Find the absolute extrema of the function on the closed interval. g(x)=x−29x2​,[−2,1]  minimum  minimum  maximum (x,y)=(​(x,y)=((x,y)=( smaller x-value ))( larger x-value )​

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

3) y = 1/3x - 1

4) y = 2/5x + 0 or just y = 2/5x

5) y = -1x +4

Step-by-step explanation:

because i aint never seen two pretty best friends, its always one of em gotta be ugly

Answer:

the thing i cant see it

Step-by-step explanation:

Answer:

Julie will reach her goal first. i dont know how to explain it but you could probably figure that out

To evaluate c ∇f · dr, we need to first find the gradient vector ∇f and the differential vector dr.

Since the function f is not given, we cannot find ∇f explicitly. However, we know that ∇f points in the direction of greatest increase of f, and that its magnitude is the rate of change of f in that direction. Therefore, we can make an educated guess about the form of ∇f based on the information given.

The function f could be any function, but let's assume that it is a function of two variables x and y. Then, we have:

∇f = (∂f/∂x, ∂f/∂y)

where ∂f/∂x is the partial derivative of f with respect to x, and ∂f/∂y is the partial derivative of f with respect to y.

Now, let's find the differential vector dr. The parameterization of c is given by:

x = t^2 + 1

y = t^3 + t

0 ≤ t ≤ 1

Taking the differentials of x and y, we get:

dx = 2t dt

dy = 3t^2 + 1 dt

Therefore, the differential vector dr is given by:

dr = (dx, dy) = (2t dt, 3t^2 + 1 dt)

Now, we can evaluate c ∇f · dr as follows:

c ∇f · dr = (c1 ∂f/∂x + c2 ∂f/∂y) (dx/dt, dy/dt)

where c1 and c2 are the coefficients of x and y in the parameterization of c, respectively. In this case, we have:

c1 = 2t

c2 = 3t^2 + 1

Substituting these values, we get:

c ∇f · dr = (2t ∂f/∂x + (3t^2 + 1) ∂f/∂y) (2t dt, 3t^2 + 1 dt)

Now, we need to make an educated guess about the form of f based on the information given. We know that f is a function of x and y, and we could assume that it is a polynomial of some degree. Let's assume that:

f(x, y) = ax^2 + by^3 + cxy + d

where a, b, c, and d are constants to be determined. Then, we have:

∂f/∂x = 2ax + cy

∂f/∂y = 3by^2 + cx

Substituting these values, we get:

c ∇f · dr = [(4at^3 + c(3t^2 + 1)t) dt] + [(9bt^4 + c(2t)(t^3 + t)) dt]

Integrating with respect to t from 0 to 1, we get:

c ∇f · dr = [(4a/4 + c/2) - (a/2)] + [(9b/5 + c/2) - (9b/5)]

Simplifying, we get:

c ∇f · dr = -a/2 + 2c/5

Therefore, the value of c ∇f · dr depends on the constants a and c, which we cannot determine without more information about the function f.

The value of c where c has parametric equations x = t2 + 1, y = t3 + t, 0 t 1. is  c ∇f · dr=  [(2t^5 + 2t^3)(∂f/∂x) + (9t^7 + 3t^5)(∂f/∂y)] dt.

We have the following information:

c(t) = (t^2 + 1)i + (t^3 + t)j, 0 ≤ t ≤ 1

f(x, y) is a scalar function of two variables

We need to find c ∇f · dr.

