What is the inequality shown?

Answer:

[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].

Substituting 3 for f(x) and x² for g(x), we get:

Simplify.

Using exponent rules, we can rewrite this as:

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.

Answer:

[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:

[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].

In this question:

Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].

Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].

For [tex]{g}^{\prime}(x)[/tex], consider the power rule:

if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].

Apply this rule to find [tex]{g}^{\prime}(x)[/tex].

[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].

Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:

[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].

Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].

Answer:

it is the first answer because it want you to roll 5 first try

Answer:

If you are looking for the answer it is.... y=-12x+180

Step-by-step explanation:

Answer:

66 pounds of tomatoes

Step-by-step explanation:

A recipe code lasagna calls for 3 pounds of tomatoes to serve 5 people. A caterer wants to make enough lasagna to serve 110 people. How many pounds of tomatoes does he neeed

From the above question:

5 people = 3 pounds of tomatoes

110 people = x pounds of tomatoes

Cross Multiply

5 people × x pounds = 110 people × 3 pounds

x pounds = 110 people × 3 pounds/5 people

x pounds = 66 pounds of tomatoes

Answer:

Solution: y=2

Answer:

a = -1

b= 1

Step-by-step explanation:

8's absolute value is 8, so 8 - 9 is -1 but 8-9 = -1 and since the answer is in the absolute value bars, -1's absolute value is 1, so the answer will be 1

but in a, only 8 is in the absolute value bars, not the complete answer

Answer:

3.75

Step-by-step explanation:

Answer:

5/6 divided by 6 = 5/48 or 0.1041666666 repeating

Answer:

20 days

Step-by-step explanation:

Because to find the number of days that Sonia will have you have to divide total money ($40) by money each day ($2). And $40 divided by $2 is 20, so 20 days is the answer.

Have a most wonderfull day, and I hope you likeee the answer....so yep.

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

6. 11.3 Miles

7. 1.5 Miles

8. No he would need 26 Miles , he only has 25 Miles.

9. 11.25 Miles

10. Not really it slightly goes over by about .80

Answer:

6: 15miles

7: 17miles

8: No, because just by going to the grocery is 13miles (times2) that's 26

9: 11.2 (not sure)

10: No, he said 5miles, the park is 5.8miles away from his house. (you don't have to but rounded is 6miles so he cant reach the park)

Step-by-step explanation:

Answer:

F.O.I.L is a method of solving quadratic equations.

P.S, i love the pics.

Plz mark brainliest!!

Answer:

Step-by-step explanation:

4x3 is the max of 12

Answer:

A. 0

B. 7

C. 3

D. 9

E.9

F.3

G.1

H.5

J.7

K.5

L.1

It's just a lot of reversing operations and seeing what fits, but if you have more you want to try, just make sure you remember borrowing and carrying numbers because they make a big difference.

Answer:

z (the arrow with teh line is pinting to the z) -4

Step-by-step explanation:

Answer:no hablo espanol

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

40-26=14 so therefore 14% of the books are non-fiction

Answer:

one solution:  x = -3,  y = 26

Step-by-step explanation:

3x + y = 17

x + 2y = 49

If you multiply the first equation by -2 and then add you will eliminate the 'y' term

-2(3x + y) = -2(17)

  -6x - 2y = -34

+    x + 2y = 49

   -5x = 15

     x = -3

-3 + 2y = 49

2y = 52

y = 26

9514 1404 393

Answer:

  2. chord theorem; t = 10.5

  3. chord theorem; x = 5

Step-by-step explanation:

For both of these problems, the relevant theorem is the "intersecting chord theorem", also referred to as the "chord theorem." It tells you the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the other chord.

2. 20t = 10·21

  t = 210/20 . . . . divide by 20

  t = 10.5 . . . . . . . simplify

__

3. 10(x +4) = 15(x +1)

  10x +40 = 15x +15 . . . . . eliminate parentheses

  25 = 5x . . . . . . . . . . . . . subtract 10x+15

  5 = x . . . . . . . divide by 5

Answer:

4 more students

Step-by-step explanation:

10% of 40 is 4, since the membership went up by 10% it is clear that there are 4 more students that joined the chess club.

Answer:

10/100*40

=4 more students joined the club

Step-by-step explanation:

Answer:

subtracting both equations

3x-10y=14

3x-9y=15

- - =-

_________

0-y=-1

y=1

then putting the value of y in first eqn

3x-10×1=14

3x=24

x=8

so x is 8and y is 1

Answer:

(- 1, 4 )

Step-by-step explanation:

Given the 2 equations

3x + 4y = 13 → (1)

2x - 2y = - 10 → (2)

Multiplying (2) by 2 and adding to (1) eliminates the term in y

4x - 4y = - 20 → (3)

Add (1) and (3) term by term to eliminate y, that is

7x + 0 = - 7

7x = - 7 ( divide both sides by 7 )

x = - 1

Substitute x = - 1 into either of the 2 equations and solve for y

Substituting into (1)

3(- 1) + 4y = 13

- 3 + 4y = 13 ( add 3 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

solution is (- 1, 4 )

Answer:

The solution is (-6,2)

Step-by-step explanation:

Answer:

Fr

Step-by-step explanation:

Answer:  11/3 or 3.6 or 3 2/3

Step-by-step explanation:

All you have to do is simplify the expression

Answer:

7)x=11

8)x=16

9)n=12

10)m=13

11)n=8

12)m=3

Step-by-step explanation:

Answer:

7= 11. 8=16. 9=12. 10=13 11=8. 12=3

Step-by-step explanation:

7= 9+2=11

8=12+4=16

9=9+3=12

10=8+5=14

11=7+1=8

12=3+0=3