Mathematics High School

d
Evaluate
arcsin
(6)]
at x = 4.
dx

DEvaluatearcsin(6)]at X = 4.dx

Answers

Answer 1

Answer:

[tex]\frac{1}{2\sqrt{5} }[/tex]

Step-by-step explanation:

Let, [tex]\text{sin}^{-1}(\frac{x}{6})[/tex] = y

sin(y) = [tex]\frac{x}{6}[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\frac{d}{dx}(\frac{x}{6})[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\frac{1}{6}[/tex]

[tex]\frac{d}{dx}\text{sin(y)}=\text{cos}(y)\frac{dy}{dx}[/tex] ---------(1)

[tex]\frac{1}{6}=\text{cos}(y)\frac{dy}{dx}[/tex]

[tex]\frac{dy}{dx}=\frac{1}{6\text{cos(y)}}[/tex]

cos(y) = [tex]\sqrt{1-\text{sin}^{2}(y) }[/tex]

          = [tex]\sqrt{1-(\frac{x}{6})^2}[/tex]

          = [tex]\sqrt{1-(\frac{x^2}{36})}[/tex]

Therefore, from equation (1),

[tex]\frac{dy}{dx}=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]

Or [tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]

At x = 4,

[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}[/tex]

[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}[/tex]

                   [tex]=\frac{1}{6\sqrt{\frac{36-16}{36}}}[/tex]

                   [tex]=\frac{1}{6\sqrt{\frac{20}{36} }}[/tex]

                   [tex]=\frac{1}{\sqrt{20}}[/tex]

                   [tex]=\frac{1}{2\sqrt{5}}[/tex]

Related Questions

WILL GIVE BRAINLIEST!!!

What is the approximate average rate of change for f(x) = 20(0.5) from
x = 2 to x = 2?

Answers

Answer:

It is: (f(2) - f(0))/(2 - 0)

f(2) = 250(0.5)(2) = 250

f(0) = 250 (0.5)(0) = 0

So: (250 - 0)/(2 - 0) = 250/2 = 175

The average rate of change is 175.

Step-by-step explanation:

What are the Slope and y- Intercept of the graph y= -4x - 5

Answers

Answer:

slope: -4, y intercept: (0, -5)

Step-by-step explanation:

Simplify: 4(x+10) -30 + 6x

Answers

Answer:

10x+10

Step-by-step explanation:

distrubute 4(x+10)-30+6

subctract 4x+40-30+6

combine 10x+10

can someone help me please?

Answers

Answer:

72/100

Step-by-step explanation:

if 3x - 6.59 = 11.41 what is the value of x

Answers

Answer: x = 6

Step-by-step explanation:

3x - 6.59 = 11.41

Add 6.59 to both sides

3x = 18

Divide both sides by 3

x = 6

Hope that helped!

Answer:

I have the same question,

Step-by-step explanation:

If the population in Charleston, SC grew exponentially from 90,620 people in 1990 to 120,083 people in 2010. Write a function to model Charleston's population from 1990 to 2010 assuming the population grew at a constant growth rate during that time period where P (population) is a function of time, t, (where t represents t).

What is the rate?

Answers

19,304 I think so. Reply if wrong x

Which inequality is represented by the graph?
t > -2
t < -2
t ≤ -2
t ≥ -2

Answers

Answer:

t > -2

Step-by-step explanation:

Since the graph is not continuous at -2, thus it is not included!

Catty Couture is a company that make designer socks for cats.

134 cats are waiting for their socks to be made.

How many socks is this in total?

Answers

Answer:

536

Step-by-step explanation:

4 paws on each cat, multiply by the amount of cats = 536

Mom buys a rectangular rug with an area of LaTeX: 7\frac{1}{6}7 1 6 square meters. The length of the rug is LaTeX: 3\frac{1}{3}3 1 3 meters. What is the width of the rug?

Answers

Answer:

2 3/20 metres

Step-by-step explanation:

Area of the rug = Length × width

Given

Area = 7 1/6 metres = 43/6 m

Length = 3 1/3 metres = 10/3 m

Required

Width

From the formula

A = LW

W = A/L

Substitute the given values

W = 43/6÷10/3

W = 43/6×3/10

W = 43/2 ×1/10

W = 43/20

W = 2 3/20 m

Hence the width of the rug is 2 3/20 metres

Answer:

32

Step-by-step explanation:

7 x 6 is 32 so u get that

What is the vertex of the function f(x) = 2+3x+ 3/2

Answers

Answer:

0=2+3x+3/2

0=7/2+3x

-3x=7/2

divide by -3 on both sides

x=-7/6

hope this helps

Step-by-step explanation:

What is –2 5/12 written as a decimal?​

Answers

It’s a number it’s a number it’s a n


Terry drove 228 miles in 6 hours at a constant speed. How long would it take him to drive 285 miles at the same speed?

