f(x)=x^4+7x^3+13x^2-3x-18

Answers

Answer 1

I assume for this problem you are looking for the derivative?
If so. I hope this helps!
Apply the sum difference rule > d/dx(x^4) + d/dx(7^3) + d/dx(13x^2) - d/dx(3x) - d/dx(18)
For d/dx(x^4), d/dx(7^3), d/dx(13x^2), d/dx(3x), and d/dx(18). We want to take the constant out and the apply the power rule of [tex] \frac{d}{dx} (x^a) = a * x^{a - 1}[/tex]

d/dx(x^4) > [tex]4x^{4 - 1} \ \textgreater \ 4x^3[/tex]

d/dx(7^3) > [tex]7 \frac{d}{dx} (x^3) \ \textgreater \ 7 * 3x^{3 - 1} \ \textgreater \ 21x^2[/tex]

d/dx(13x^2) > [tex]13 \frac{d}{dx} (x^2) \ \textgreater \ 13 * 2x^{2 - 1} \ \textgreater \ 26x[/tex]

d/dx(3x) > [tex]3 \frac{d}{dx} (x) \ \textgreater \ 3 * 1 \ \textgreater \ 3[/tex]

d/dx(18) > [tex]Deriv OFconstant \ \textgreater \ \frac{d}{dx}(a) = 0 \ \textgreater \ 0 [/tex]

Now we can combine these all.
[tex]4x^3 + 21x^2 + 26x - 3 - 0 \ \textgreater \ Simplify \ \textgreater \ 4x^3 + 21x^2 + 26x - 3[/tex]
Therefore our final answer is
[tex]4x^3 + 21x^2 + 26x - 3[/tex]

Related Questions

If we put five math, six biology, eight history, and three literature books on a bookshelf at random, what is the probability that all the math books are together?

Answers

To solve you, find the probability of five items being in consecutive order of a sample size of (5+6+8+3). 5 out of 22 items must be in a contiguous group in any order among the 22 total items.

Final answer:

The probability that all the math books are together can be calculated by considering the number of ways the math books can be arranged together and dividing it by the total number of ways all the books can be arranged.

Explanation:

First, calculate the total number of ways the books can be arranged on the bookshelf. Since there are 22 books in total, the number of arrangements is 22!.

Next, calculate the number of ways the math books can be arranged together. Since there are 5 math books, the number of arrangements is 5!.

Finally, divide the number of arrangements of the math books by the total number of arrangements to find the probability. So the probability is 5! / 22!.

It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?

Answers

it woud be at l.east 30 miles

The velocity of the bus is:

velocity (bus) = 36 miles / 40 min

velocity (bus) = 0.9 miles / min

Since the car is 1.5 times faster, so the velocity of the car is:

velocity (car) = 1.5 * 0.9 miles / min

velocity (car) = 1.35 miles / min

At the meeting point, the sum of the distance is equal to 36 miles. Therefore:

1.35 t + 0.9 t = 36

2.25 t = 36

t = 16 min

So they will meet after 16 minutes.

The fuel efficiency in miles per gallon of all bmw 320i's is (approximately) normally distributed with a mean of 25 and a standard deviation of 2. a dealer receives a shipment of a random sample of 320i's (random with respect to m.p.g., that is) from the factory. find the probability that average fuel efficiency for this shipment is less than 24 miles per gallon if the dealer receives (i) one car, (ii) four cars and (iii) sixteen cars. explain briefly why these three answers differ.

Answers

Given:
μ = 25 mpg, the population mean
σ = 2 mpg, the population standard deviation

If we select n samples for evaluation, we should calculate z-scores that are based on the standard error of the mean.
That is,
[tex]z= \frac{x-\mu}{\sigma / \sqrt{n} } [/tex]

The random variable is x = 24 mpg.

Part (i): n = 1
σ/√n = 2
z = (24 -25)/2 = -0.5
From standard tables,
P(x < 24) = 0.3085

Part (ii): n = 4
σ/√n = 1
z = (24 -25)/1 = -1
P(x < 24) = 0.1587

Part (iii): n=16
σ/√n = 0.5
z = (24 - 25)/0.5 = -2
P(x < 24) = 0.0228

Explanation:
The larger the sample size, the smaller the standard deviation.
Therefore when n increases, we are getting a result which is closer to that of the true mean.

How many faces has an icosahedron?

