Find the derivative of f(x) = (1 + 6x2)(x − x2) in two ways.

Answers

Answer 1

Using product rule;

f(x)=(1+6x²)(x-x²)

f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1

Solving the bracket first;

f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4

f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1

Related Questions

GUYS HELP PLEASE URGENT!!!!!!

A newborn baby weighs 3.136x10^3 units. Which unit of measure was used? grams ounces pounds tons

Answers

its grams because it cant be pounds because a baby isnt 3000 pounds, thats is just crazy!

The unit 'gram' will used to measure the weight of newborn baby in this case.

Unit conversion:

Conversion of units is the conversion between different units of measurements for the same quantity.

1 pound = 0.454kilogram1 kg = 1000 g1 ton = 1000 kg1 ounce = 0.0283 kg

According to the given question we have,

Weight of the new born baby = [tex]3.136[/tex] × [tex]10^{3}[/tex] = 3136

From the unit conversion,

3136 pound = 1,423.744kg

3136 gram = 3136/1000 = 3.136gram

3136 ton = 3136000 kg

3136 ounce =88.7488 kg

The range of weight of new born baby in kg is 3 to 4.

Hence, only 3136 gram is possible .So, the unit 'gram' will used to measure the weight of newborn baby in this case.

Learn more about the unit conversion here:

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An __________ is used to indicate the repeating part of a repeating decimal.

Answers

line above the repeating number

Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?
A.130
B.109.16
C.109.76
D.71.35
E.60

Answers

Newton's Law of cooling is a differential equation that is simplified by using limits in temperature and time. The simplified equation is:

ln(T-Ts) = ln(T0-Ts) - kt

where
T is the final temperature
T0 is the initial temperature
Ts is the temperature of the surroundings
t is the time
k is a constant

Substituting the values:
ln(T-70) = ln(200-70) - (0.6)(2)
T = 109.16°F

The answer is B.

Use the form of the definition of the integral given in theorem 4 to evaluate the integral x^3-3x^2

Answers

[tex]\int{(x^{3} - 3x^{2})}\,dx[/tex]
[tex]= \int{x^{3}}\,dx - \int{3x^{2}}\,dx[/tex]
[tex]= \frac{1}{4}x^{4} - \frac{3}{3}x^{3} + C[/tex]
[tex]= \frac{1}{4}x^{4} - x^{3} + C[/tex]

A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?

Answers

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height\\ ----------\\ h=12\\ V=236 \end{cases}\implies 236=\cfrac{1}{3}B(12) \\\\\\ 3\cdot 236=12B\implies \cfrac{708}{12}=B\implies 59=B[/tex]

now, is a square pyramid, like the picture below, so the base is just a square, so B = length * width, thus

[tex]\bf B=length\cdot width\quad \begin{cases} length=x\\ width=x\\ B=59 \end{cases}\implies B=x\cdot x\implies B=x^2 \\\\\\ 59=x^2\implies \sqrt{59}=x[/tex]

what is the x-intercept of the graph of the function f(x)=x2-16x+64?

Answers

Answer:

x-intercept: (8,0)

Step-by-step explanation:

Given: [tex]f(x)=x^2-16x+64[/tex]

For x-intercept, Put y=0 and solve for x.

x-intercept: It is a point where y-coordinate zero.

[tex]x^2-16x+64=0[/tex]

[tex]x^2-8x-8x+64=0[/tex]

[tex](x-8)(x-8)=0[/tex]

Equate each factor to 0 and solve for x

x-8 = 0 , x-8 = 0

x=8,8

x-intercept: (8,0)

Hence, The x-intercept is 8.