Answers

Answer:

7.5 hours

228 ÷ 6

38 × 7.5 = 285

Find the solution to the system of equations

−8x+9y=−21
-3x+9y=−36

Answers

Answer:

(-51,-21) solve for the first variable in one of the equations. then substitute the result into the other equation

This is the answer to the question mark me the brainliest
X=-3
Y=-5

please help me please will give brainliest to anyone who is good​

Answers

Answer:

C

Step-by-step explanation:

N = st

Number of toothpicks = (number of students) x (toothpicks)

Answer.

D.

Step by step explanation

simplify 1/2 (4x+2) - (-2x)​

Answers

-6x is the answer-6x

Answer:

4x + 1 is the simplified expression

Step-by-step explanation:

We have to use order of operations in order to solve. We basically need to simplify it with multiplication and addition.

The first step involves mulitplication and distribution property:

1) Do 1/2(4x + 2). If you use distribution property, it would be 1/2(4x) + 1/2(2)

2) Then use multiplication 1/2(4x) is 2x (since 4 multiplied by 1/2 is 2) and 1/2(2) is 1 (since 1/2 times 2 is 1).

Bow the expression is almost simplified as it is:

2x + 1 -(-2x)

The 2nd stop involves addition. First we have to know what -(-2x) means. Think of the negative sign on the outside as -1. This way it would be:

3) -1(-2x), and then do -1(-2) which is 2 since a negative times a negative is positive.

4) Now we know that -(-2x) is the same as: + 2x.

5) So the expression would be 2x + 1 + 2x. Combine like terms ( 2x and 2x) and you will get 4x + 1.

Hope you understood this and have a nice day!

A prism has a height of 5 inches and a volume of 80 cubic inches.

Select all figures that could be the base for this prism.

O a square with side length 4 inches

O a 2 inch by 8 inch rectangle

O a circle with radius 2 inches

O a right triangle with legs 4 inches long

O a heart-shaped base with an area of 16 square inches

Answers

Answer:   a square with side length 4 inches

a 2 inch by 8 inch rectangle

a heart-shaped base with an area of 16 square inches

Step-by-step explanation: The given height is 5. Any base with an area of 16 square inches will be an acceptable base.

For example, if the circular base had a radius of about 2.257 inches, its area would be 16 square inches

(2.257)² ≈ 5.093

5.093 × 3.1416 ≈ 16

16 × 5 = 80

The base for this prism should be like

a square with side length 4 inches.

a 2 inch by 8 inch rectangle.

a heart-shaped base with an area of 16 square inches.

Could be the base for the prism:

Since

The given height is 5.

Any base with an area of 16 square inches should be considered as an acceptable base.

Like if the circular base had a radius of about 2.257 inches, its area would be 16 square inches

So, it be like

(2.257)² ≈ 5.093

Now

5.093 ( 3.1416) ≈ 16

16 ( 5) = 80

Learn more about prism here; https://brainly.com/question/24606047

11. Which regular polygon has a minimum rotation of 45° to carry the polygon onto itself?

A. octagon

B. decagon

C. hexagon

D. pentagon

Answers

Answer:

the answer is a octagon that has rotation of 45degrees

help me, please............

Answers

Answer:

reflected over the y axis

please help me i need help quick plz

Answers

Answer:

Step-by-step explanation:

L is 11

H is 48

Q2 = (32 + 33) / 2 = 32.5

Q1 is 23

Q3 is 46

2) The distribution is skewed right

hope this helps :)

What is the solution to the system of equations? 3x - 4y = 22 -9x + 4y = 38​

Answers

Answer:

[tex]3x - 4y = 22 - - - - (i) \\ - 9x + 4y = 38 - - - - (ii) \\ from \: (i) \\ 4y = 3x - 22 - - - - (iii)\\ substitute \: for \: 4y \: in \: (ii) \\ - 9x + (3x - 22) = 38 \\ ( - 9 + 3)x = 38 + 22 \\ - 6x = 60 \\ x = \frac{60}{ - 6} \\ x = - 10 \\ \\ substitute \: for \: x \: in \: (iii) \\ 4y = (3 \times - 10) - 22 \\ 4y = - 30 - 22 \\ 4y = - 52 \\ y = \frac{ - 52}{4} \\ y = - 13[/tex]

The graph of an equation drawn through which two points would best represent the
relationship between the number of miles and the cost of the trip?
Plis helppp

Answers

Answer:

The answer is A

Explanation:

I just took this quiz.

PLEASE ANSWER THIS IN SLOPE INTERCEPT FORM!!!