We start by finding the gradient of f:

∇f = (∂f/∂x)i + (∂f/∂y)j

Then, we evaluate ∇f at the point (x, y) = (t^2 + 1, t^3 + t):

∇f(x, y) = (∂f/∂x)(t^2 + 1)i + (∂f/∂y)(t^3 + t)j

Next, we need to find the differential vector dr = dx i + dy j:

dx = dx/dt dt = 2t dt

dy = dy/dt dt = (3t^2 + 1) dt

dr = (2t)i + (3t^2 + 1)j dt

Now, we can evaluate c ∇f · dr:

c ∇f · dr = [c(t^2 + 1)i + c(t^3 + t)j] · [(∂f/∂x)(2t)i + (∂f/∂y)(3t^2 + 1)j] dt

= [c(t^2 + 1)(∂f/∂x)(2t) + c(t^3 + t)(∂f/∂y)(3t^2 + 1)] dt

= [(t^2 + 1)(2t^3 + 2t)(∂f/∂x) + (t^3 + t)(9t^4 + 3t^2)(∂f/∂y)] dt

Therefore, c ∇f · dr = [(2t^5 + 2t^3)(∂f/∂x) + (9t^7 + 3t^5)(∂f/∂y)] dt.

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(a) The average rate of change from −8 to 4 is 306 and (b) An equation of the secant line containing (−8,g(−8)) and (4,g(4)) is y=27x+170.

(a)Average rate of change from -8 to 4

= [g(4)-g(-8)]/(4+8)

= (306)/(12)= 25.5

(b) Slope of the secant line containing

(-8,g(-8)) and (4,g(4))

= [g(4)-g(-8)]/(4+8)

= (306)/(12)= 25.5

Therefore, the equation of the secant line containing (-8,g(-8)) and (4,g(4)) is:

y-(-1) = 25.5(x-(-8))y= 25.5x +170

Thus, the equation of the secant line containing (-8,g(-8)) and (4,g(4)) is y= 27x+170.

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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The probability distribution used to model a random variable x that equals the number of events that occur within an interval or area of opportunity is the Poisson distribution. This is used to model a random variable representing the number of events occurring within a fixed interval or area of opportunity, given an average rate of occurrence.

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space, given the average rate at which events occur and the assumption that the events are independent of each other. It is commonly used in fields such as biology, physics, and engineering to model occurrences of rare events such as accidents, defects, or rare diseases.

The Poisson distribution has a single parameter λ, which represents the average rate of events occurring in the interval or area of opportunity. The probability of observing exactly k events in this interval is given by the Poisson probability mass function:

P(X=k) = (e^-λ * λ^k) / k!

where X is the random variable representing the number of events, e is the mathematical constant approximately equal to 2.71828, and k! is the factorial of k.

The Poisson distribution is similar to the binomial distribution but is used when the number of trials is very large and the probability of success is very small. In this case, the binomial distribution becomes impractical to use, and the Poisson distribution is a more appropriate model.

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Answer:

298.15

Step-by-step explanation:

Answer:

9/20

Step-by-step explanation:

Step-by-step explanation:

it is either 9/20 if it's just 0.45

or if you want 0.45 recurring then it 5/11

Answer:

there is no problem

Step-by-step explanation:

The slope of each pair point is listed below:

Case A: m = - 4

Case B: m = 6 / 7

Case C: m = - 3

Case D: m = 4

Case E: m = - 5 / 2

In this problem we find five cases of two points that are part of a line, whose slope (m) can be calculated by means of secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Now we determine the slope for each case:

Case A:

m = (10 - 2) / (7 - 9)

m = 8 / (- 2)

m = - 4

Case B:

m = [- 5 - (- 11)] / [- 1 - (- 8)]

m = 6 / 7

Case C:

m = [3 - (- 6)] / (2 - 5)

m = 9 / (- 3)

m = - 3

Case D:

m = (- 1 - 3) / (5 - 6)

m = - 4 / (- 1)

m = 4

Case E:

m = (2 - 7) / (6 - 4)

m = - 5 / 2

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Given function in the question is,

\(f(x)=2-5x-x^2\)

To find the difference coefficient for the given function, we use the expression as \(\frac{f(3+h)-f(3)}{h}\).

\(f(3+h)=2-5(3+h)-(3+h)^2\)

             \(=2-15-5h-(9+h^2+6h)\)

             \(=(2-15-9)-(5h+6h)-h^2\)

             \(=-22-11h-h^2\)

             \(=-(22+11h+h^2)\)

\(f(3)=2-5(3)-(3^2)\)

       \(=2-15-9\)

       \(=-22\)

Now substitute these values in the expression for the difference coefficient,

\(\frac{f(3+h)-f(3)}{h}=\frac{-(22+11h+h^2)-(-22)}{h}\)

                 \(=\frac{-22-11h-h^2+22}{h}\)

                 \(=\frac{-11h-h^2}{h}\)  

                 \(=-(11+h)\)

     Therefore, Value of the difference quotient for the given function is\(-(11+h)\).

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There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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Answer:

I attached it.

Step-by-step explanation:

This is the graph.

Answer:

Step-by-step explanation:

a.

\(AC=\sqrt{AB^2-BC^2} =\sqrt{13^2-5^2} =\sqrt{169-25} =\sqrt{144} =12\\\)

applying sine formula

AB=c

AC=b

BC=a

\(\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C} \\\\\frac{5}{sin A} =\frac{12}{sin B} =\frac{13}{sin 90} \\using~last~two\\\frac{12}{sin B}= \frac{13}{1} \\sin B=\frac{12}{13}\\ B=sin^{-1}(\frac{12}{13}) \approx 67.38 ^\circ\)

b.

third angle ∠Y=180-(30+90)=180-120=60

using sine formula

\(\frac{xz}{sin Y} =\frac{xy}{sin Z} = \frac{yz}{sin X} \\\frac{30}{sin 60} =\frac{xy}{sin 90} =\frac{h}{sin 30} \\using ~first~and~last\\\frac{30}{\frac{\sqrt{3} }{2} } =\frac{h}{\frac{1}{2} } \\2h=\frac{60}{\sqrt{3} } \\h=\frac{30}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } =10\sqrt{3}\)

Answer:

120

Step-by-step explanation:

the volume of the box( which is a rectangle ) is: V =(l)(w)(h), which means length x width x height, which is also 6x5x4, which equals to 120

In  Arithmetic Progression , 56 inches of snowfall will cause the snowplow to be immobile.

What is Arithmetic Progression in math?

Let x inches of snowfall will cause the showplow to be immobile .

By a.p. formula ,

                aₙ = a + ( n - 1) d

                 aₙ= 0 ( show plow's speed is 0 ,miles/hour )

              a = 39

              n = x inches

             d = - 2.5 mile/hour

         0 = 39 + ( n - 1 ) ( -2.5)

            ( n - 1 ) ( -2.5) = -39

              n- 1 = -39/2.5 = 15.6

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Answer:yes it is a triangle

Step-by-step explanation:

let's assume this triangle's sides are a,b and c.

we know this equation: \(a+b > c > |a-b|\\c+b > a > |c-b|\\a+c > b > |a-c|\\a=6\\b=7\\c=9\\13 > 9 > 1--- > which is true\\16 > 6 > 2----- > which is true as well\\15 > 7 > 3------ > it is true,too\\all of this equations are true so, this is a triangle\)

I'm sorry, but as a text-based AI model, I don't have the ability to analyze or visualize graphs directly. If you can provide a textual description or specific details about the graph, I would be happy to help you analyze and extract information from it.

Answer:

ab+ac=a(b+c)

where a is the greatest common factor

find gcf of each

factor each

18=2*3*3

12=2*2*3

GCF=2*3=6

so

18+12=6(3)+6(2)=6(3+2)

Step-by-step explanation:

Answer:

-4

Beni beyinsiz yap lütfen

Step-by-step explanation:

Answer:

D. 19.6in

Step-by-step explanation:

ΔAFC is similar o ΔA'FC'. Therefore, their sides are in ration to one another:

FA/F'A'=AC/A'C'

9/(9+12)=8.4/A'C'

9/21=8.4/A'C'

3/7=8.4/A'C'

A'C'=8.4/(3/7)=19.6

Answer:

D. 19.6in have a good rest of yo life :)

Answer:

If I understood what you mean properly... 0

Step-by-step explanation:

(a) The product of 39 and -45 using the Booth multiply algorithm is -56.