Answers

There are 20 faces
^-^6^

Final answer:

An icosahedron is a symmetrical, solid shape with 20 triangular faces and 12 corners.

Explanation:

An icosahedron is a symmetrical, solid shape that has 20 faces. Each of these faces is an equilateral triangle. The structure of an icosahedron also includes 12 corners, where the faces meet. This geometric shape is an example of a regular polyhedron, one of the five Platonic solids, which are convex polyhedra with faces made of congruent regular polygons.

What is 3 tenths + 1 hundredths as a decimal

Answers

3 tenths = 0.3
1 hundredth = 0.01
0.31 is the answer

.31 is the answer :)))

You have a map where indy and fort wayne are 13 centimeter apart. kokomo and indy are 6.5 cm apart on the map. if you know that indy and fort wayne are actually 120 miles apart, how far apart would indy and kokomo be in real life? express your answer rounded to the nearest tenth of a mile

Answers

since 6.5 is half of 13,you just need to find out what is half of 120,and that would be 60 miles apart,if all three are in a straight line and indy is in the middle,is there a map to go along with this question?

The distance between Indy and Kokomo be in real life is given by the proportion A = 60 miles

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Let the distance between Indy and Fort Wayne in map = 13 cm

Let the distance between Indy and Fort Wayne in real = 120 miles

And , let the distance between Kokomo and Indy map = 6.5 cm

So , the proportion is

120 / 13 = A / 6.5

Multiply by 6.5 on both sides , we get

A = 120 / 2

A = 60 miles

Hence , the distance is 60 miles

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Ron's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 65 coffees in all, 26 of which were regular. What percentage of the coffees were regular?

Answers

Attached the solution and work.

Can you help me on #5

Answers

For 5 a, the y intercept is 2, because when x is 0, y is 2.
The growth is 5, because the y values increase by 5 whenever x is increased by 1.

For 5 b, This problem is linear because it goes up or down a set amount (it's not exponential).
Since this is a linear equation, we can use slope intercept form to represent this.
Slope intercept form is y=mx+b, where m is the slope (rise over run) and b is the y intercept.
Plugging in the slope and y-intercept, we get an equation of y=5x+2

For 5 c, we can plug 52 into the equation we just made.
52=5x+2
-2 -2
50=5x
[tex] \frac{50}{5}= \frac{5x}{5}[/tex]
10=x

Hope that helps!

which is longer 84 inches or 12 feet

Answers

The answer is 12 feet

The answer is 12 feets

solve the following: all fractions should be reduced to lowest terms and mixed numbers. -1 1/4 x (-2/5)=

Answers

-1 1/4 * (-2/5) =

= -5/4 * (-2/5)

= 10/20

= 1/2

Convert -1 1/4 to the mixed number -5/4.

Then the product of -1 1/4 and -2/5 is (-5/4)(-2/5) = 10/20, or 1/2.

Please, do not use " x " to indicate multiplication. " x " is reserved for naming variables. Instead, use " * " to indicate mult.

Thus, your problem is best written -1 1/4 * -2/5

Madeline bought 30 hotdogs and burgers altogether. 2/5 of the food bought were burgers. How many hotdogs did she buy?

Answers

she bought 18 burgers and 12 hotdogs.

Show how to multiply 6 x 298 using friendly numbers and then using properties and mental math.Write about which method you like better and why

Answers

Final answer:

To multiply 6 x 298 using friendly numbers, you multiply 6 by 300 and then subtract 12, getting 1788. Using properties and mental math, you break 298 into 200 + 90 + 8, multiply each by 6, and add the results together to get the same answer, 1788. The second method is preferred for its accuracy and reinforcement of the associative property.

Explanation:

To multiply 6 x 298 using friendly numbers, we can adjust 298 to a number that is easier to multiply, such as 300. This method involves approximation for ease of calculation. Here's how it would look:

First, multiply 6 by 300 to get 1800 (since 6 x 3 = 18, and then we add two zeros because we're multiplying by 300).Since we multiplied by 2 more than the original number (298 + 2 = 300), we subtract 2 times 6 from the result (which is 12) to correct for our approximation.Therefore, the final result is 1800 - 12 = 1788.

Using properties and mental math, we can use the distributive property to break 298 into more manageable numbers. Here's the step-by-step process:

Break 298 into 200 + 90 + 8.Multiply each part by 6: (6 x 200) + (6 x 90) + (6 x 8).Calculate each multiplication separately: 1200 + 540 + 48.Add the results together: 1200 + 540 + 48 = 1788.

