Answer:
20times
Step-by-step explanation:
A fair of die has 6sides.
If 4 appears 'once' out of a 6.
Then, 4 will appear 2times out of 12 i.e
6faces = 1time
12faces = 2times.
But remember that we want to know how many times 4 will appear out of a 120
120faces = x times
Since 6faces = 1time (i.e 4 occur one time in six faces)
cross multiplying:
6 × x = 120
x = 120/6
x = 20times
This means 4 will appear 20times out of a 120
Cecil recivies $15 per week for complting chores. He spend $12 on a video game. What percent of his monthly allowence did cecil spend on teh video gmae
Final answer:
Cecil spent 20% of his monthly allowance on the video game, calculated by dividing the $12 spent on the game by his $60 monthly allowance and then multiplying by 100 to get the percentage.
Explanation:
To find out what percent of his monthly allowance Cecil spent on the video game, we first need to calculate his total monthly allowance. Cecil receives $15 per week for completing chores. There are typically 4 weeks in a month, so Cecil's monthly allowance is 15 dollars/week * 4 weeks/month = $60 per month.
Next, we will calculate the percentage of his allowance that was spent on the video game. Cecil spent $12 on a video game. To find this percentage, we use the formula:
Percentage spent = (Amount spent / Total allowance) * 100
Percentage spent = ($12 / $60) * 100
Percentage spent = 0.2 * 100
Percentage spent = 20%.
Therefore, Cecil spent 20% of his monthly allowance on the video game.
Fred has saved 3 quarters from washing cars how many cents does Fred have
Answer:75 cents
Step-by-step explanation:
one quarter is equal to 25 cents and since you have 3 of them you multiple 25 times 3 and get 75.
Fred has 3 quarters, and since each quarter is worth 25 cents, he has a total of 75 cents from washing cars.
Fred has saved 3 quarters from washing cars, and we need to determine how many cents he has. In U.S. currency, one quarter is equivalent to 25 cents. To find out the total number of cents Fred has, we can perform the following multiplication:
25 cents × 3 quarters = 75 cents
Therefore, Fred has a total of 75 cents.
if the radius of circle r is 7 and the radius of circle s is 9, what is the ratio of the circumference of circle r to circle s
Answer:
43.96 : 56.52
Step-by-step explanation:
Circumference = 2 * pi * Radius
Circumference = Diameter * pi
Circle R's Circumference = 43.96 (7 * 2 * 3.14)
Circle S's Circumference = 56.52 (9 * 2 * 3.14)
The ratio of the circumference of circle r to s = 43.96:56.52
Connor went to a carnival with 22.50$. He bought a hot dog and a drink for $3.75 and he wanted to spend the rest of his money on ride tickets which cost $1.25 each. What is the maximum number of ride tickets that he can buy
Answer:
15
Step-by-step explanation:
22.50-3.75=18.75
18.75/1.25=15
BRAINLIEST WOULD BE APPERCIATED
The maximum number of ride tickets that he can buy is; 15
Division:Connor has 22.50$, bought a hot dog and a drink for $3.75.
In essence, the amount Connor has left is;
$22.50 - $3.75= $18.75
Therefore, if he wanted to spend the rest of his money on ride tickets which cost $1.25 each, the maximum number of ride tickets that he can buy can be evaluated as follows;
No. of ride tickets = $18.75/$1.25
No. of ride tickets = 15
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A photo of an ant in a science book is increased 515% as large as the actual size. If the ant is 16 millimeters, what is the size of the ant in the photo
Answer:
82.4 millimeters is the size of the ant in the photo
Step-by-step explanation:
In this question, we are asked to calculate the size of an ant in a science book given the actual size of the ant and the percentage increase is the size of the ant in the book.
From the question, we can identify that the actual size is 16 millimeters
Now let’s find 515% of this to know the size to which it would be magnified in the science book.
