Last question Can anybody help

Answer:

1) [tex]\frac{dy}{dx}=12x^2+6x-6[/tex]

2) [tex]x\leq-1\text{ or } x\geq 1/2[/tex]

Step-by-step explanation:

So we have the equation:

[tex]y=4x^3+3x^2-6x-1[/tex]

Part A)

We want to find the derivative of the above function. So:

[tex]\frac{dy}{dx}=\frac{d}{dx}[4x^3+3x^2-6x-1][/tex]

Expand:

[tex]\frac{dy}{dx}=\frac{d}{dx}[4x^3]+\frac{d}{dx}[3x^2]+\frac{d}{dx}[-6x]+\frac{d}{dx}[-1][/tex]

Use the power rule. Therefore, our derivative is:

[tex]\frac{dy}{dx}=3(4x^2)+2(3x)+(-6)+(0)[/tex]

Simplify:

[tex]\frac{dy}{dx}=12x^2+6x-6[/tex]

Part B)

We want to find the range of the values of x such that:

[tex]\frac{dy}{dx}\geq 0[/tex]

So, all we have to do is substitute our derivative in:

[tex]12x^2+6x-6\geq0[/tex]

And solve for this quadratic inequality!

Solve it normally. Pretend the inequality is with an equal sign. So:

[tex]12x^2+6x-6=0[/tex]

Divide everything by 6:

[tex]2x^2+x-1=0[/tex]

Factor. We can use -2 and 1. So:

[tex]2x^2+2x-x-1=0[/tex]

From the first two terms, factor out 2x.

From the third and fourth terms, factor out a negative. So:

[tex]2x(x+1)-(x+1)=0[/tex]

Grouping:

[tex](2x-1)(x+1)=0[/tex]

Zero Product Property:

[tex]2x-1=0\text{ or } x+1=0[/tex]

Solve for x in each case:

[tex]x=1/2\text{ or } x=-1[/tex]

So, the zeros of our function is -1 and 1/2.

Looking above, we can see that this is a greater than inequality.

Since this is a greater than inequality, our solution is all values to the left of the first zero and all values to the right of the second zero.

Therefore, our solution is:

[tex]x\leq-1\text{ or } x\geq 1/2[/tex]

In interval notation, this is:

[tex](-\infty,-1]\cup[1/2,\infty)[/tex]

So, for all values within the above interval, our derivative, dy/dx, will be greater than or equal to 0.

And we're done!

Edit: Typo. Brainly is rather buggy right now.

Answer:

0.2

Step-by-step explanation:

0.002 x 10 as it is 1/10 of the size

The answer is 0.2.

Here,

We have to find the number as 'the answer to 0.02 is 1/10 of the number.'

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Now,

Let the number is x.

Then, By given condition the expression is written as;

0.02 = (1/10) * x

(1/10) * x = 0.02

x = 0.02 * 10

x = 0.2

Hence, The value is 0.2

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Answer:

{3, 4, 5, 6, 7, 8, 9, 10, 11}

Step-by-step explanation:

Let integer be x

x > 2 and x < 12

gives

2 < x < 12

All such integers are {3, 4, 5, 6, 7, 8, 9, 10, 11}

Answer:

-27

Hope this helps.

Hey there! I'm happy to help!

We see that Kevin travels 12 1/2 miles in 1/3 hours. We want to see how far he travels in one hour. To do this, we simply multiply by 3!

12 1/2×3=37 1/2

Therefore, Kevin travels at 37 1/2 mph.

Have a wonderful day! :D

=========================================================

Work Shown:

There are 13 diamond cards. The probability of getting a diamond card is 13/52 = 1/4.

Assuming the first card is not replaced, the probability of getting another diamond card is 12/51. Note how I subtracted 1 from the numerator and denominator of 13/52 to get 12/51.

Multiply the two fractions to get

(1/4)*(12/51) = 12/204 = 1/17

The probability of getting two diamonds in a row is 1/17

We'll use this later, so let A = 1/17.

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

There are 4 kings. The probability of pulling out a king is 4/52 = 1/13

The probability of pulling out another king is 3/51 = 1/17

The probability of pulling out two kings in a row is (1/13)*(1/17) = 1/221

Let B = 1/221

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

Add the values of A and B

A+B = 1/17 + 1/221

A+B = 13/221 + 1/221

A+B = (13+1)/221

A+B = 14/221

A+B = 0.0633 which is approximate

That converts to 6.33% when you move the decimal point over 2 spots to the right.