The x-intercept of the function is 8

The equation of the function is given as:

[tex]f(x) = x^2 - 16x + 64[/tex]

Expand the equation

[tex]f(x) = x^2 - 8x - 8x + 64[/tex]

Factorize the above equation

[tex]f(x) = x(x - 8) - 8(x -8)[/tex]

Factor out x - 8

[tex]f(x) = (x - 8) (x -8)[/tex]

Set f(x) to 0, to calculate the x-intercept

[tex](x - 8) (x -8)=0[/tex]

Rewrite as:

[tex](x - 8)^2=0[/tex]

Take the square roots of both sides

[tex]x - 8=0[/tex]

Solve for x

[tex]x = 8[/tex]

Hence, the x-intercept of the function is 8

Answers

Consider an indefinite Line L as shown in the diagram below
Point A and Point B are two points on Line L
The line between point A and point B that is also a part of Line L is called line segment

The correct definition of a line segment is given by the option e)
Line segment is a part of a line that has two end points

Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4

Answers

Martin deposits $200 in a savings account that earns 5% annual interest.

year         interest                     balance

1              200 * 5%                    200(1.05)

2              200(1.05) * 5%          200(1.05)^2

3            200(1.05)^2*5%        200(1.05)^3

y                                              200(1.05)^y

=> m = 200 (1.05)^y

four years later, cary deposits $200 in an account earning the same interest.

year         interest                     balance

5              200 * 5%                    200(1.05)

6              200(1.05) * 5%          200(1.05)^2

7           200(1.05)^2*5%        200(1.05)^3

y                                              200(1.05)^(y-4)

=> c = 200(1.05)^ (y-4)

Answer:
Martin: 200(1.05)^y
Cary: 200(1.05)^(y–4)

Answer:

d then d again

Step-by-step explanation:

Jessica purchased items worth $41.23 at the local
grocery store. The cashier made a mistake while
ringing up her items, and Jessica ended up paying
$50.23. How many extra dollars did she pay?

Answers

he purchased items worth 41.23.....she was charged 50.23

50.23 - 41.23 = 9 <== she paid 9 extra dollars

Why is world population distribution uneven what factors contribute to this uneven distribution?

Answers

World population distribution is uneven because of the different measures of the factors affecting population, such as life expectancy, economic development etc

If f(x)=square root of x+12 and g(x)=2square root of x, what is the value of (f – g)(144)? –84
–60
0
48

Answers

f(x)=(√x)+12
g(x)=2√x

(f-g)(x)=f(x)-g(x)

(f-g)(144)=f(144)-g(144)=
(√144)+12-(2√144)=
12+12-2(12)=
24-24=
0
result is 0

f(x) = √(x)+12
g(x) = 2√x

(f – g)(144) = √(144)+12 - 2√144

(f – g)(144) = 12 +12 - 2(12)

(f – g)(144) = 24 - 24

(f – g)(144) = 0

he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3

Answers

Answer:

0 0

5 27.5

10 55

15 82.5

Step-by-step explanation:

Joel and Melinda provide the following proofs for vertical angles to be equal:

Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)

Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)

Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct

Answers

Vertical angles are two opposite angles between two intersecting lines. Based on the following statements, Joel is correct and Melinda is quite wrong.

Let's discuss Joel's first. It is clear from the picture than line t and line PQ are straight lines. So the first two statements are true. Transitive property is illustrated as, if a=b and c=b, then a=c. Since angles 1+2 and angles 2+3 are each equal to 180, then these sum of angles are then equal. Subtraction property of equality is illustrated as, if a-c=d and b-c=d, then a=b. Hence,it applies. The proof is correct.

For Melinda's solution, the logic is missing after the statement: Therefore, angle 1 + angle 4 = 180° (t is a straight line). There must be additional proofs before she could use the transitive property of equality.

Therefore, the answer is letter A.

The answer is A! I just did it and gotit right

Find the difference.

Correct and best explained answer gets brainliest.

Answers

I can't see the Attachment but if you can message me or comment the question i'd be more than happy to help

Hello!

(-3x^4-9x^3-4x^2-4)-(5x^3-7x^2+6)

= -3x^4-9x^3-4x^2-4-(5x^3-7x^2+6)

= -3x^4-9x^3-4x^2-4-5x^3+7x^2-6

=-3x^4-14x^3+3x^2-10

hence, option D is the answer.

