The curve
[tex]y = \sqrt{x - 3} [/tex]
has a tangent with gradient
[tex] \frac{1}{2} [/tex]
at point N.
Find the coordinates of N.​

Answers

Answer 1

Answer:

Point N(4, 1)

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)FunctionsFunction NotationTerms/CoefficientsAnything 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

[tex]\displaystyle y = \sqrt{x - 3}[/tex]

[tex]\displaystyle y' = \frac{1}{2}[/tex]

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]:                                   [tex]\displaystyle y = (x - 3)^{\frac{1}{2}}[/tex]Chain Rule:                                                                                                        [tex]\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3][/tex]Basic Power Rule:                                                                                             [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)[/tex]Simplify:                                                                                                             [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1[/tex]Multiply:                                                                                                             [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]:                                          [tex]\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]:                                 [tex]\displaystyle y' = \frac{1}{2\sqrt{x - 3}}[/tex]

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]:                                                                             [tex]\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides:                      [tex]\displaystyle 1 = \frac{1}{\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply √(x - 3) on both sides:            [tex]\displaystyle \sqrt{x - 3} = 1[/tex][Equality Property] Square both sides:                                                           [tex]\displaystyle x - 3 = 1[/tex][Addition Property of Equality] Add 3 on both sides:                                    [tex]\displaystyle x = 4[/tex]

y-coordinate

Substitute in x [Function]:                                                                                [tex]\displaystyle y = \sqrt{4 - 3}[/tex][√Radical] Subtract:                                                                                          [tex]\displaystyle y = \sqrt{1}[/tex][√Radical] Evaluate:                                                                                         [tex]\displaystyle y = 1[/tex]

∴ Coordinates of Point N is (4, 1).

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

Unit: Derivatives

Book: College Calculus 10e


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The correct answer is C

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Answer:

a. 3100 wpm

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Answers

Answer:

1. Three fourths

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Step-by-step explanation:

i dont know which one you want

Answer:

.75

Step-by-step explanation:

3 over 4 means [tex]\frac{3}{4}[/tex], and a fraction is just a division problem. 3 ÷ 4 = .75

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Answer:

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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The equivalent expression is ~

[tex] \boxed{ \frac{9}{14} }[/tex]

[tex] \huge \boxed{ \mathfrak{Explanation}}[/tex]

[tex]2 \frac{1}{4} \div 3 \frac{1}{2} [/tex]

[tex] \dfrac{9}{4} \div \dfrac{7}{2} [/tex]

[tex] \dfrac{9}{4} \times \dfrac{2}{7} [/tex]

[tex] \dfrac{9}{2 \times 7} [/tex]

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Answer: D

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Answer:

3/5

Step-by-step explanation:

both 6 and 10 divide by 2. divide each number by 2 and you get 3/5

Answer:

3/5

Step-by-step explanation:

To find the simplest form of 6/10, you must reduce the fraction.

I did this by dividing both the numerator and denominator by 2, therefore making it 3/5, (because it cannot be reduced evenly anymore).

Hope this helps :)

EASY POINTS!!
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What is the area of the cutting board in terms of pi?


A. 32 square inches
B. 64 square inches
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D. 16 square inches

Answers

Answer:

B. 64 square inches

Step-by-step explanation:

you just add

Answer:

Step-by-step explanation:

4

The triangular face of the given prism has an interior angle with a measure of 55° and an exterior angle with a measure of 95°. What is the measure of the marked interior angle?

Answers

Answer:

40 degrees

Step-by-step explanation:

sum of angles in a triangle = 180 degrees

if the exterior angle measures = 95, the interior angle beside it would measure 180 - 95 = 85

marked interior angle = 180 - (85 + 55) = 40 degrees

Answer:

As ewomazinoade states 40° should be the correct answer.

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Answer:

Step-by-step explanation:

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20 POINTS! The managers of an automotive insurance company investigated whether the customers in region A have a higher proportion of speeding tickets than the customers in region B. The managers selected 154
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Answer:

Every year, a pet food company sells its food to stores across the nation. ... In the first month of the new year, the Midwest region secured sales orders from ... Suppose the strategy of the pet food company is to increase the proportion of ... Do you think additional field training is necessary for all of the sales representatives?

Step-by-step explanation:

Please help I give out brainliest .....Kellie bought 8 towels and spent $39.60. Each towel costs the same amount.
Part A
Use the drop-down menus to create an equation that can be used to determine t, the
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Part B
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Enter your answer in the box.

Answers

Answer:

Each Towel is 4.95 each

Step-by-step explanation:

We can use 8t = 39.60 as our equation

8t = 39.60

Divide 8 on both sides.

t = 4.95

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Answers

Answer:

so 3%5+=67K and 9+=-8 is -1

Step-by-step explanation:

What is the volume of the pyramid in the diagram?
9 cm
height = 3 cm
5 cm
S cm
OA 25 cm3
OB.
75 cm
O C.
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Answers

Answer:

A. 25 cm^3.

Step-by-step explanation:

Volume = 1/3 * area of base * perpendicular height,

= 1/3 * 5^2 * 3

= 5^3

= 25.

The correct option is A. Volume of the pyramid is 25 cm³ which is option A.

What is the volume of the pyramid?

The volume of a pyramid is given by lbh/3. It is also given by the product of the base area and height of the pyramid and then divided by 3.

The base of the pyramid is in the form of a square as all sides are 5 cm. Find the area of the square that is the base area.

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Now multiply 25 by the height of the pyramid which is 3 cm.

25×3=75 cm³

Divide 75 by 3 to find the volume of the pyramid.

75÷3=25 cm³

Thus, the volume of the pyramid is 25 cm³ which is option A.

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Answer:

It's the second answer down : Angle B, A and C

Step-by-step explanation:

The sequence from the smallest to the largest is angle B, angle A, angle C .

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Answers

Answer:

See solutions below

Step-by-step explanation:

2) angle at the vertex is half that of its intercepted arc;

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51*2 = 14x-38

102 = 14x-38

14x = 102 + 38

14x = 140

x = 140/10

x = 14

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9x + 7 = 34

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Step-by-step explanation:

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Answers

Answer:

He has to pay 15% as that is 32 and more than $25

Step-by-step explanation:

If you take 15% out of 216 it will become 32.


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Answers

Answer:

See below.

Step-by-step explanation:

X-intercepts: (-1, 0) & (5, 0)

Y-intercept: (0, -5)

Vertex: (2, -9)

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Answer:

Answer is 100 sq m

Step-by-step explanation:

A = [tex]a^{2}[/tex]

A = [tex]10^{2}[/tex]

A = 100 sq m

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Answer:

4 /9

Step-by-step explanation:

All we have to do is evaluate the options in other to compare the result :

4 / 10 = 0.4

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What is the correct algebraic representation of the transformation displayed on the graph?
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Answer:

[tex]transformation: (y,-x)[/tex]

----------------------------

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Step-by-step explanation:

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hi

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Step-by-step explanation:

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Answers

Answer:

(Xm, Ym) = [ x1+x2/2, y1 + y2/2]

Given (6,3) (-3,-7)

x1 y1 x2 y2

Step-by-step explanation:

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Hi for this I got; (1.5, 2)

4
How would you tell someone to plot (4,-3)?
pick the two best answers
1
go right 4
go left 4
go up 3
go down 3
What I pic

Answers

Step-by-step explanation:

go right 4

go down 3

it is the answer

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Answer:

No

Step-by-step explanation:

It will be a right triangle if it follows Pyhthagoras Theorem . Where the sum of squares of two smaller sides is equal to the square of the 3rd side. Let's check ,

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