That would be;
515/100 * 16 = 82.4 millimeters
Hence, this means the ant will have a size of 82.4 millimeters in the science book
Answer:
The size of the ant in the photo is 88 mm
Step-by-step explanation:
Here, we have the percentage increase = 515 %
Size of ant = 16 millimeters in real life,
Therefore, the size of the ant in the in the photo, is given by,
[tex]\frac{16 \, mm}{100} = \frac{y\, mm}{550} = \frac{16 \times 550}{100} = \frac{y \times 100 \, mm}{100} \rightarrow 88 \, mm = y[/tex]
y = 88 mm
The size of the ant in the photo = 88 mm.
whats 11/12 of a full rotation?
Pls mark Brainliest.
Answer:
330°
Step-by-step explanation:
A full rotation is 360°. Saying 11/12 of a full rotation is equivalent to saying 11/12 * 360°, which equals 330°.
We have that for the Question "whats 11/12 of a full rotation?" it can be said that 11/12 of a full rotation is
[tex]X=330 \textdegree[/tex]
From the question we are told
whats 11/12 of a full rotation?
Generally the equation for the Statement is mathematically given as
[tex]x=\frac{11}{12}[/tex]
Where
360° signifies full rotation
Therefore
11/12 of a full rotation is
[tex]\frac{11}{12}*360[/tex]
[tex]X=330 \textdegree[/tex]
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Find the domain of the following function:
y = x^3 − 8
_________
x^2 + 9
Select the appropriate response:
A) 483xy
B) domain: all values of y
C) all values of x
D) Not possible to solve
Answer:
C) all values of x
Step-by-step explanation:
Domain is the set of values of input 'x'
Since the denominator is not 0 for any x, there's no domain restriction
If six people decide to come to a basketball game, but three of them are only 2/5 sure that they will stay for the entire time (the other three are sure they'll stay the whole time), what is the probability that at the end, at least 5 people stayed the entire time
Answer:
the probability that at the end, at least 5 people stayed the entire time = 0.352
Step-by-step explanation:
From the question, 3 of the people are sure to stay the whole time. So, we'll deduct 3 from 6.which leaves us with 3 that are only 2/5 or 0.4 sure that they will stay the whole time.
Thus, what we need to compute to fulfill the probability that at the end, at least 5 people stayed the entire time of which we know 3 will stay, so for the remaining 3,we'll compute;
P[≥2] which is x~bin(3,0.4)
Thus;
P(≥2) = (C(3,2) x 0.4² x 0.6) + (C(3,3) x 0.4³)
P(≥2) = 0.288 + 0.064
P(≥2) = 0.352
Determine if each equation is a linear equation.
[Linear equation / Not a linear equation]
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
Answer:
Linear-1,2,3,6
Nin-Linear-4,5
Step-by-step explanation:
A linear equation is an equation in which the highest power of the variable is 1.
Out of the given equations, the following are linear.
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
These equations on the other hand are nonlinear.
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
No 4 contains a term which is the product of two variables therefore it is not linear.
No 5 contains a term whose highest power is 3. Such an equation is a Cubic Equation.
what are 3 equivalent ratios to 3/4?
Answer:
6/8, 9/12, 12/16
Step-by-step explanation:
Multiply the numerator and denominator by the same amount to maintain the same ration.
[tex]\frac{3}{4} =\frac{6}{8} = \frac{9}{12} =\frac{12}{16}[/tex]
79. Revenue. The revenue (in dollars) from the sale of x infant car seats is given by R1x2 = 60x - 0.025x2 0 ... X ... 2,400 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R′1x2. (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and write a brief verbal interpretation of these results.
Question:
59 Revenue. The revenue (in dollars) from the sale of x infant car seats for infants is given by
R(x) =60·x - 0.025·x² 0 ≤ x ≤ 2400
(A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats.
