Can somebody give me the answer to this?

The derivative and domain of the function f(x) = x²-2x³  is :\((-\infty, \infty)\).

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

\(\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}\)

       \(\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}\)

       \(=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}\)

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      \(\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}\)

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :\((-\infty, \infty)\).

′To know more about differentiation, here

https://brainly.com/question/954654

#SPJ4

The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

Answer:

Step-by-step explanation:

First, you need to find the GCF of both denominators.

That would be 21.

You would need to multiple the 7 in 4/7 by 3, to get to 21. That means you would also have to multiply 3 by the 4. You should get 12/21.

Do you same thing to 1/3.

After that you should get the 2 factions, 12/21 and 7/21

12/21 + 7/21 = 19/21

There isn't anyway to simplify it, meaning the final answer is 19/21.

Answer:

A can with capacity 44 litres

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

The blanks representing the numerator and the denominator are filled as follows

numerator  : 2d

denominator:  t²

The equation given in the problem is

d = 1/2 * a * t²

To make a the subject of the formula we take the following steps

multiply each side by 2

2 * d = a * t²

divide both sides by t²

2 * d / t² = a

rearranging

a = 2 * d / t²

Learn more about fractions at

https://brainly.com/question/78672

#SPJ1

Answer:

B

Step-by-step explanation:

(3,0)

The first coordinate is x, so go over 3

The second coordinate is y so go up 0

Answer:

lts answer is B

Step-by-step explanation:

3 is x-axis and o is y -axis

Answer:

c=12.5

Step-by-step explanation:

Multiply both sides by 2 to get rid of the fraction.

You are left with 2c-9=16

Add 9 To both sides

You are left with 2c=25

Divide both sides by 2 to get C by itself

You are left with c=25/2

Simplify

c=12.5

Answer:

740

Step-by-step explanation:

42% of 1761 = 0.42 * 1761 = 739.62

Answer: 740

a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

Learn more about Angle

brainly.com/question/28451077

#SPJ11

Answer:

What is the question? How many hours does she need to babysit??

18 hours

Step-by-step explanation:

There wasn't a question so um yeah...

The number of days between May 20 and November 22 is 182 days. Option C, 183 is the closest answer to the correct answer.

To determine the number of days between May 20 and November 22, we first need to determine the number of days in each month. Here are the days in each month of the year: January: 31 days, February: 28 days (or 29 in a leap year)March: 31 days, April: 30 days, May: 31 days, June: 30 days, July: 31 days, August: 31 days, September: 30 days, October: 31 days, November: 30 days, December: 31 days. Using the formula D = (M2 - M1) × 30 + (D2 - D1) where D is the number of days, M is the month, and D is the date, we can calculate the number of days between May 20 and November 22:D = (11 - 5) × 30 + (22 - 20)D = 6 × 30 + 2D = 180 + 2D = 182.

Let's learn more about month:

https://brainly.com/question/20927686

#SPJ11

Primitivity refers to the fundamental property of an operation or function in mathematics, where the operation or function cannot be expressed in terms of simpler operations. Associativity, on the other hand, describes the property of an operation where the grouping of elements does not affect the result.

In simple terms, primitivity means that a particular operation cannot be broken down into smaller, more basic operations. For example, addition is considered a primitive operation because it cannot be expressed in terms of simpler operations. On the other hand, multiplication is not primitive since it can be expressed as repeated addition.

Associativity, on the other hand, refers to the fact that when we have three or more elements operated together, the result is the same regardless of how we group them. For example, addition is associative because (a + b) + c is equal to a + (b + c). However, subtraction is not associative since (a - b) - c is not equal to a - (b - c).

In summary, primitivity refers to the irreducibility of an operation, while associativity determines whether the grouping of elements affects the result of the operation.

Learn more about: fundamental property

brainly.com/question/28190339

#SPJ11

Answer:

x = \(\frac{11}{c}\)

Step-by-step explanation:

Given

cx - 4 = 7 ( add 4 to both sides )

cx = 11 ( isolate x by dividing both sides by c )

x = \(\frac{11}{c}\)

If functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

A relation is a function if it has only One y-value for each x-value.

The given two functions are f(x) = 2x² + 4x - 5

and g(x) = - 6x³+2x² - 3

We need to find  (f + g)(x).

(f + g)(x)=f(x)+g(x)

=2x² + 4x - 5 - 6x³+ 2x² -3

Now add the like terms

= 6x³+ 4x² +4x-8

(f + g)(x)=6x³+ 4x² +4x-8

Hence, if functions f(x) = 2x² + 4x - 5, g(x) = - 6x³+2x² - 3 then (f + g)(x)=6x³+ 4x² +4x-8

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1

Answer:

x = 5°

Step-by-step explanation:

Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.  The sum of the exterior angles of a polygon is 360°.