We have that  the probability that both are diamonds or both are kings.

P(D+K)=32\%

From the question we are told

Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.

Generally the equation for the  both are diamonds or both are kings  is mathematically given as

[tex]P(D+K)=\frac{d}{52}+ \frac{k}{52}[/tex]

Therefore

[tex]P(D+K)=\frac{13}{52}+ \frac{4}{52}\\\\P(D+K)=0.32[/tex]

P(D+K)=32\%

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Answer:the answer would be 3 ) For every 1 cup of peanut butter, there is 5 cups of cookie dough

Step-by-step explanation:

Answer:

07

Step-by-step explanation:

The coordinate of A is (-5, 9) if M (-1,2) is the midpoint of AB and if B has coordinates of (3,-5).

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

The coordinate of the midpoint of AB is M (-1,2)

The coordinate of B is (3, -5)

Let (x, y) be the coordinate of A.

From the mid-point theorem:

(x + 3)/2 = -1

x + 3 = -2

x = -2 - 3

x = -5

(y - 5)/2 = 2

y - 5 = 4

y = 4 + 5

y = 9

The coordinate of A is (-5, 9) and the coordinate of B is (3, -5)

The mid-point of the line segment AB

The coordinate of M is (-1, 2).

Thus, the coordinate of A is (-5, 9) if M (-1,2) is the midpoint of AB and if B has coordinates of (3,-5).

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Answer:

16, 16, 32, 32

Step-by-step explanation: If you take 92 and divide it by 4 you get 24 but you need one side to be longer than the other, subtract 6 and you get 16, and 16x2 is 32, if you add 16+16+32+32 you get 96.

Answer:

Hello...

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1. One= $25 Two= $40 Three= $55

2. One= $35 Two= $45 Three= $55

Answer:

Well, the club can buy atleast 15 canvases

Step-by-step explanation:

If they have 350 left, Minus 125, = 225

What they can buy, 225 divided by 15 = 15.

Answer:56000

Step-by-step explanation:

Answer:

Number 25

C. I and III.

and 26 is B

Answer:

The slope is 3/1 or 3.

Step-by-step explanation:

The slope equation is y2-y1/x2-x1. Plug the coordinates into the equation and you get -6-3/-1-2 = -9/-3 = 9/3 = 3/1 = 3.

Answer:

D. -1.8c+0.7

Step-by-step explanation:

Combine like terms so

1.9c-3.7c= -1.8c

2.1-1.4=0.7

Answer:

D.0.7 - 1.8c​

Step-by-step explanation:

1. Simplify the Like terms.

(2.1-1.4)+(-3.7c-1.9c)

2. Simplify

0.7-1.8c

Answer:

After 4 months she will have $454.50.

Step-by-step explanation:

4 x $120 = $480

$480 - $25.50 =$454.50

Answer:

$454.50

Step-by-step explanation:

Answer: x>16/3

Step-by-step explanation :0

Answer:

C

Step-by-step explanation:

Any fraction with a denominator of 0 is irrational.

Answer:4

Step-by-step explanation:

Answer:

D = 4.2

Step-by-step explanation:

-5.5 ( d - 2 ) = - 12.1

-5.5d + 11 = - 12.1

11 + 12.1 = 5.5d

23.1 = 5.5d

d = 23.1 ÷ 5.5

d = 4.2

According to the first scale, 2 red balls = 1 star.

According to the second scale, 2 triangles = 1 star

So,

1 triangle = 1 red ball

1 star = 2 red balls

1 red ball = 1 red ball

Therefore, 2 + 1 + 1 = 4 red balls

The last scale needs 4 red balls

Answer:

15

Step-by-step explanation:

Answer:

n=-3

Step-by-step explanation:

so its actually 3n+9=0 so you can subtract 9 to get 3n=-9

                            -9  -9

then divide 3n and -9 by 3 to get n by itself so it looks like n=-3 hope this helps :)

Answer:

You would find it in the 1st quadrant (top-right) on the y axis

Hope this helps

That is a difficult one

Assuming A, B and C are all on the same straight line, this means,

AB+BC = AC

through the segment addition postulate.

So,

AC = AB+BC

AC = (6x+2)+(5x+3)

AC = 6x+2+5x+3

AC = (6x+5x)+(2+3)