HOPE IT HELPED :D ☺☺

What is the area of the polygon given below?

Answers

Divide the polygon into three separate rectangles
(4*7)+(13*9)+(6*6)=181

Answer:

181 square units

Step-by-step explanation:

HELP!! QAQ

Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).

An visual of the function would be really appreciated. Thanks!

Answers

You can use y = {-1, x ≤ 0 and y = {x - 1, x > 0 as two functions for your piecewise function. The first function will be a horizontal line. The second function will be a straight line with a slope of 1 and y-intecept of -1. Messaged you the graph.

The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equivalent length in inches. If a table is 7.25 feet long, what is its length in inches? A. 84 inches B. 87 inches C. 81 inches D. 90 inches

Answers

Final answer:

The length of the table in inches is 87 inches.

Explanation:

To solve this problem, you can use the equation y = 12x to convert the length from feet to inches. Given that the table is 7.25 feet long, you can substitute x = 7.25 into the equation to find y.

y = 12(7.25) = 87

Therefore, the length of the table in inches is 87 inches.

Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)

Answers

Hey there!

For Part A, all you need to do is write out an equation for how many dollars Andrew would make for x hours during regular hours (not overtime). Since he makes 6 dollars per hour, this will be 6x.

W = 6x

For Part B, create a similar equation for overtime hours. Overtime hours only apply after Andrew has worked 40 hours, so plug that into your first equation and add that to the second equation.

W = 6x
W = 6(40)
W = 240

S = 240 + 9y

For Part C, consider what we now know. If Andrew earns any money over 240 dollars (which is how much he earns after 40 hours), we know he worked overtime. So, we can just plug 330 into the second equation for S and solve for the number of additional hours he worked, y.

330 = 240 + 9y
– 240 – 240

90 = 9y
9 9

10 = y

Now, we can add up the initial 40 hours plus the additional 10 hours, which is 50 hours total.

Hope this helped you out! :-)

Which classifications apply to the polygon? Check all that apply.
convex
concave
regular
hexagon
octagon

Answers

Answer: Concave and Hexagon.

Step-by-step explanation: In the given figure we have one angle is greater than 180 degrees.

A polygon has an angle between 180 to 360 is called a concave polygon.

Therefor given polygon is a concave polygon.

Also the given polygon has six sides.

A polygon with six sides is a hexagon.

Therefore, correct options are Concave and Hexagon.

The classifications that apply to the polygon are concave and hexagon.

What is a polygon?

A polygon is a shape with at least three straight sides and angles. A regular polygon has at sides and angles of the same length and size. A convex polygon is a shape in which all of its vertices point in the outward direction. A concave polygon is a shape in which all of its vertices point in the outward direction. A hexagon is a polygon with eight sides.

To learn more about polygons, please check: https://brainly.com/question/390279

The product of the roots of 8x² - 2x = 1 is:

Answers

AB = c/a = -1 / 8 = -1/8

Answer:

[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]

Step-by-step explanation:

The quadratic equation is given to be : 8x² - 2x = 1

We need to find the product of its zeros

First finding the number of zeros :

⇒ 8x² - 2x - 1 = 0

⇒ 8x² - 4x + 2x - 1 = 0

⇒ (4x + 1)(2x - 1) = 0

[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]

[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]

what is the final step to solving the inequality -2(5-4x)<6x-4

Answers

Here's the whole equation; tldr divide -6 by -2 and flip the inequality from < to >.
[tex]-2(5-4x) \ \textless \ 6x - 4 \\ -10+8x \ \textless \ 6x -4 \\ -6+8x \ \textless \ 6x \\ -6 \ \textless \ -2x \\ 3 \ \textgreater \ x [/tex]

Answer:

x< 3

Step-by-step explanation:

-2(5-4x)<6x-4

multiply -2 inside the parenthesis

-2 * 5 = -10

-2 * -4x= 8x

-2(5-4x)<6x-4

-10 + 8x < 6x -4

To solve for x we need 'x' on the left hand side

Subtract 6x from both sides

-10 + 8x -6x< 6x -6x -4

-10 +2x < -4

Add 10 on both sides

-10 +10 +2x < -4+10

2x < 6

divide by 2 on both sides

x< 3

Lena will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same

Answers

50 + 0.50m = 0.70m
50 = 0.70m - 0.50m
50 = 0.20m
50 / 0.20 = m
250 = m......the plans will cost the same at 250 miles <==

50 + 0.50(250) = 50 + 125 = 175
0.70(250) = 175

and they would both cost $ 175 <==

The two plans cost the same when Lena drives 250 miles, resulting in a cost of $175 for both plans, as per the given linear equation.

A linear equation is a mathematical expression that represents a straight line relationship between variables, typically in the form of ax + b = 0.

The two plans cost the same when the amount of driving satisfies the equation:

50 + 0.50x = 0.70x

Where:

50 represents the initial fee for the first plan,

0.50x represents the cost per mile for the first plan, and

0.70x represents the cost per mile for the second plan.

Now, let's solve for x:

50 + 0.50x = 0.70x

Subtract 0.50x from both sides:

50 = 0.20x

Now, divide both sides by 0.20:

x = 50 / 0.20

x = 250

So, the two plans cost the same when Lena drives 250 miles. To find the cost at this point, plug x = 250 into either plan:

For the first plan:

Cost = 50 (initial fee) + 0.50 (cost per mile) * 250

Cost = $50 + $125

Cost = $175

For the second plan:

Cost = 0.70 (cost per mile) * 250

Cost = $0.70 * $250

Cost = $175

So, when Lena drives 250 miles, both plans cost $175.

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Two trains leave stations 306 miles apart at the same time and travel toward each other. one train travels at 75 miles per hour while the other travels at 95 miles per hour. how long will it take for the two trains to meet?

Answers

combined speed = 95+75= 170 mph

they will meet in 306/170 = 1.8 hours or 1 hour 48 minutes.

Answer: It will take 1.8 hours for the two trains to meet.

Step-by-step explanation:

Since we have given that

Speed of one train = 75 mph

Speed of other train = 95 mph

Since they travel towards each other.

so, Relative speed = 75+95 = 170 mph

Distance between them = 306 miles

We need to find the time taken:

So, it becomes,

[tex]time=\dfrac{Distance}{Speed}\\\\Time=\dfrac{306}{170}\\\\Time=1.8\ hours[/tex]

Hence, it will take 1.8 hours for the two trains to meet.

If angle A measures 57 degrees and angle C is adjacent to angle A, what is the measure of angle C if the two angles are complementary?

Answers

33 degrees,
90-57=33
complementary angles mean that together, the angles add up to equal 90 degrees

The definition of complementary angles is that the sum of two angles should be equal to 90 degrees. We can see that in this case angles A and C are complementary angles. So we can do 90-57 to get 33 and we can see that angle C would equal 33 degrees. Hope this helps. Feel free to ask more questions, or ask questions about my explanation.

What is the process that you need to follow in order to prove a circle?

Answers

The radii has to have the exact same length. The definition of a circle is "a round plane figure whose boundaries consist of points equidistant from the center". So to prove a circle, if you don't have the exact equation for it, would be to prove the radii all the same length.

Your goal is to save at least $240.00 over the next 4 week. How much money must you save each week in order to meet that goal? Write and solve an inequality

Answers

4 *x >= 240 ---> x >= 60,

So at least $60/week (notice the = sign, because it at at least, and not 'more than')

The solution is x ≥ $ 60

The value of the inequality equation is x ≥ 60

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the minimum money per week to be saved be = x

The number of weeks = 4

The goal is to save at least $240.00 over the next 4 week

So , substituting the values in the equation , we get

x ≥ 240 / number of weeks

x ≥ 240 / 4

On simplifying the equation , we get

x ≥ 60

Therefore , the value of A is x ≥ 60 and should save a minimum of $ 60 per week

Hence , the inequality equation is x ≥ 60

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A mother gives birth to a 9 pound baby. every 4 months, the baby gained 2 pounds. if x is the age of the baby in months, then y is the weight of the baby in pounds. find an equation of a line in the form y = mx + b that describes the baby's weight.

Answers

For the equation of the line of the form y = mx + b, m is the slope of the line and b is the y-intercept which is the value of y when x is equal to zero. The slope is the rate of change of y per change in x. "y" would represent the dependent variable which is the weight of the baby while "x" represents the independent variable which is the number of months or the age of the baby in months. We calculate the slope as follows:

slope = (11 - 9) / ( 4 - 0) = 2/4 = 0.5
at x = 0, it is said that the weight of the baby is 9 lbs so the value of b would be 9.

The equation of the line would be y = 0.5x + 9

Final answer:

The equation of the line that represents the baby's weight as it grows is y = 0.5x + 9, where x is the age of the baby in months, and y is the weight of the baby in pounds.

Explanation:

The student is looking for an equation of a line that represents the weight of a baby as it grows. This situation can be described using a linear equation in the form of y = mx + b, where y represents the weight of the baby in pounds, x represents the age of the baby in months, m is the rate at which the baby gains weight, and b is the initial weight of the baby at birth.

Given that the baby weighs 9 pounds at birth, we have our b value as 9. It is also given that the baby gains 2 pounds every 4 months, which can be converted to a monthly weight gain of ½ pound per month (since 2 pounds ÷ 4 months = ½ pound per month). Consequently, the value of m is ½ or 0.5.

Using these values, the equation of the line that describes the baby's weight over time can be written as:

y = 0.5x + 9

This equation indicates that the baby's weight (y) is 9 pounds at birth (when x = 0) and increases by 0.5 pounds each month.

A forensic detective is called to the scene of a murder at 2 am. When she checks the temperature of the body, she sees that it is 80 degrees Fahrenheit. The temperature of the room in which the body is found is 65 degrees. If the detective uses Newton's law of cooling, what will she say is the time of death? T(t)=Ta+(To-Ta)e^(-0.1947t).
Thank you to anyone who helps! :)

Answers

Newton's Law of cooling is
[tex]T(t)=T_{a}+(T_{0}-T_{a})e^{-0.1947t}[/tex]
where
T(t) = temperature of the body after t hours, 80 °F
[tex]T_{a}[/tex] = ambient temperature, 65 °F
[tex]T_{0}[/tex] = normal body temperature, assumed to be 98.6 °F

The elapsed time since death is obtained from
[tex]65+(98.6-65)e^{-0.1947t|} = 80[/tex]
[tex]33.6e^{-0.1957t}=15[/tex]
[tex]-0.1947t=ln \frac{15}{33.6} [/tex]
[tex]t= \frac{ln(15/33.6)}{-0.1947} =4.142[/tex]

4.142 hours before 2 am is 9:52 pm (the previous day) approximately.

Answer: 9:52 pm the previous day.

Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.

Which equation can she use to find the required width of the border x?

Answers

To solve this problem, let us recall that the formula for Area of a rectangle is:

A = l * w

Where,

l = length of one side = 4 ft

w = width of one side = 1 ft

Therefore the original area is:

Ao = 4 ft * 1 ft

Ao = 4 ft^2

Since each border would be increased by x, therefore the new l and w would be:

l = 4 + 2x

w = 1 + 2x

The new area becomes:

A = (4 + 2x) (1 + 2x)

The difference of the two would be the area of the remaining scarf:

A – Ao = 6 square ft

(4 + 2x) (1 + 2x) – 4 = 6 ---> 1

(4 + 2x) (1 + 2x) = 10 ---> 2

The equation to use can be equation 1 or equation 2.

What is the difference of 28y - 16y

Answers

Both of the terms are like terms. So, we can find the difference of them.

28y - 16y = 12y

So, 12y is the answer.

Other Questions

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