(B) Use the four-step process to find
(C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and write a brief verbal interpretation of these results
Answer:
(A) $437.5
(B) R'(x) = 60 - 0.05·x
(C) $10
Step-by-step explanation:
(A) Here we have the change in revenue when production is increased from 1,000 car seats to 1,050 car seats is given as follows;
R(1050) - R(1000) = 60×1050 - 0.025×1050² - (60×1000 - 0.025×1000²)
R(1050) - R(1000) = 63000 - 27562.5 - 35000 = $437.5
(B) R'(x) is given by
Step 1. R(x + h) = 60·(x+h) - 0.025·(x+h)²
Step 2 R(x + h) - R(x) = 60·(x+h) - 0.025·(x+h)² - 60·x - 0.025·x² = [tex]-\frac{h^2+(2x-2400)h}{40}[/tex]
Step 3
[tex]\frac{R(x+h)- R(x)}{h} = -\frac{h^2+(2x-2400)h}{40 \times h} = -\frac{h +2x - 2400}{40}[/tex]
Step 4
[tex]\lim_{h \to 0} \frac{R(x+h)- R(x)}{h} = \lim_{h \to 0} -\frac{ h +2x - 2400}{40}[/tex]
∴ R'(x) = 60 - 0.05·x
(c) The revenue at a production level of 1000 car seats is
R(1000) = (60×1000 - 0.025×1000²) = $35,000
The instantaneous rate of change of revenue is given as follows
R'(x) = 60 - 0.05·x = 60 - 0.05×1000 = $10.
A) The average change in revenue when production is changed from 1,000 car seats to 1,050 car seats is $8.75. B) The derivative of the revenue function R1(x) with respect to x is R′1(x) = 60 - 0.05x. C) At a production level of 1,000 car seats, the revenue is $35,000 and the instantaneous rate of change of revenue is $10.
Explanation:(A) To find the average change in revenue, we need to calculate the change in revenue and divide it by the change in the number of car seats produced. Let's calculate:
For 1,000 car seats, the revenue is R1(1000) = 60(1000) - 0.025(10002) = $60,000 - $25,000 = $35,000.For 1,050 car seats, the revenue is R1(1050) = 60(1050) - 0.025(1050x2) = $63,000 - $27,562.50 = $35,437.50.The change in revenue is $35,437.50 - $35,000 = $437.50.The change in the number of car seats produced is 1,050 - 1,000 = 50.The average change in revenue is $437.50/50 = $8.75.(B) To find R′1(x), we need to calculate the derivative of the revenue function R1(x) with respect to x. Let's differentiate:
R′1(x) = d/dx(60x - 0.025x2) = 60 - 0.05x
(C) At a production level of 1,000 car seats, the revenue is $35,000. The instantaneous rate of change of revenue (also known as the marginal revenue) at this production level can be found by substituting x = 1,000 into R′1(x):
R′1(1000) = 60 - 0.05(1000) = 60 - 50 = $10. The revenue at this production level is $35,000 and the instantaneous rate of change of revenue is $10, which represents the additional revenue obtained from producing one additional car seat.
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what’s the 2nd term in the sequence?
Answer:a fgbvffjnfv
Step-by-step explanation:
1. 2x + y = 7 and 6x + 5y = 27*
Your answer
2x-5y=-1;6x-5y=27
Solution :
{x,y} = {7,3}
System of Linear Equations entered :
[1] 2x - 5y = -1
[2] 6x - 5y = 27
Graphic Representation of the Equations :
-5y + 2x = -1 -5y + 6x = 27
Solve by Substitution :
// Solve equation [2] for the variable x
[2] 6x = 5y + 27
[2] x = 5y/6 + 9/2
// Plug this in for variable x in equation [1]
[1] 2•(5y/6+9/2) - 5y = -1
[1] - 10y/3 = -10
[1] - 10y = -30
// Solve equation [1] for the variable y
[1] 10y = 30
[1] y = 3
// By now we know this much :
x = 5y/6+9/2
y = 3
// Use the y value to solve for x
x = (5/6)(3)+9/2 = 7
Solution :
{x,y} = {7,3}
Hope I helped! :)
Halla la media aritmética para las siguientes situaciones: i. Para poder clasificar a las finales de Jokie, el equipo debe tener un promedio de goles mayor a 20 puntos. Los siguientes son los puntajes obtenidos: 25, 12, 15, 23, 24, 39, 13, 31, 19, 16. ¿Clasificaron a finales? AYUDENME
Answer:
The team qualified for the finals.
Step-by-step explanation:
The question is:
Find the arithmetic mean for the following situations: i. In order to qualify for the Jokie Finals, the team must have a goal average greater than 20 points. The following are the scores obtained: 25, 12, 15, 23, 24, 39, 13, 31, 19, 16. Did they qualify for the finals? HELP ME
The average goal the team must have to win the Jokie finals is more than 20 points.