I prefer the second method because it guarantees accuracy and still takes advantage of the associative property to simplify calculations without approximations. Additionally, this type of mental math helps to reinforce an understanding of multiplication as a series of simpler, added-together parts.

there are 4 bears. some are black and some are brown. there are fewer than 2 black bears. how many bears are Brown?

Answers

there are 3 brown bears

There are either three or four brown bears, and brown bear > 2 is the inequality that best describes the circumstance.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

given, there are 4 bears. some are black and some are brown. there are fewer than 2 black bears.

Since,

Black bear < 2

mathematically it can be 0 or 1

the inequality that represents the number of brown bears> 4 - 2

brown bear > 2

theoretically, it could be 3 or 4

therefore, there are either 3 or 4 brown bears, and the inequality that represents the situation is brown bear > 2.

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Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
A:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
B:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
C:Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
D:Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.

Answers

Correct answer: B
The first thing to be done is to convert the 2 tons into pounds.
1 pound is equal to 0.0005 tons (US). So, 2 tons divided by 0.0005 will give us the aluminium pounds per week that are processed by the Recycling Centre B.
[tex] \frac{2}{0.0005} [/tex]=4000
Recycling Centre B processes 4000 pounds/week. In order to compare to Recycling Centre A, we need to find the rate in pounds per hour. To do so divide the 4000 pounds by 168 (24×7 = number of hours in a week).
[tex] \frac{4000}{168} [/tex]≈23.8
The Recycling Centre B processes about 23.8 pounds/hour whereas the Recycling Centre A processes 100pounds/hour.

C: Recycling center B processes aluminum faster; It’s rate is About 120 Pounds per hour

A digit thermometer reports a temperature of 32*F as being 32.02*F. Which of the followings true?

A. The thermometer is both accurate and precise.
B. The thermometer is neither accurate nor precise.
C. The thermometer is precise, but not accurate.
D. The thermometer is accurate, but not precise.

Answers

Answer: The thermometer is both accurate and precise

Step-by-step explanation: Hope this helped!!

what is the greatest common factor of 27 and 36

Answers

9 because the gcf of 36 is 1,2,3,4,6,9,12,18,36
and then the gcf of 27 is 1,3,9,27
the gcf for both is 9

Find the prime factors of each number
27= 3 x 3 x 3
36= 2 x 2 x 3 x 3
---------------------
Now identify the common factors and determine GCF
27= [3 x 3] x 3
36= 2 x 2 x [3 x 3]
--------------------
Therefore
GCF= 3 x 3 = 9

A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 4 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.

Answers

L = 4D + 54 <== ur equation

the crew worked for 31 days...so sub in 31 for D

L = 4(31) + 54
L = 124 + 54
L = 178 miles <==

QUESTION 2

A $5000 investment earns $550 annual simple interest in one year. What is the annual interest rate?

11.5%

11%

12%

10.5%

QUESTION 5

Marie mixes 16 liters of 18% acid solution with a 27% acid solution to make a 21% acid solution.

How many liters of 27% solution did she use?

8 liters

12 liters

13.7 liters

16 liters

Answers

for Question 2 is 11%

And for question 5 is 8. hope i helped you

Question 2 is 11 i am sure

The table shows the five most populated countries in the world. How many times as many people live in China than in the United States? Round to the nearest tenth if necessary

Answers

Divide 1.325 by 0.304 to answer this question.

This comes out to 4.4. China has 4.4 times as many people as does the US.

How do I solve for x?

Answers

Write and solve an equation of ratios based upon the fact that the small and large triangles shown are similar:

5 6
---- = ---------
14 6 + x

Then 30 + 5x = 84, and 5x = 54, and so x = 54/5, or 10.8, or 10 4/5.

Suppose the number 1155 is written as the product of three positive integers. What is the smallest possible value of the sum of those three integers?

Answers

3. the equation I used is: 3×5×77

My first thought when I read this problem was "11 is a factor of 1155." Indeed,
1155 equals 11 times 105. Next, determine factors of 105. I see that 5 is a divisor of both 10 and 5, so that 105 equals 5 times 21.

Adding together these three integers: 11+5+21 = 37

But wait! 21 can be factored (e. g., into 7 times 3).

