If the gradient of the tangent to
[tex]y = \sqrt{x} [/tex]
is
[tex] \frac{1}{6} [/tex]
at point A, find the coordinates of A.​

Answers

Answer 1

Answer:

Point A(9, 3)

General Formulas and Concepts:

Pre-Algebra  

Order of Operations: BPEMDAS  

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties  

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I  

Coordinates (x, y) Functions Function Notation Terms/Coefficients Anything to the 0th power is 1Exponential Rule [Rewrite]:                                                                              [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]:                                                                     [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]  

Calculus  

Derivatives  

Derivative Notation  

Derivative of a constant is 0  

Basic Power Rule:  

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \sqrt{x}[/tex]

[tex]\displaystyle y' = \frac{1}{6}[/tex]

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]:                                   [tex]\displaystyle y = x^{\frac{1}{2}}[/tex]Basic Power Rule:                                                                                             [tex]\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}[/tex]Simplify:                                                                                                             [tex]\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]:                                          [tex]\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]:                                 [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}[/tex]

Step 3: Solve

Find coordinates of A.

x-coordinate

Substitute in y' [Derivative]:                                                                             [tex]\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides:                      [tex]\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}[/tex][Multiplication Property of Equality] Cross-multiply:                                      [tex]\displaystyle \sqrt{x} = 3[/tex][Equality Property] Square both sides:                                                           [tex]\displaystyle x = 9[/tex]

y-coordinate

Substitute in x [Function]:                                                                                [tex]\displaystyle y = \sqrt{9}[/tex][√Radical] Evaluate:                                                                                         [tex]\displaystyle y = 3[/tex]

∴ Coordinates of A is (9, 3).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e


Related Questions

Loagn used the net below to design a nylon tent

Answers

Answer:

Part A: The tent is shaped like a square pyramid

Part B: a 36ft tent

Step-by-step explanation:

Answer:

Step-by-step explanation:

i don’t know

What is the percent for 82?

Answers

82% of 100 = 82%

Depends on what you’re asking 82% of but usually it would be of 100.. hope this helps

In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Arun sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 128 visitors purchased no costume. 3 visitors purchased exactly one costume. 5 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.​

Answers

Answer:

3/136

Step-by-step explanation:

128 + 3 + 5 = 136

= 3/136 (simplest form)

Um..Please help me with this...

Answers

Answer:

2,1  4,2  6,3  8,4  10,5  12,6  14,7  16,8  18,9  20,10  etc.

Step-by-step explanation:

what's equivalent to (9 7/8 + 2 4/5) - 1/2​

Answers

Answer:

12.175

Step-by-step explanation:

also

Step-by-step explanation:

C) 9 7/8 - (- 2 4/5) - (- 1/2) =

= 9 7/8 + 2 4/5 + 1/2 (F)

D) - (- 9 7/8 + 2 4/5) - 1/2) =

= 9 7/8 - 2 4/5 - 1/2 (F)

E) 9 7/8 - (- 2 4/5 - 1/2) =

= - 7/8 + 2 4/5 + 1/2 (F)

Answer:

12 7/40

Step-by-step explanation:

9 7/8 = 9 35/40

2 4/5 = 2 32/40

add:  11 67/40

67/40 = 1 27/40

11 + 1 27/40 = 12 27/40

12 27/40 - 20/40 = 12 7/40

Expand and simplify (x – 2)(2x + 3)(x + 1)

Answers

Answer:

Step-by-step explanation:

(x-2)(2x+3)(x+1)

=x(2x+3)-2(2x+3)(x+1)

=(2x^2+3x-4x-6)(x-1)

=(2x^2-x-6)(x-1)

=2x^2(x-1)-x(x-1)-6(x-1)

=2x^3-2x^2-x^2+x-6x+6

=2x^3-3x^2-5x+6

( x - 2 )( x + 1 )( 2x + 3 ) =

( x^2 - x - 2 )( 2x + 3 ) =

2x^3 - 2x^2 - 4x + 3x^2 - 3x - 6 =

2x^3 + ( -2 + 3 )x^2 + ( - 4 - 3 )x - 6 =

2x^3 + x^2 - 7x - 6

A freezer was set at 0 C, sophia reset it to 8.5 C. Would the temperature in the freezer likey rise or drop? By how many degrees?

