Which of the following numbers is the opposite of -
m 100
?
m 100
8
3
| დ |ო ო |
3
8

Answer & step-by-step explanation:

Stationary points are the points where the first derivative is equal to zero.

Let's calculate it using the power rule (exponent comes forward, decrease exponent by 1) and the fact that the derivative is a linear operation (that is [tex]D[a\ f(x) + b\ g(x)] = a Df(x) + b Dg(x)[/tex])

The first derivative is then

[tex]y' = \frac13 (3x^2) - \frac12 (2x) -6 = x^2-x-6 = (x+2)(x-3)[/tex]

Note that the last passage is not strictly needed, but it's really helpful to find stationary points, when in this next passage we set it equal to zero. Alternatively, you can use the quadratic formula if you can pull the factors out of your head right away.

[tex]y'=0 \rightarrow (x+2)(x-3) = 0 \implies x=-2 || x=3[/tex]

These two point could be maxima, minima, or inflection points. To check them you can either see how the sign of the first derivative goes, or check the sign of the second derivative, as you're required.

The rules states that if the second derivative evaluated in that point is negative we have a maximum, if it's positive we have a minimum, and if we have a zero we keep derivating until we get a non-zero  value.

In our case, the second derivative we get by calculating the derivative again and we get [tex]y'' = 2x-1[/tex] . Evaluating it at both points we get

[tex]y''(-2) = 2(-2)-1 = -5\\y''(3) = 2(3) -1 = 5[/tex]

so -2 is a maximum and 3 is a minimum.

Answer:

[tex]\left( 3, -\dfrac{13}{2} \right) \textsf{minimum}[/tex]

[tex]\left( -2, -\dfrac{43}{3} \right)\textsf{maximum}[/tex]

Step-by-step explanation:

To find the stationary points, differentiate, set to zero, and solve for x.  Input found values of x into original equation to find y-coordinates.

[tex]y=\dfrac13x^3-\dfrac12x^2-6x+7[/tex]

[tex]\implies \dfrac{dy}{dx}=3\cdot \dfrac13x^{(3-1)}-2 \cdot \dfrac12x^{(2-1)}-6x^{(1-1)}+7\cdot0[/tex]

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

[tex]\dfrac{dy}{dx}=0[/tex]

[tex]\implies x^2-x-6=0[/tex]

[tex]\implies (x-3)(x+2)=0[/tex]

[tex]\implies x=3, x=-2[/tex]

[tex]\textsf{at }x=3: y=\dfrac13(3)^3-\dfrac12(3)^2-6(3)+7=-\dfrac{13}{2}[/tex]

[tex]\textsf{at }x=-2: y=\dfrac13(-2)^3-\dfrac12(-2)^2-6(-2)+7=\dfrac{43}{3}[/tex]

To determine the nature of each point, differentiate again, input found values of x into the second derivative. If positive then minimum point, if negative then maximum point.

[tex]\dfrac{d^2y}{dx^2}=2 \cdot x^{(2-1)}-x^{(1-1)}-6 \cdot0[/tex]

[tex]\implies \dfrac{d^2y}{dx^2}=2x-1[/tex]

[tex]\textsf{at }x=3:\dfrac{d^2y}{dx^2}=2(3)-1=5 > 0\implies \textsf{minimum}[/tex]

[tex]\textsf{at }x=-2:\dfrac{d^2y}{dx^2}=2(-2)-1=-5 < 0\implies \textsf{maximum}[/tex]

That means that the maximum number of fruit cans is 16 and the maximum number of vegetable cans is 6.

Hope that helps!

The answer is... the max for fruit cans is 16 fruit cans, and for vegetables is 6.

Answer:

"Through" (and any subsequent words) was ignored because we limit queries to 32 words.

Answer:

[tex] - 3 \leqslant x < 2[/tex]

Step-by-step explanation:

the black dot on -3 represents less than equal to X and the white dot on 2 represents X is less than 2

Answer:

The lines intersect at 90°

Step-by-step explanation:

If two lines are perpendicular, they intersect to form right angles.

Right angle = 90°

Line is different from line segment or a ray. The given lines MR and XY are best described by: Option A: The lines intersect at a 90° angle.

To get to know about intersection of MR and XY, we need to know what a line is.

If they are not parallel (having 0 degree angle between each other) and not coincident (not lying over each other), then those two lines always intersect.

Since the considered lines MR and XY are said to be perpendicular (having 90° angle between them, thus, they will intersect each other).

Therefore, the given lines MR and XY are best described by: Option A: The lines intersect at a 90° angle.

Learn more about angle between two lines here:

https://brainly.com/question/24329241

Answer:

$162

Step-by-step explanation:

5r=20 10p=100 14t=42

100+42+20=162

5r+10p+14t=$162

Answer:

[tex]\begin{gathered} \: \end{gathered}[/tex]

[tex]\begin{gathered} \: \end{gathered}[/tex]

Step-by-step explanation:

the whole solution is in the picture

Answer: 57=-10z+7 Answer: z=-- -

Step-by-step explanation: 57=-10z+7 Answer: z=-- -

Answer:

He uses 2 pints.

Step-by-step explanation:

One cup equals 0.5 pints, if he used 4 cups of the cream total, we'd do 0.5 x 4 which gives us 2

Answer:

1.) Approximately 68%We can summarize use of the standard deviation as a yardstick with the Empirical Rule, also known as the 68-95-99.7% Rule. In any normal distribution with mean μ and standard deviation σ : Approximately 68%of the data fall within one standard deviation of the mean.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

p(A) = (number of A's on the spinner)/(total number of letters on the spinner)

p(A) = 2/6 = 1/3

Answer:

about 4,400 times

Step-by-step explanation:

its simple

Answer:

3w-4.5

Step-by-step explanation:

im pretty sure this is right. good luck

Answer:

1. 0.69

2. 1.16

Step-by-step explanation:

1.