The goals obtained by the team are:
X = {25, 12, 15, 23, 24, 39, 13, 31, 19, 16}
The arithmetic mean is the average value of a data set. The formula to compute the arithmetic mean is:
[tex]\bar X=\frac{1}{n}\sum X_{i}[/tex]
Compute the arithmetic mean of the goals scored by the players as follows:
[tex]\bar X=\frac{1}{n}\sum X_{i}[/tex]
[tex]=\frac{1}{10}\times (25+12+15+23+24+39+13+31+19+16)[/tex]
[tex]=\frac{1}{10}\times 217\\[/tex]
[tex]=21.7[/tex]
The arithmetic mean of the goals scored by the players is 21.7 points.
The average score is greater than 20 points.
Thus, the team qualified for the finals.
plz help ill give brailest
Answer:
[tex]\frac{4^{15} }{b^{21} }[/tex]
Step-by-step explanation:
First, multiply the exponent 7 and the -3 together, giving you:
[tex]b^{-21}[/tex]
Then, multiply the exponent 5 and the -3 together, giving you:
[tex]4^{-15}[/tex]
But since you can't have a negative exponent, you need to switch the numbers in their places. This is because, when you have a negative exponent, you either switch it to under 1 or over 1, depending on where it currently is:
[tex]\frac{4^{15} }{b^{21} }[/tex]
hey guys:) how can one solve this?
x⁴ - 2x + 2
please with an explanation
Answer:
81x+2
Step-by-step explanation:
2x+x=3x
3×3×3×3=81x
4m=4(m−1)
I'm not sure if this is right but i got 0= -4
Answer:
Don't worry, there is no solution.
Step-by-step explanation:
If you end up with 0 equaling something that isntn0 when you're simply solving a variable, there is no solution. But if you get 0=0, it's all real numbers.
answers to bad dog breakout
Without specific context or questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. It's recommended to read the text carefully, breakdown the text, and note down important points such as characters, plot, and themes.
Explanation:I apologize but without the detailed context or exact questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. 'Bad Dog Breakout' might be a literary work or a segment from an English curriculum, and the questions can vary greatly. However, I encourage you to read and comprehend the text carefully. Breaking it down paragraph by paragraph, identifying characters, noting down the plot, any significant themes and important details might help.
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Find the area of a circle with a circumference of \blueD{50.24}50.24start color #11accd, 50, point, 24, end color #11accd units.
Answer:
[tex]201 cm^2[/tex]
Step-by-step explanation:
The circumference of a circle is given by:
[tex]c=2\pi r[/tex]
where
r is the radius of the circle
For the circle in this problem,
c = 50.24 cm
Therefore the radius is:
[tex]r=\frac{c}{2\pi}=\frac{50.24}{2\pi}=8 cm[/tex]
The area of a circle is given by the formula
[tex]A=\pi r^2[/tex]
where r is the radius.
For the circle in this problem,
r = 8 cm
So the area is
[tex]A=\pi \cdot 8^2 = 201 cm^2[/tex]
The area of the circle is 201 cm square.
Calculation of the area of the circle:Since we know that
Circumference of the circle = [tex]2\pi r[/tex]
So here radius should be
[tex]= c\div 2\pi \\\\= 50.24\div 2\pi[/tex]
= 8 cm
Now the area of the circle is
[tex]= \pi r^2\\\\= 3.14\times 8^2[/tex]
= 201
Hence, we can conclude that The area of the circle is 201 cm square.
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Please help me with these Square Root problems. Part 2. Please Show and check the work.