Answers

Answer:

Step-by-step explanation:

1) the temperature rise, because 8.5 is C higher than 0 C

2) 8.5 - 0 = 8.5

So it rised by 8.5 degrees ( to know how many dgrees is is rised subtract the second number from the first number)

make sure answer is in degrees.

sin^-1(sin 17°)

Answers

Answer:

uhm 0 degrees

Step-by-step explanation:

The value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.

What is inverse trigonometry?

Simply put, inverse trigonometric operations are the opposites of the fundamental trigonometric parameters sine, cosine, secant, cosecant, tangent, and cotangent.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The inverse trigonometric expression is given below.

⇒ sin⁻¹(sin 17°)

We know that the value of sin⁻¹(sin θ) is θ.

Then the value of the inverse trigonometric expression will be

⇒ sin⁻¹(sin 17°)

⇒ 17°

Thus, the value of the inverse trigonometric expression sin⁻¹(sin 17°) will be 17°.

More about the inverse trigonometry link is given below.

https://brainly.com/question/20595059

#SPJ2

someone help me please i need this by today

Answers

Answer:

In the picture above

Step-by-step explanation:

I solved all questions except no.7 ; I don't know how can be solved.

I hope that its a clear solution. Goodluck

What is the measure of XZ?

A. 36°
B. 144°
C. 72°
D. 18°

Answers

Answer:

C.72

Step-by-step explanation:

angle XYZ is an inscribed angle and arc XZ is the arc it intercepts

If you didn't know the measure of an inscribed angle is equal to half the measure of its arc it intercepts or an intercepted arc equals twice the measure of its inscribed angle

Hence, angle XYZ * 2= arc XZ

If Angle XYZ = 36

then 36 * 2 = arc XZ

36 * 2 = 72

hence the answer is C

The measure of arc is 72 degree, the correct option is C.

What is an arc?

An arc is formed by two radii and their intercepted part on the circumference.

According to the theorem of arc and subtended angles, the central angle subtended by the arc is double the angle subtended by it on the circumference.

The angle subtended by arc XZ on the circumference is 36 degree.

The angle subtended by the arc at the center is = 2 * 36 = 72 degree.

The arc subtended by the arc at the center of the circle is the measure of the arc.

To know more about Arc

https://brainly.com/question/18741430

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PLZZZZZZZZZZZZ


She had a coupon for 15% off. The tax rate was 7.75%. If the subtotal was $35, how much money did Ms. Morel actually pay in total (after the discount and tax)? *

Answers

Answer:32.05

Step-by-step explanation:

SO after tax the total would be  $37.71.With original price $37.71 and 15% discount,

Price after discount: $32.05

You saved: $5.66

Can anyone help me with this problem

Answers

Answer:3^2

Step-by-step explanation:

I think it is 3 with exponent of 3 because if its asking for side length of 9 then 3 x 3=9


Determine whether the triangle with the given side lengths is acute,
right, obtuse or not a triangle 3,8,15

Answers

Answer:

Step-by-step explanation:

Not a triangle, because the leg lengths 8 and 3 add up to 11, not to 15.

The sum of the leg lengths must be greater than the length of the 3rd side for a triangle to exist.

I need answer Immediately pls!!!!!!!!

Answers

Step-by-step explanation:

write what you know

the flat fee doesnt chamge no matter how much he uses his data

the charge for every gigabyte does change

Ex: if he uses 3 gigabytes of data in one month, that's

5 + 5 + 5 = $5 x 3 = $15

So taking this into consideration youd write the following

$41.50 + $5x = $52.50 (since this is what we want to equal)

then solve for x

Please answer this for me correctly. THANK YOU!!

