which option is correct?

C. For each term in this expression, you can just apply the power rule.

[tex]y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}[/tex]

Every other choice involves composite functions that do require the chain rule to differentiate.

Option C  : [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]  can be differentiated without using chain rule.

The differentiation of  [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   without using chain rule can be done as follows:

[tex]\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}[/tex]

The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.

Thus, the function [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   can be differentiated without using chain rule.

Thus, option C:   [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   is correct option.

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Answer:

D

Step-by-step explanation:

0.4 = 4/10 = 2/5

Finding the value of x,

→ 2x + 3 - 3 = - 6

→ x + (3 - 3) = - 6/2

→ [ x = -3 ]

Thus, the value of x is -3.

Answer:

36 feet

Step-by-step explanation:

shadow/height = shadow/height

11/6 = 66/h

h = 66 * 6 / 11

h = 36

Answer:

2×-6+9=5+×-1

2×-×=5-1+6-9

×=1

Answer:

5

Step-by-step explanation:

Just 1/4 from each of 5 bars so 5.

Answer:

20

Step-by-step explanation:

So if we divide 5 by 1/4 that gives us 20, which is the total amount of friends she can give 1/4 of a bar too

Answer:

Answer:

x=4

Step-by-step explanation:6x+8x=2x

5+3=8 (when you move a number to the other side of an equals sign, it changes its value)

2x=8

2x/2 and 8/2

x=4

The related function for –6x + 8x – 5 = 3 is;

x = 4

We are given the equation;

–6x + 8x – 5 = 3

Let us simplify the numbers that have the variable x first. Thus;

–6x + 8x – 5 = 3 gives;

8x - 6x - 5 = 3

>> 2x - 5 = 3

Use addition property of equality to add 5 to both sides;

2x - 5 + 5 = 3 + 5

>> 2x = 8

Use division property of equality to divide both sides by 2 to get;

x = 8/2

Thus;

x = 4

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Answer:

The rule for a profit-maximizing perfectly competitive firm is to produce the level of output where Price= MR = MC, so the raspberry farmer will produce a quantity of 90, which is labeled as e in Figure 4 (a). Remember that the area of a rectangle is equal to its base multiplied by its height.

Answer:

x - 4 < 18

Step-by-step explanation:

< means less than

> means more than

[tex]\\ \sf\longmapsto 2(n-1)+47=2(3n-1)[/tex]

[tex]\\ \sf\longmapsto 2n-2+47=6n-2[/tex]

[tex]\\ \sf\longmapsto 2n+47=6n[/tex]

[tex]\\ \sf\longmapsto 4n=47[/tex]

[tex]\\ \sf\longmapsto n\approx 12[/tex]

Answer:

n = 11.75

Step-by-step explanation:

2(n - 1) + 47 = 2(3n - 1)              Distribute the multiplier

2n - 2 + 47 = 6n - 2                 Combine terms

              47 = 4n                       divide

                n = 11.75

Answer:

Yes.

Step-by-step explanation:

If you use the vertical line test, you'll see that the line only touches the graph at one point.

Answer:

a mi casa aunque no es lejos

Answer:

Step-by-step explanation:

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ  is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

Trigonometric Identities are equality conditions that hold for all possible values of the variables in the equation and use trigonometry functions. There exists numerous unique trigonometric identities that relate a triangle's side length and angle.

here, we have,

Sine, cosine, and tangent are the fundamental three operations in trigonometry. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions exists built.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These exists identities that, geometrically speaking, involve certain functions of one or more angles.

we have,

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ  is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

Hence, The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

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Step-by-step explanation:

30-(12-7)= red pens

30-19

11

Probability=

11/30

Answer:

12

Step-by-step explanation:

12x - 4 = 10x + 20

2x - 4 = 20

2x = 24

x = 12

Answer:

a

Step-by-step explanation:

Answer:

C. (2, -3)

Step-by-step explanation:

Answer:

The answer should be A.

Step-by-step explanation:

Answer:

About 11.025

Step-by-step explanation:

[tex]\sin{58^\circ}=\dfrac{x}{13}\\\\x=13\cdot\sin{58^\circ} \approx11.025[/tex]

H₂SO₄ is Sulfuric Acid and the number of atoms Sulfur has is 4 atoms

What is a Chemical Formula?

A chemical formula is a formula that lists the constituent parts of a compound together with their relative proportions. No subscript is used if there is just one atom of a certain kind. A subscript is added to the symbol for an atom if it contains two or more of a certain type of atom.

Given data ,

The chemical is represented as H₂SO₄  which is Sulfuric Acid

Sulfuric acid has 2 atoms of Hydrogen , 1 atom of Sulfur and 4 atoms of Oxygen

As per the chemical formula , we can see that there is no subscript added to the Sulfur S in the chemical formula equation.

Therefore , The number of Sulfur atoms present in H₂SO₄  is 1

Hence , H₂SO₄  has only 1 sulfur atom

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Answer:

45 degrees

Step-by-step explanation:

Subtract 360° 360 ° from 405° 405 ° . The resulting angle of 45° 45 ° is positive, less than 360° 360 ° , and coterminal with 765° 765 ° .

Answer:

The relation is a function.

Step-by-step explanation:

In the given relation, {(A, 8), (B, 8), (D, 5), (F, 5), (G, 8)}:

A relation is a function for which none of the ordered pairs have the same first component and different second components.  

In the given relation:

The given relation represents a function since none of the first components  have the same corresponding second components.  In other words, there are no repeating values of A, B, D, F, and G. Each of these values has its own corresponding second component.  

Therefore, the relation, {(A, 8), (B, 8), (D, 5), (F, 5), (G, 8)} is a function.

Answer:

x=6

Step-by-step explanation:

Answer:

E = 120

F = 60

G = 120

H = 60

Step-by-step explanation:

Since the number of trials is not fixed, an inverse binomial distribution is used.

For each car, there are only two possible outcomes, either they use a blinker during lane change, or they do not. The probability of a car using a blinker during lane change is independent of any other car, which means that the number of cars that do not use a blinker during a lane change is a binomial variable.

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Answer:

graph A shows all natural numbers less than 3

Step-by-step explanation:

Answer:

The Answer Is B

Step-by-step explanation:

Answer:

2.38

Step-by-step explanation:

William wish1wish woman weeks whereby when wishful willful

As you may know, the 8 would be located in the hundreaths place.

2.3892

If the number right of 8 is five for less, it says the same. If it's 5 or more, then 8 would change. In this case, 9 is more than 5 meaning that 8 becomes 9. However, we aren't quite finished yet. 9 and everything left of that number must become 0.

Your answer would be 2.39.

Answer:

x = 10

Step-by-step explanation:

the unmarked angle in the triangle is the supplement to 6x - 7

180 - (6x - 7)

180 - 6x + 7

187 - 6x

The sum of the angles in a triangle is 180

therefor

(2x + 7) + 26 + (187 - 6x) = 180

Combine like terms

-4x + 220 = 180

Subtract 220 from both sides

-4x = -40

divide both sides by -4

x = 10

Answer : 31

Explanation : Every numbers have a gap of 6 as you can see:

1 + 6 = 7

7 + 6 = 13

13 + 6 = 19

19 + 6 = 25

So,

25 + 6 = 31

Hope This Helps You!