[tex]5. \sqrt{x+4} = 3 - \sqrt{x} \\\\6. \sqrt{x+4} =3 + \sqrt{x} \\\\7. \sqrt{x+ 3} = \sqrt{5x+6} - 3\\\\8. \sqrt{2x+1} = x - 1[/tex]
Answer:
5. 25/36
6. 25/36
7. -3/4 or 6
8. 0 or 4
Step-by-step explanation:
5. Square both sides: x + 4 = 9 - 6[tex]\sqrt{x}[/tex] + x
Subtract x from both sides and subtract 9 from both sides:
-5 = -6[tex]\sqrt{x}[/tex]
Square both sides again: 25 = 36x
Divide both sides by 36: x = 25/36
6. Square both sides: x + 4 = 9 + 6[tex]\sqrt{x}[/tex] + x
Subtract x and 9 from both sides: -5 = 6[tex]\sqrt{x}[/tex]
Square both sides: 25 = 36x
Divide both sides by 36: x = 25/36
7. Square both sides: x + 3 = 5x + 6 - 6[tex]\sqrt{5x+6}[/tex] + 9
Add 6[tex]\sqrt{5x+6}[/tex] to both sides and isolate it: 6[tex]\sqrt{5x+6}[/tex] = 4x + 12
Divide both sides by 2 and then square both sides again:
3[tex]\sqrt{5x+6}[/tex] = 2x + 6
9 * (5x + 6) = 4x^2 + 24x + 36
45x + 54 = 4x^2 + 24x + 36
4x^2 - 21x - 18 = 0
Factorize: (4x + 3)(x - 6) = 0 ⇒ x = -3/4 or x = 6
8. Square both sides: 2x + 1 = x^2 - 2x + 1
Move all the terms to one side and combine like terms: x^2 - 4x = 0
Factorize: x(x - 4) = 0 ⇒ x = 0 or x = 4
Hope this helps!
Answer:
5. x = 25/36
6. No real solutions
7. x = 6
8. x = 4
Step-by-step explanation:
5. sqrt(x + 4) = 3 - sqrt(x)
Square both sides
x + 4 = 9 - 6sqrt(x) + x
6sqrt(x) = 5
sqrt(x) = 5/6
x = 25/36
6. sqrt(x + 4) = 3 + sqr(x)
x + 4 = 9 + 6sqrt(x) + x
6sqrt(x) = -5
sqrt(x) = -5/6
Not possible. A + square root can not be negative
7. sqrt(x + 3) + 3 = sqrt(5x + 6)
Square both sides
x + 3 + 6sqrt(x + 3) + 9 = 5x + 6
6sqrt(x + 3) = 4x - 6
3sqrt(x + 3) = 2x - 3
Square both sides
9(x + 3) = 4x² - 12x + 9
4x² - 21x - 18 = 0
Using quadratic formula:
x = [21 +/- sqrt(21² - 4(4)(-18)]/(2×4)
x = [21 +/- 27]/8
x = 6, -¾
x = -¾ is rejected because it doesn't satisfy the initial equation
8. sqrt(2x + 1) = x - 1
2x + 1 = (x - 1)²
2x + 1 = x² - 2x + 1
x² - 4x = 0
x(x - 4) = 0
x = 0, 4
0 is rejected because it doesn't satisfy the initial equation
Helga signs up to coach hockey. she wants to make at least $775 during the season. she gets $200 at the start of the season and $50 for each practice session she has. how many practice sessions does Helga need to have this season?
Answer:
12
Step-by-step explanation:
Well 775-200 = 575
575÷50= 11.5
round up because you cannot got to a half of practice.
So 12 practices.
find perimeter and area of figure
find the value of sin(θ) for an angle θ in standard position with a terminal ray that passes through the point (-5, -12)
Answer:
c. -12/13
Step-by-step explanation:
it will be the y-coordinate divided by the distance from the origin, or (-12) / [tex]\sqrt{5^2+12^2}[/tex] = -12/13
Answer:
C. -12/13
Step-by-step explanation:
(-5,-12) is in the third quadrant
So sin would be negative
Hypotenuse = sqrt(5² + 12²)
sqrt(169)
13
sin(theta) = -12/13
Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1) Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20 What is the next step after using the distributive property? Use the multiplication property of equality to isolate the variable term on one side of the equation. Use the multiplication property of equality to isolate the constant on one side of the equation. Combine the like terms on the right side of the equation. Combine the like terms on the left side of the equation.