Answers

Answer:

The answer is <MQL.

iq scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of people have an IQ between 130 and 100 a)13.5% b)47.5% c)95% d)27%

Answers

Answer:

"approximately 47.%"

Step-by-step explanation:

Using the statistical function normalcdf( on my old TI-38 calculator:

normalcdf(100,130, 100, 15) returns the fraction 0.477,

so the final answer here is "approximately 47.%"

quick please
7.find the area of the shaded region of the rectangle:

Answers

Answer:

6x+2

-2x+1

=

4x+1

just find the area of each and subtract the non-shaded one from the shades area.

In a Triangle,2angles are 56°and 45°,then find the third angle​

Answers

Answer:e answer is 79

Step-by-step explanation:

to find the third angle subtract the angles from

180

=56°+45°

=99

third angle=180°-99°

=81°

HOW TO DO THIS QUESTION PLEASE ​

Answers

Answer:

34

Step-by-step explanation:

[tex]\frac{2}{5}*85[/tex]

Long way

multiply the two numeratorsmultiply the two denominatorssimplify the new fractions

[tex]\frac{85}{1}*\frac{2}{5} \\ \\ \frac{170}{5} \\ \\ =34[/tex]

short way

-can be simplified before mulitplying

factor out common factors in the numerator and denominator

[tex]\frac{85}{1} *\frac{2}{5} \\ \\ \frac{17}{1}*\frac{2}{1} =34[/tex]

Think 85 and 5 as nickels. You need 20 nickels to make 100. Subtract 100 by 85 to get 15. You get 3 nickels and 17 nickels. 17 is the common factor. Multiply 17 by 2 to get your answer.

The solution of the quadratic equation 3x^2=4x is written by a student as the following: According to you, is this students solution correct or not? Explain your answer with reasons?
Solution:
Step 1:3x2 = 4x
Step 2: 3xx = 4x
Step 3:3x = 4
Step 4: x = 4/3​

Answers

Well the answer is correct but the working out is wrong because you are supposed to subtracts 4x by both sides first then factor out x thirdly find the equation solutions and then solve



Step 1) 3x^2 - 4x = 0
Step 2) x(3x - 4) = 0
Step 3) x = 0
Step 4) 3x - 4 = 0 + 4 hereby leaves 3x = 4
Step 5) x = 0 and x = 4/3

please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

hello, the measure of T is 34 when you round it to the nearest tenth

Answer:

x=34

Step-by-step explanation:

Again we are given an angle's ( x to be more specific )  opposite side length and the adjacent side length so we will use trig ratio tangent

Recall that tan = opposite over hypotenuse

[tex]tan(x)=\frac{29}{43}[/tex]

* multiply each side by the inverse of tan ( [tex](tan)^-^1[/tex] )

[tex]tan(x)*tan^-^1=x\\tan^-1*\frac{29}{43} =33.99645915\\x=33.99645915[/tex]

Finally we round to the nearest tenth of a degree and get that x = 34

what is the area of the triangle.​

Answers

Answer:

A=hbb= 2

Step-by-step explanation:

your welcome plz brainlist

Answer:

21.75u2

Step-by-step explanation:

first use pythag for this

use rule c2=b2+a2

reverse the rule so that

b2=c2-a2

b2=100-81

b2=19

b=4.35

how u got the height of the triangle

use formula bh/2

10x4.35/2

=43.5/2

=21.75u2

The length of a rectangle flower bed is 5ft longer than its width. A sidewalk with a width of 3ft surrounds the bed. If the total area of the bed and sidewalk is 546ft^2, what are the dimensions of the flower bed ?

Answers

Answer:

[tex]W=15ft[/tex]

[tex]L=20ft[/tex]

Step-by-step explanation:

From the question we are told that:

Length of Bed [tex]L=5+W[/tex]

Width of sidewalk [tex]W_s=3ft[/tex]

Area of the bed and sidewalk [tex]A_t= 546ft^2[/tex]

Generally the equation for Area of the bed and sidewalk[tex]A_t[/tex] is mathematically given by

 [tex]Area=L*B[/tex]

 [tex]A_t=((3+3)+L)*((3+3)+W)[/tex]

Therefore

 [tex]546=((3+3)+(5+W))*((3+3)+W)[/tex]

 [tex]0=((6+(5+W))*((6)+W)-546[/tex]

 [tex](11+W)*(6+W)-546=0[/tex]

 [tex]W^2+17B-480=0[/tex]

Solving the Quadratic Equation

 [tex]W=15ft[/tex] (Using only positive root)

Generally the Length L is mathematically given by

 [tex]L=5+15[/tex]

 [tex]L=20ft[/tex]

The Spanish Club has 40 members, 5 girls and 35 boys. What is the ratio of
girls to boys in the Spanish Club?
O A. 1:4
B. 1:7
C. 7:1

Answers

Answer:

B. 1:7

Please give me brainliest, thank you!

Step-by-step explanation:

Information given and needed:

- 40 members

- 5 girls

- 35 boys

Solve:

girls to boys

5 to 35

(You can now simplify)

1 to 7

Answer:

B. 1:7

Answer:

1:4

Step-by-step explanation:

Which is the answer ? Please help

Answers

Answer:

C

Step-by-step explanation:

1/2 is equal to 2/4 so 1/2 is greater than 1/4

Answer:

C

Step-by-step explanation:

A)

[tex]\frac{1}{2} = \frac{4}{8}[/tex]

[tex]\frac{4}{8} < \frac{1}{8}\ is\ wrong!\ Therefore\ A\ is\ wrong[/tex]

B)

[tex]\frac{2}{1} = \frac{4}{2}[/tex]

[tex]\frac{1}{2} = \frac{4}{2}\ is\ wrong!\ Therefore\ B\ is\ wrong[/tex]

C)

[tex]\frac{1}{2} = \frac{2}{4}[/tex]

[tex]\frac{2}{4} > \frac{1}{4}\ is\ correct!\ Therefore\ C\ is\ correct[/tex]

D)

[tex]\frac{1}{2} = \frac{2}{6}[/tex]

[tex]\frac{2}{6} < \frac{1}{6}\ is\ wrong!\ Therefore\ D\ is\ wrong[/tex]

Find the distance between (-7, -2) and (13, -23)

Answers

Answer:

5,030?

Step-by-step explanation:

A.)17.5
B.)20
C.)18
D.)17

Answers

Answer: A

Step-by-step explanation: 35 / 2 = 17.5

Answer:

C. is correct

Step-by-step explanation:

i hope this helps :) brainliest please?

As you can tell I’m back to help my idiotic Brother just do the first 3 ty

Answers

1:plus 4 2: times 2 3:minus 10

3. Graph the following exponential function and
label the asymptote. (9 pts)
y = - 3(2)
(x, y)
-2
-1
X
Х
2012

Answers

Answer:

y=3(2)

(x:y)

-3-2÷(-2-(-1)

=-5÷2

A small town has two local high schools. High School A currently has 750 students and is projected to grow by 45 students each year. High School B currently has 850 students and is projected to grow by 25 students each year. Let A represent the number of students in High School A int years, and let B represent the number of students in High School B after t years. Write an equation for each situation, in terms of t, and determine after how many years, t, the number of students in both high schools would be the same.​

Answers

Answer: A=750 +75*t

B=900 +25*t

There would be 975 students in each high school in year 3 when they are expected to have the same number of students.

Step-by-step explanation:

A = B

750 +75*t=900 + 25*t

Solving:

75*t -25*t= 900 - 750

50*t= 150

t=3

This indicates that in year 3 both High Schools are projected to have the same number of students. To get that amount, you simply replace this value in the expressions:

A=750 +75*t= 750 +75*3= 975

B=900 + 25*t=900 + 25*3= 975

There would be 975 students in each high school in year 3 when they are expected to have the same number of students.

 

Equation for high school A: A(t)=750+45t
Equation for high school B: B(t)=850+25t

750+45t=850+25t, solve for t:
45t-25t=850-750
20t=100
t=5

Answer: After 5 years, both high schools will have the same number of students.

Check:
750+45t=750+(45*5)=750+225=975
850+25t=850+(25*5)=850+125=975
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