You'll need to identify all of the several sets of 3 positive integers each and find the sum of each set. Only after you've done this can you choose the set whose sum of the three integers is the smallest. Please show your work, so that others can give you feedback on it.

Allens score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How how many targets did he miss?

Answers

Allen missed 5 targets.

I have this same problem too and I just finished it! :)

The answer is that she missed 5 targets

Hope this helps

Find the second of two consecutive integers if the second is 13 less than twice the first.

Answers

What is the range in which the integers can be in? I cannot fully answer this question. But I think there could be more than one answer. One answer would be the first is 36 and the second is 66.

Hope this helps!
Can u plz mark me as brainliest? I really need it!

For the data in the table does Y very directly with X

Answers

I will explain and show you how to solve this kind of problems with an example.

Example:

Table:

x          y

16        4

32      16

48      36

Direct relation means that the ratio y / x is constant.

So, let's examine this ratio:

Ratio y / x

4/16 = 1/4

16/32 = 1/2

36/48 = 3/ 4

Given that the ratio y/x is not constant, the conclusion is that y does not vary directly with x.

Mateo make six loaves of banana bread he sells 2/3 of the loaves a bake sale which expression represents how many loaves Mateo sold at the bake sale

Answers

2/3=n/6
2/3*6=4
Hope this helps

Help Please.

1 inch=2.54 centimeters
68 centimeters= ..... inches

(round the answer to two decimal places)

Answers

26.7717 ................

68 x 2.54 centimeters = 172.72 centimeters

Given that the points (-1, 6), (3, 6), (3, 1), and (-1, 1) are vertices of a rectangle, how much shorter is the width than the length?

Answers

check the picture below, you can pretty much count the units off the grid.

Answer:

1 unit shorter

Step-by-step explanation:

By plotting the given points in the coordinate plane,

We get a rectangle ABCD having vertices,

A(-1,6), B (3,6), C (3,1), D (-1,1)

By the distance formula,

Shorter side or width of the rectangle,

[tex]AB=\sqrt{(3-(-1))^2+(6-6)^2}=\sqrt{4^2+0}=4\text{ unit}[/tex]

Longer side or length of the rectangle,

[tex]BC=\sqrt{(3-3)^2+(1-6)^2}=\sqrt{5^2}=5\text{ unit}[/tex]

The difference between length and width,

[tex]BC - AB = 5 - 4 = 1\text{ unit}[/tex]

Hence, the width of rectangle is 1 unit less than the length.

please can you help me!

z-² as a fraction

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ z^{-2}\implies \cfrac{1}{z^2}[/tex]

Which change would make the statement below true?Circle the letter of the correct answer. 3.7 < 3.56 A.put a 0 in the hundredths place to change 3.7 to 3.70. B.Change the hundredth digit in 3.56 to 8.
C.Change the tenths digit in 3.56 to 6.
D. Change the tenths digit in 3.56 to 8.

Answers

The answer's D, I think. Hope this helps.

Final answer:

To make 3.7 < 3.56 true, you would need to change the tenths digit in 3.56 to a smaller number. Option C, changing the tenths digit in 3.56 to 6, would make the statement true.

Explanation:

To make 3.7 < 3.56 true, you would need to change the tenths digit in 3.56 to a smaller number. Option C, changing the tenths digit in 3.56 to 6, would make the statement true. By changing the tenths digit to 6, the new number would be 3.66, which is greater than 3.7.

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What are the solutions of the following system?

Answers

x^2 + y^2 = 25
2x + y = -5.....y = -2x - 5

x^2 + (-2x - 5)^2 = 25
x^2 + (-2x - 5)(-2x - 5) = 25
x^2 + (4x^2 + 20x + 25) = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x + 4) = 0

5x = 0 2(0) + y = -5
x = 0 y = -5

x + 4 = 0 2(-4) + y = -5
x = -4 -8 + y = -5
y = 3

solutions are : x = 0, y = -5.....and x = -4, y = 3

Final answer:

To solve the system of equations, set the demand and supply equation equal to each other and solve for the unknown. Substitute Qd with Qs and solve for P.

Explanation:

We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since Qd = Qs, we can set the demand and supply equation equal to each other:

Qd = 16 - 2PQs = 2 + 5P

By substituting Qd with Qs, we get:

16 - 2P = 2 + 5P

From here, we can solve for P to find the value of the unknown.

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