Sum of exterior angles:

⇒ 45° + 90° + 25° + 90° + x° + (180° - 140°) + (180° - 115°) = 360°

⇒ 355° + x° = 360°

⇒ x = 5°

Answer:

Deductible

Step-by-step explanation:

you pay the first $1,000 of covered services yourself

$1000 represents the deductible amount.

In the case of an accident, the policyholder must pay a deductible as the first amount; the insurance company will only cover any expenses (losses) incurred after the deductible has been paid by the policyholder.

The consumer can first set his deductible while purchasing insurance.

Smaller deductibles often result in higher rates, and larger deductibles frequently result in lower premium payments.

The insurance company has asked Manny to pay the first $1000 in an instance when he was involved in an accident and incurred charges totaling $11,500. The $1,000 deductible amount.

Hence, the answer is deductible amount.

Learn more about deductible amount here:

https://brainly.com/question/30098276

#SPJ6

Sameer walked for double the time of Rex.

We are told that Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. We need to find the comparison how much times Samir walked than Rex.

We are given the times in mixed fractions. We will first convert them to simple fractions. The time for which Rex walked is 5/3 hours. The time for which Sameer walked is 10/3 hours. We can see that Sameer walked for double the time of Rex.

Hence, Sameer walked for double the time of Rex.

To learn more about fractions, visit :

https://brainly.com/question/10354322

#SPJ1

The line of best fit represents the trend or average relationship between the average study time and quiz grade. It provides an approximation of the expected quiz grade based on the average study time.

To obtain the line of best fit on a scatter plot, you would typically use a method called linear regression. Linear regression aims to find the best-fitting line that minimizes the overall distance between the line and the data points.

Here's a general overview of the steps involved in obtaining the line of best fit:

Plot the scatter plot with average study time on the x-axis and quiz grade on the y-axis.

Visually observe the distribution of the data points. Look for any overall trend or pattern.

Determine the type of relationship between the variables. In this case, we are looking for a linear relationship.

Use a statistical software or calculator that supports linear regression to perform the analysis. This will generate the equation of the line that best fits the data.

The line of best fit is determined by its slope (m) and y-intercept (b), represented by the equation y = mx + b.

For such more questions on Average relationship:

https://brainly.com/question/31098693

#SPJ11

Given:

Length of a rectangular monitor screen is 5 in more than it's width.

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

To find:

The length and width of the screen.

Solution:

Let width of the screen be x inches.

Length of a rectangular monitor screen is 5 in more than it's width. So,

Length of screen = (x+5) inches

Area of screen is

\(Area=length\times width\)

\(A_1=(x+5)\times x\)

\(A_1=x^2+5x\text{ in}^2\)

If the length were doubled and if the width were deceased by 1 in the area would be increased by 170 in².

New length = 2(x+5) inches

New width = (x-1) inches

So, new area is

\(A_2=2(x+5)(x-1)\)

\(A_2=(2x+10)(x-1)\)

\(A_2=2x^2+10x-2x-10\)

\(A_2=2x^2+8x-10 \text{ in}^2\)

Area increased by  170 in².

\(A_2-A_1=170\)

\((2x^2+8x-10)-(x^2+5x)=170\)

\(2x^2+8x-10-x^2-5x=170\)

\(x^2+3x-10=170\)

Subtract 170 from both sides.

\(x^2+3x-10-170=0\)

\(x^2+3x-180=0\)

Splitting the middle term, we get

\(x^2+15x-12x-180=0\)

\(x(x+15)-12(x+15)=0\)

\((x+15)(x-12)=0\)

\(x=-15,12\)

Width cannot be negative. So, x=12.

Width = 12 inches

Length = 12+5 = 17 inches

Therefore, the length of screen is 17 inches and width is 12 inches.

Answer:

The answer is graph D since y int = 3(1)+4 which is 7, that graph crosses y at 7

Answer:

r=9

Step-by-step explanation:

13r=117

r=117/13

r=9

Answer:

2+5*3=17

Step-by-step explanation:

The blanks should be filled in with a plus (+) and a times sign (*), respectively. To solve this question you must understand PEMDAS. This stands for paratheses, exponents, multiplication, division, addition, subtraction. When solving an equation, operations should be done in this order. Therefore, numbers should be multiplied before they are added.

So, to solve this equation multiply 5*3; this equals 15. Then add 2, which equals 17. And 17=17, so the equation must be true.

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

\(f(x) = 2(x^{2} -2x+\frac{1}{2})\)  

Step 2: Use the complete square method.

\(f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )\)  

Step 3: Have it to \(a(x+b)^{2} +c\)

\(f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1\)

Line of symmetry:  

To find line of symmetry, we use -b/2a formula.

Based from \(2x^{2} -4x+1\):

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

If the probability that a household owns a pet is 0.55 then the probability that all households will have pets is equal to 0.0503.

Given that the probability that a household owns a pet is 0.55 and there are 5 houses on a block.

We are required to calculate the probability that all the five households will have pets.

Probability is basicallly the chance of happening an event among all the events possible. It cannot be negative.

Binomial probability distribution is basically the probability calculations but in different combinations.

In this we have to calculate the probability that all the houses will have the pets then the probability that all five households will have pets is equal to \(5C_{5}(0.55)^{5} (1-0.55)^{0}\)

=1(0.0503)\((0.45)^{0}\)

=1*0.0503*1

=0.0503

Hence the probability that all the five households will have pets is equal to 0.0503.

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

Answer:

4

Step-by-step explanation:

Answer:

1/4 is the answer

Step-by-step explanation:

just look at it show you that it is 1/4

Answer:

x+65≤84

Step-by-step explanation:

Inequality that represents the number 'x' of additional people who can enter the restaurant​ is -

x + 65 ≤ 84

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given is a restaurant which has 65 people in it. The restaurant has a maximum capacity of 84 people.

Assume that 'x' more people can enter inside the restaurant. Then -

the inequality can be written as follows -

x + 65 ≤ 84

65 people were already inside. 'x' more people can enter it such that the total number of people inside is either less or greater than 84.

Therefore, inequality that represents the number 'x' of additional people who can enter the restaurant​ is -

x + 65 ≤ 84

To solve more questions on inequality, visit the link below-

https://brainly.com/question/21857626

#SPJ5

For the function f(x) = (-1 - x) / (x² - x - 6), the domain is all real numbers except x = 3 and x = -2.

For the function f(x) = √(1/2 - 3x), the domain is all real numbers x such that x is less than or equal to 1/6.

a) To find the domain of the function f(x) = (-1 - x) / (x² - x - 6), we need to consider the values of x for which the function is defined. The function is defined for all values of x except those that make the denominator equal to zero, as division by zero is undefined.

The denominator of the function is x² - x - 6. To find the values of x that make the denominator zero, we can factorize it:

x² - x - 6 = (x - 3)(x + 2)

Setting the factors equal to zero, we have:

x - 3 = 0   -->   x = 3

x + 2 = 0   -->   x = -2

Therefore, the function is undefined at x = 3 and x = -2, as they would result in division by zero.

The domain of f(x) is all real numbers except x = 3 and x = -2.

b) To find the domain of the function f(x) = √(1/2 - 3x), we need to consider the values of x that make the expression inside the square root non-negative. This is because the square root of a negative number is not defined in the real number system.

The expression inside the square root is 1/2 - 3x. To ensure it is non-negative, we set it greater than or equal to zero:

1/2 - 3x ≥ 0

Solving this inequality, we have:

1/2 ≥ 3x

x ≤ 1/6

Therefore, the domain of f(x) is all real numbers x such that x is less than or equal to 1/6.

To learn more about domain of the function click here: brainly.com/question/13109733

#SPJ11

The answer is to find the critical value for constructing the standard deviation  80% confidence interval for the population mean magnesium concentration.


To find the critical value for the 80% confidence interval, we need to use the z-distribution since the sample size is greater than 30 and the population standard deviation is unknown.

The formula for finding the critical value is:
Critical value = z(alpha/2) * (standard deviation / sqrt(sample size))
Where alpha is the level of significance (1 - confidence level), z(alpha/2) is the z-score at alpha/2 level of the standard normal distribution, standard deviation is the sample standard deviation, and sample size is the number of samples.
Using a z-table or calculator, we can find that the z-score at the 40th percentile (80% confidence level) is 1.282.
Plugging in the values, we get:
Critical value = 1.282 * (0.0418 / sqrt(17)) ≈ 0.022
Therefore, the critical value for constructing the 80% confidence interval is approximately 0.022 (rounded to three decimal places).

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ11

Where the above conditions exist,

The random variable T = L + C represents the total time it takes Lorelei and Chance to finish a randomly selected 3-layer wedding cake. Since L and C are independent and Normally distributed, T is also Normally distributed with mean:

Mu_T = Mu_L + Mu_C = 37 + 52 = 89

and variance:

Var(T) = Var(L) + Var(C) = 12^2 + 7^2 = 193

So the standard deviation of T is:

Sigma_T = sqrt(Var(T)) = sqrt(193) = 13.89

The shape of T is also Normally distributed, since it is a sum of two independent Normally distributed variables.

To find the probability that Lorelei and Chance finish a randomly selected 3-layer wedding cake in under 90 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table. The z-score is:

z = (90 - 89) / 13.89

= 0.072

From the z-table, we find that the probability of a Z-score less than or equal to 0.072 is 0.5287.

Therefore, the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287 or approximately 53%.

Learn more about probability  at:

https://brainly.com/question/30034780

#SPJ1

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

Learn more about dataset here:

https://brainly.com/question/26468794

#SPJ11