(b) The product of -53 and -43 using the Booth multiply algorithm is -17.

(a) To compute the product of 39 and -45 using the Booth multiply algorithm, follow these steps:

1. Convert the numbers to binary representation:

  - 39: 00100111

  - -45: 11010011 (2's complement representation)

2. Set up the algorithm with the following initial values:

  - A = 00100111 (39 in binary)

  - Q = 11010011 (-45 in binary, 2's complement representation)

  - Q(-1) = 0 (initial value)

  - M = 11010011 (-45 in binary, 2's complement representation)

3. Perform the Booth multiply algorithm steps:

  Iteration 0:

  - Check the least significant bit (LSB) of Q and Q(-1). Since Q0 = 1 and Q(-1) = 0, perform subtraction.

  - A = A - M = 00100111 - 11010011 = -1010110

  - Q0 = Q(-1) = 1

  Iteration 1:

  - Shift A and Q right by 1 bit:

    - A = 11101011 (arithmetically shifted right)

    - Q = 11101001 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 1 and Q(-1) = 1, perform addition.

  - A = A + M = 11101011 + 11010011 = 101001010

  - Q0 = Q(-1) = 1

  Iteration 2:

  - Shift A and Q right by 1 bit:

    - A = 11010101 (arithmetically shifted right)

    - Q = 11110100 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 0 and Q(-1) = 1, perform addition.

  - A = A + M = 11010101 + 11010011 = 101100000

  - Q0 = Q(-1) = 0

  Iteration 3:

  - Shift A and Q right by 1 bit:

    - A = 11101000 (arithmetically shifted right)

    - Q = 11111010 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 0 and Q(-1) = 0, no operation is required.

4. The final result is obtained by combining the value of A and Q:

  - A = 11101000 (in binary, which is -56 in decimal)

  - Q = 11111010 (in binary, which is -42 in decimal)

Therefore, the product of 39 and -45 is -56.

(b) To compute the product of -53 and -43 using the Booth multiply algorithm, follow the same steps as in part (a) with the respective binary representations of the numbers and perform the necessary calculations.

The product of -53 and -43 is -17.

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Answer:

Q 1 is option B and q 2 is option D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of the digit "3" in "156.32" is 3/10 (3 tenths). 10 times that value would be 3 (3/10 * 10 = 3). So now we need a number that has the digit "3" in it and the value of that digit is "3".

How about 143.26? The digit "3" is in the ones place and so its value is 3*1 or 3. The rest of the number is just made up, nothing special about any of the other numbers.

The value of digit 3 in 156.32 is 3/10 (3 tenths).

10 times that value would be 3 (3/10 * 10 = 3).

The face value of a digit is the magnitude that it possesses naturally. It is independent of the digit's position in the number.

The place value of a digit depends on its position in the number.

So now we need a number that has the digit 3 in it and the value of that digit is 3.

How about 143.26. The digit 3 is in the one place and so its value is 3*1 or 3.

The rest of the number is just made up, nothing special about any of the other numbers.

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Answer:

4 1/2 percent inch at the other side

Answer : y = - 8

3/4y+6=0

Step 1: Subtract 6 from both sides :

3/4y + 6 - 6 = 0 - 6

3/4y = -6

Step 2: Multiply both sides by 4/3 :

( 4/3 ) × ( 3/4y ) = ( 4/3 ) × ( -6 )

Final answer is y = - 8

Answer:

x = 110; y=65

Step-by-step explanation:

X = 110 because A||B

in the small triangle we have 45° , y° and n° ( n is the missing angle )

n + x = 180

n = 180 -110

n = 70

triangle :

70 + 45 + y = 180°

115 + y =180

y = 180 - 115

y = 65°