Decrease of 31% = 100% - 31% = 69%

Convert 69% to a decimal = 69/100 = 0.69

2.

Increase of 16% = 100% + 16% = 116%

Convert 116% to a decimal = 116/100 = 1.16

Answer:

it's going to be 30 and 18

The possible measurements for arc AD and arc BC are 130° and 34° respectively.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given is a circle.

We have the outside angle formed by the two secants is ∠AED and the measure for it is 48°.

Outside Angle Theorem states that " the measure of an angle which is formed by joining two tangents, or two secants, or one of either of them is equal to the measure of half of the difference of the intercepted arcs.

Here outside angle, ∠AED = 48°

Intercepted arcs are AD and BC.

Using the theorem,

∠AED = (Arc AD - Arc BC) / 2

This holds only if AD = 130° and BC = 34°.

(130 - 34) / 2 = 48

Hence the correct option is D. 130° and 34°.

Learn more about Circle Arcs here :

https://brainly.com/question/3384740

#SPJ3

Answer:

i think the answer would be 4c + 6m = 100, 8c + 12m = 200

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expression => | -2 |

Equation => 6 - 1 = 2 + 3

Inequality => 8^m > 64

Answers:

Expression is [tex]|-2|[/tex]

Equation is [tex]6-1 = 2+3[/tex]

Inequality is [tex]8^m > 64[/tex]

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

Explanation:

If it has an equal sign, then it's an equation.

If it has an inequality sign of one of the following [tex]< , \ > , \ \le, \ \ge[/tex], then it's an inequality.

Otherwise, it's an expression.

Answer: 8:14

Step-by-step explanation:

Your answer would be 8:14, as Steven answered 8 questions incorrectly along with the total number of problems being 14 when you add his correct answers with his incorrect ones: "6+8"

Answer: x=5

Step-by-step explanation:

divide both sides by the numeric factor on the left side, then that will give the answer for x

Answer: WE have to find if x + 3 is a factor

Here's how we do it :

x + 3 = 0

x = -3

Plug that in :

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

81 - 54 + 6 - 6

27

So, when we divide, we get a remainder of 27. This is not zero.

So, since f(a) was not zero, (x - a) is not a factor

P(-3) = 27 ---> ANSWER

Thus here (x + 3) is NOT a factor ---> ANSWER

Answer:

x^222/7

Step-by-step explanation:

Equation at the end of step 3:                x74

 ((78 • x73) • ———) • x75

               79

STEP 4 :Multiplying exponential expressions : 4.1    x147 multiplied by x75 = x(147 + 75) = x222

Answer:

1.57

Step-by-step explanation:

2000/8=250      250/160.67= 1.56

Answer:

Step-by-step explanation:

To find the lengths, we use the Pythagorean theorem, which states (a^2)+(b^2)=(c^2) where c^2 is the hypotenuse, length opposite of the right angle. For the first set of coordinates J and K, we find the horizontal and vertical differences between them to represent sides a and b. Which would be a horizontal length of 8 and a vertical length of 3.

(8^2)+(3^2)=c^2

73=c^2

c=square root of 73

(I've added a picture of a graph I drew below)

I would suggest you draw graphs of the points and use the Pythagorean theorem to conceptualize it, but I'll list the rest of the measurements below.

MN:

Vertical length between 2 and -3 = 5

Horizontal length between 7 and 1 = 6

(6^2)+(5^2)=c^2

36+25=c^2

61=c^2

c= square root of 61

PQ:

Vertical length between -6 and -2 = 4

Horizontal length between -8 and -3 = 5

(5^2)+(4^2)=c^2

25+16=c^2

41=c^2

c= square root of 41

As for the "checking all the statements" part, none of them are true because none of the lengths are equal.

Hope this helps! (Sorry for being so late)

Answer:

4/3

Step-by-step explanation:

reduce the fraction by a factor of 6

pretty sure you mean write 24/18 in simplest form so that's the answer

Hope this helps! :)

Answer:

The width would be 8.

Hope this helps!! PLEASEEE give Brainlist!!

Solution:

Given:

Substitute the values into the equation:

Simplify the numerator and the denominator:

Simplify the fraction:

Correct option is B.

Answer:

[tex][-\frac{1023}{4} ][/tex]

Step-by-step explanation:

[tex]\frac{x^6-x}{4y}[/tex]

x = -4

y = 4

Replace all the variables with the corresponding values given:

[tex]\frac{-4^6-(-4)}{4(4)}[/tex]

Now solve,

-4 to the power of 6 is equal to -4096

[tex]\frac{-4096-(-4)}{4(4)}[/tex]

we see that we are subtracting a negative number, meaning that it'll cancel out and turn into an addition sign. Therefore:

[tex]-4096 + 4[/tex]

[tex]-4092[/tex]

[tex]\frac{-4092}{4(4)}[/tex]

4(4) is equal to 16

[tex]\frac{-4092}{16}[/tex]

When divided, you'll get a mixed fraction of [tex]-255\frac{3}{4}[/tex]

To turn into an improper fraction, simply multiply the whole number by the denominator, then add the numerator to the result.

[tex]-255 * 4 + 3[/tex]

[tex][-\frac{1023}{4} ][/tex]