Answers

Answer:

The answer is

[tex]y = - \frac{3}{4} x + \frac{13}{4} [/tex]

on day 1 a patient measures 5 feet and 11 inches tall. after 4 days of stretching the patient measures 5 feet and 11 inches tall. What is the slope and is it negative or positive?

Answers

Answer:

slope is zero

Step-by-step explanation:

zero slope is neither positive or negative; it indicates no change whatsoever

Put these expressions in order of size, from smallest to larg-
est, when a = 3 and b = 5.
46
3
2a + 3b

Answers

Answer:

that hiw you do it .hope it helps

ask me if you don't understand something

Step-by-step explanation:

thankyou...

Each box is 20 inches long, 30 inches wide, and 20 1/2 inches in hieght.

What is the volume of the box?

Answers

Answer:

Volume = 12,300

Step-by-step explanation:

20 x 30 = 600

600 x 20.5 =12300

Answer:

Volume of the box is length ×breadth×height

[tex]20 \times 30 \times 20 \frac{1}{2} \\ = 600 \times \frac{41}{2} \\ = 12300[/tex]

12300 inches cube is the right answer.

ABC is a triangle.
B
х
5.6 cm
9.3 cm
50°
Α'
78°
D
С
Work out angle x.
Give your answer correct to 3 significant figures.

Answers

Answer: 50.5

Step-by-step explanation:

If it’s mathswatch you don’t need an explanation just type in the answer it gives you all the marks <3

The value of the angle,x=50.531°. The angle is obtained by the sin law.

What is the triangle?

A triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

From the sin rule;

[tex]\rm \frac{AB}{sin \angle ACB} =\frac{BC}{sin \angle BAC} \\\\ \rm \frac{5.6}{sin \angle ACB} =\frac{9.3}{sin \angle 50^0} \\\\ \angle ACB=27.49^0[/tex]

For the same angles;

[tex]\rm \angle ACB=\angle BCD[/tex]

From the exterior angle theorm ;

[tex]\rm \angle BCD+\angle CBD= \angle ADB[/tex]

∠CBD=x

∠ABD=78°

Putting the obtained values;

27.469°+x=78°

x=78°-27.469°

x=50.531°

Hence,the value of the angle,x=50.531°.

To learn more about triangle refer;

https://brainly.com/question/25813512

#SPJ2

A person deposited Rs 60000 in a bank for 2 years at the rate of 10%pa compounded annually.But after one year,bank has changed the policy and decided to pay semi-annual compound interest at the same rate.What is the percentage difference between compound interest of first year and second year?

Answers

Answer:

[tex]1.159\%[/tex]

Step-by-step explanation:

Given: Principal or P [tex]=\textrm{Rs }60,000[/tex].

Rate or R [tex]=10\%[/tex] per annum compounded annually.

Time or T [tex]=2[/tex] years.

To find: Percentage difference between compound interest of first year and second year.

Solution:

First year interest [tex]=\frac{\textrm{P}\times \textrm{R}\times \textrm{T}}{100}=\frac{60000\times 10\times 1}{100}=\textrm{Rs }6000[/tex].

First year amount [tex]=\textrm{Rs }60,000+\textrm{Rs }6,000=\textrm{Rs }66,000[/tex].

For the second year, the interest is compounded semi-annually.

So, time is doubled and the rate is halved.

Second year compounded amount [tex]=66,000\times [1+\frac{10}{2\times 100}]^2=66,000\times1.1025=\textrm{Rs }72,765[/tex].

Second year compound interest [tex]=\textrm{Rs }72,765-\textrm{Rs }66,000=\textrm{Rs }6,765[/tex].

Difference in interest of first and second year [tex]=\textrm{Rs }6,765-\textrm{Rs }6,000=\textrm{Rs }765[/tex].

Percentage difference [tex]=\frac{765}{66000}\times 100\%=1.159\%[/tex].

Hence, the percentage difference between compound interest of first year and second year is [tex]1.159\%[/tex].

what's 5x5800000000000000000000000000 help

Answers

Step-by-step explanation:

so why you are asking?????

hi can you guys help with this ? thx

Answers

Answer:

a) 13%

b) 45%

c) 16%

Step-by-step explanation:

To calculate what percentage is one number (a) of another (b), you have to divide a by b and then multiply result by 100. In this case number of students with grade A is 4, total number of students is 31,  therefore 4/31 * 100 = 12.9%. Rounding it to the nearest percentage will give you 13.

Just repeat the same steps for the remaning questions.

Mark: 1.00
The volume of a cuboid is 140 cm
The area of its base is 88 cm2. Then
its height is
5cm
6 cm
8 cm
7 cm​

Answers

Volume of cuboid =l×b×h

area of base of the cuboid =l×b

hence

volume of cuboid is = area of base × height

140=88×h

h=140÷88

h=5

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