x+4

Step-by-step explanation:

Answer:

y=1/3x+5

Step-by-step explanation:

Write each fraction as a decimal Use abar as needed.
Please help! Give me answers!

Answers

Answer:

9/20 = 0.45

3/10 = 0.3

7/12 = 0.5833333

4/5 = 0.8

2/3 = 0.66667

5/6 = 1.6667

1/6 = 0.16667

15/16 = 0.9375

2/15 = 0.13333

4/11 = 0.3636

5/8 = 0.625

13 / 16 = 0.8125

3/25 = 0.12

4/9 = 0.4444

8/9 = 0.88889

11/16 = 0.6895

14 / 25 = 0.56

11/15 = 0.7333

Step-by-step explanation:

9/20 = 0.45

3/10 = 0.3

7/12 = 0.5833333

4/5 = 0.8

2/3 = 0.66667

5/6 = 1.6667

1/6 = 0.16667

15/16 = 0.9375

2/15 = 0.13333

4/11 = 0.3636

5/8 = 0.625

13 / 16 = 0.8125

3/25 = 0.12

4/9 = 0.4444

8/9 = 0.88889

11/16 = 0.6895

14 / 25 = 0.56

11/15 = 0.7333

Problem 1
State whether each sequence is arithmetic and justify your
answer.
1.1, 1.5, 1.9, 2.3, 2.7, ...
Yes
No

Answers

Answer:

[tex]\boxed{\boxed{\pink{\bf \leadsto Yes \ the \ gi en \ sequence \ is \ Arithmetic \ Sequence. }}}[/tex]

Step-by-step explanation:

Given sequence to us is , 1.1, 1.5, 1.9, 2.3, 2.7, . And we need to find whether they are in arithmetic sequence or not .

Arthemetic Sequence :-

A sequence is said to be in Arithmetic sequence if the difference of two consecutive terms is same. That is constant .

Here if we look at the sequence , 1.1, 1.5, 1.9, 2.3, 2.7, . The diffrence of consecutive terms is same.

That is ,

• 1.5 - 1.1 = 0.4

• 1.9 - 1.5 = 0.4

• 2.3 - 1.9 = 0.4

• 2.7 - 2.3 = 0.4

Hence here the difference of two consecutive terms is same . That is 0.4 .

Hence the given sequence is a Arithmetic sequence.

Un motociclist se deplaseaza cu viteza medie de 30m pe secunda, iar la ora 19:00 trece prin dreptul bornei kilometrice 104. Casa motociclistului este in dreptul bornei kilometrice 158. Determina ora la care biciclistul a ajung acasa.

Answers

Answer:

uh ???????????????????????

For race Martha ran 1 /9 of a mile and then swam 4/9 of a mile. What was the total distance of the race?

Answers

Answer: 5/9Step-by-step explanation: We just add the numerators and we leave the denominator the same because they are the same!

There are 3.76 × 10 atoms in 1 gram of oxygen. How many atoms are there in 700 grams of oxygen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.

Answers

Answer:

7.376 × 10²

Explanation:

3.76 x 10 * 700

help with slope please !

Answers

Answer:

-1

Step-by-step explanation:

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x ≤ 8


x > 8


x < 8


x ≥ 8

Answers

Answer:

x < 8

Step-by-step explanation:

the dot isnt filled so symbol wont have a line under it

line moving left of 8 so less than 8.

From a cylinder of height of 24cm and base diameter 14cm, a cone having equal radius and height is hollowed out. Find the volume of the remaining solid of the cylinder.​

Answers

Answer:

2463 cm^3

Step-by-step explanation:

Given that a cylinder of height of 24cm and base diameter 14cm, a cone having equal radius and height is hollowed out. Find the volume of the remaining solid of the cylinder.

Let first calculate the volume of the cylinder

V = πr^2h

Where the radius = 7 cm

V = π × 7^2 × 24

V = 3694.5 cm^3

Let's calculate the volume of a cone

V = 1/3πr^2h

V = 1/3 × π × 7^2 × 24

V = 1/3 × 3694.5

V = 1231.5 cm^3

To Find the volume of the remaining solid of the cylinder, minus the volume of a cone from the volume of a cylinder

Remaining volume V = 3694.5 - 1231.5

V = 2462.99 cm^3

V = 2463 cm^3 approximately

To ride a roller coaster, a visitor must be taller than 54 inches. Use h to represent the height (in inches) of a visitor able to ride.

Answers

Answer: h>54

Step-by-step explanation:

The inequality that represents the condition given is h > 54 inches.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, To ride a roller coaster, a visitor must be taller than 54 inches.

Since "h" represents the height (in inches) of a visitor able to ride.

Since the visitor's height can not be smaller than 54.

thus inequality:

h > 54

therefore, h > 54 inches is the inequality that depicts the stated condition.

Learn more about inequalities here:

https://brainly.com/question/30231190

#SPJ2

2x+5y =-20, 2x-3y=28

Answers

Answer:

x=5 and y=-6

Step-by-step explanation:

2(5) + 5(-6) = -20 (so true)

and

2(5) - 3(-6) = 28 (true)

Answer:

2x=-20-5y

divide both sides by 2

x=-20-5y/2

2x-3y=28

-3y=28-2x

divide both sides by -3

y=28-2x/-3

Step-by-step explanation: FOR THE FIRST ONE, I MADE X THE SUBJECT AND FOR THE SECOND ONE I MADE Y THE SUBJECT.

find the value of x. then find the measure of each labeled angle

x°=
(x-56)°=​

Answers

Answer:

x°=118

(x-56)°= 62

Step-by-step explanation:

90×2 = 180

360-180=180

x+(x-56) =180 x=118

118-56=62

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