Answer: It’s D
Step-by-step explanation:
Just took assignment
Answer:
-DStep-by-step explanation:
I got 100% on this assignmentfind the length of the third side to the nearest tenth
Answer:
7.1
Step-by-step explanation:
You can use the Pythagorean Theorem to solve this:
[tex]a^{2} + b^{2} = c^{2}[/tex]
All you need to do is plug in the numbers (in this case, they've already given you the hypotenuse, which is c in the formula, are you're solving for the leg).
[tex]7^{2} + b^{2} = 10^{2}[/tex]
49 + [tex]b^{2}[/tex] = 100
Subtract 49 from both sides:
49 + [tex]b^{2}[/tex] = 100
-49 -49
___________
[tex]b^{2}[/tex] = 51
Square root both sides:
[tex]\sqrt{b^2} = \sqrt{51}[/tex]
b = 7.14
b = 7.1
Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades? Express your first answer as a fraction in simplest form
Answer:
Hence the probability of getting 2 spades will be 1/16
Step-by-step explanation:
Given:
Two deck if playing cards
To Find:
Probability that will get two spades
Solution:
As we know that ,there 52 playing cards in a deck
and 13 of that are spades
So probability of getting spade from a deck is ,
P(spades)=total number of spades /Total number of cards.
P=13/52
P=1/4
Similar for the second deck of card,
Required probability is that , getting spades from each deck
It is given by,
Required probability =Probability of spades in 1st AND Probability of spade in 2nd deck
As there is use of AND operator there should multiplication of two events,
Required probability =1/4*1/4
=1/16
Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?
Answer:
The answer to your question is y = 4x + 2
Step-by-step explanation:
Data
slope = m = 4
Point = (1, 6)
Process
1.- Write the equation of the line in the point slope form.
y - y1 = m(x - x1)
2.- Identify the values of x1 and y1
x1 = 1 y1 = 6
3.- Substitution
y - 6 = 4(x - 1)
4.- Simplification
y - 6 = 4x - 4
5.- Solve for y
y = 4x - 4 + 6
6.- Result
y = 4x + 2
What is the domain of the function y=sqrt x+4
Answer:
domain of y = sqrt (x+4) is [-4, +inf)
Step-by-step explanation:
[-4, +inf), -4 is included because sqrt(-4 + 4) is defined but is undefined at the points from (-inf, -5].
antiderivative of Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 6 x 5 − 8x4 − 9x2.) f(x) = 6x5 − 8x4 − 9x2 the function.
Answer:
x^6 - (8/5)x^5 - 3x^3 + C.
Step-by-step explanation:
f(x) = 6x^5 - 8x^4 - 9x^2.
Using the general form antiderivative of Ax^m = Ax(m+1) / (m+1)+ C:
Antiderivative = 6 * x^(5+1) / 6 - 8 * x^(4+1) / 5 - 9 * x^(2+1) / 3 + C
= 6x^6/6 - 8x^5/5 - 9x^3/3 + C
= x^6 - (8/5)x^5 - 3x^3 + C.
Differentiating:
f'(x) = 6x^(6-1) - 8 x^(5-4) - 9x^(3-1) + 0
f'(x) = 6x^5 - 8x^4 - 9x^2.
The most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2 is F(x) = x^6 - 8/5 * x^5 - 3x^3 + C, where C is the constant of the antiderivative.
Explanation:To find the most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2, we need to perform the process of integration, which is the reverse of differentiation. The antiderivative F(x) will be found by integrating each term of the function separately.
The antiderivative of f(x) will then be:
F(x) = ∫6x5 dx - ∫8x4 dx - ∫9x2 dx,
Transitioning to the next step by applying the power rule for integration, we add 1 to the exponent and divide by the new exponent, we obtain
F(x) = 6/6 * x^(5+1) - 8/5 * x^(4+1) - 9/3 * x^(2+1) + C
Simplified, the antiderivative F(x) becomes:
F(x) = x^6 - 8/5 * x^5 - 3x^3 + C,
where C is the constant of the antiderivative.
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A writer’s last four articles and fees paid have been recorded below. What is the rate of change in the writer’s fee from writing a 700-word article to an 800-word article
Answer:
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Step-by-step explanation: