Answer:
You are squaring x and -5 on the first equation, and on the second equation you are just squaring x and subtracting 5.
Step-by-step explanation:
And since on the first equation x and -5 are in parenthesis that means that the square goes to both of them.
And the second one there is no parenthesis so the square only goes to the x.
I hope this helps you.
A. Differentiate the following functions using product rule and quotient rule.
B. Differentiate the following using Chain Rule.
The following results by product rule and quotient rule are listed below:
[tex]f'(x) = 3\cdot x^{2}-15\cdot x - 9[/tex][tex]f'(x) = \frac{15}{2} \cdot x^{4}-6\cdot x^{3}+\frac{45}{2}\cdot x^{2}-\frac{81}{2} \cdot x +13[/tex][tex]f'(x) = \frac{90\cdot x^{2}-45\cdot x^{2}-40\cdot x +72}{25\cdot x^{4}-80\cdot x^{2}+64}[/tex][tex]f'(x) = \frac{\left(9\cdot x^{2}-18\cdot x-6\right)\cdot \left(\frac{x^{2}}{2}+7\cdot x-8 \right)-\left(3\cdot x^{3}-9\cdot x^{2}-6\cdot x +1 \right)\cdot \left(\frac{2}{3}\cdot x+7 \right)}{\left(\frac{x^{2}}{2}+7\cdot x-8 \right)^{2}}[/tex]
The following results by chain rule are listed below:
[tex]f'(x) = 3\cdot (2\cdot x^{2}-2\cdot x +1)^{2}\cdot (4\cdot x-2)[/tex][tex]f'(x) = \frac{15\cdot x^{2}-16\cdot x+9}{2\cdot \sqrt{5\cdot x^{3}-8\cdot x^{2}+9\cdot x-6}}[/tex][tex]f'(x) = \frac{2\cdot \left(6\cdot x-\frac{2}{3}-4\cdot x^{-5} \right)}{3\cdot \sqrt[3]{3\cdot x^{2}-\frac{2}{3}\cdot x +x^{-4} } }[/tex]How to apply product rule and quotient rule to obtain the derivative of function
In this part we must apply the following rules to calculate the derivatives:
Product rule[tex]\frac{d}{dx}[f(x)\cdot g(x)] = f'(x) \cdot g(x) + f(x) \cdot g'(x)[/tex] (1)
Quotient rule
[tex]\frac{d}{dx}\left[\frac{f(x)}{g(x)} \right] = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{[g(x)]^{2}}[/tex] (2)
Now we proceed to obtain each expression:
1) [tex]f'(x) = 3\cdot x\cdot (x-6)+3\cdot x-9[/tex]
[tex]f'(x) = 3\cdot x^{2}-15\cdot x - 9[/tex] [tex]\blacksquare[/tex]
2) [tex]f'(x) = \left(\frac{9}{4}\cdot x^{2}-4\cdot x+\frac{1}{4}\right)\cdot (2\cdot x^{2}-2\cdot x + 4) + \left(\frac{3}{4}\cdot x^{3}-2\cdot x^{2}+\frac{x}{4}-6\right)\cdot (4\cdot x-2)[/tex]
[tex]f'(x) = \frac{9}{2}\cdot x^{4}-8\cdot x^{3}+\frac{1}{2}\cdot x^{2}-\frac{9}{2}\cdot x^{3}+8\cdot x^{2}-\frac{x}{2}+9\cdot x^{2}-16\cdot x+1 +3\cdot x^{4}-8\cdot x^{3}+x^{2}-24\cdot x-\frac{3}{2}\cdot x^{3}+4\cdot x^{2}-\frac{x}{2} +12[/tex]
[tex]f'(x) = \left(\frac{9}{2}+3 \right)\cdot x^{4}+\left(-8-\frac{9}{2}+8-\frac{3}{2} \right)\cdot x^{3} + \left(\frac{1}{2}+8+9+1+4 \right)\cdot x^{2} + \left(-16-24-\frac{1}{2} \right)\cdot x + \left(1+12\right)[/tex]
[tex]f'(x) = \frac{15}{2} \cdot x^{4}-6\cdot x^{3}+\frac{45}{2}\cdot x^{2}-\frac{81}{2} \cdot x +13[/tex] [tex]\blacksquare[/tex]
3) [tex]f'(x) = \frac{-9\cdot (5\cdot x^{2}-8)-(-9\cdot x+4)\cdot (10\cdot x)}{(5\cdot x^{2}-8)^{2}}[/tex]
[tex]f'(x) = \frac{-45\cdot x^{2}+72+90\cdot x^{2}-40\cdot x}{25\cdot x^{4}-80\cdot x^{2}+64}[/tex]
[tex]f'(x) = \frac{90\cdot x^{2}-45\cdot x^{2}-40\cdot x +72}{25\cdot x^{4}-80\cdot x^{2}+64}[/tex] [tex]\blacksquare[/tex]
4) [tex]f'(x) = \frac{\left(9\cdot x^{2}-18\cdot x-6\right)\cdot \left(\frac{x^{2}}{2}+7\cdot x-8 \right)-\left(3\cdot x^{3}-9\cdot x^{2}-6\cdot x +1 \right)\cdot \left(\frac{2}{3}\cdot x+7 \right)}{\left(\frac{x^{2}}{2}+7\cdot x-8 \right)^{2}}[/tex] [tex]\blacksquare[/tex]
How to apply chain rule to find derivativesLet be a function of the form [tex]f[u(x)][/tex], the derivative of this function is defined by the following rule:
[tex]\frac{d}{dx}[f[u(x)]] = \frac{df}{du}\cdot \frac{du}{dx}[/tex]
Now we proceed to present the following results:
1) [tex]f'(x) = 3\cdot (2\cdot x^{2}-2\cdot x +1)^{2}\cdot (4\cdot x-2)[/tex] [tex]\blacksquare[/tex]
2) [tex]f'(x) = \frac{15\cdot x^{2}-16\cdot x+9}{2\cdot \sqrt{5\cdot x^{3}-8\cdot x^{2}+9\cdot x-6}}[/tex] [tex]\blacksquare[/tex]
3) [tex]f'(x) = \frac{2}{3}\cdot \left(3\cdot x^{2}-\frac{2}{3}\cdot x+x^{-4} \right)^{-\frac{1}{3} } \cdot \left(6\cdot x-\frac{2}{3} -4\cdot x^{-5} \right)[/tex] [tex]\blacksquare[/tex]
[tex]f'(x) = \frac{2\cdot \left(6\cdot x-\frac{2}{3}-4\cdot x^{-5} \right)}{3\cdot \sqrt[3]{3\cdot x^{2}-\frac{2}{3}\cdot x +x^{-4} } }[/tex] [tex]\blacksquare[/tex]
To learn more on derivatives, we kindly invite to check this verified question: https://brainly.com/question/23847661
What can Slope be???????
Answer:
Slope = -5
Step-by-step explanation:
(x,y) ⇒ (13,11), (14,6), (15,1), (16,-4)
Pick any two points:
(x₁, y₁) and (x₂, y₂) ⇒ (15, 1) and (16, -4)
Use the slope formula:
⇒ y₂ - y₁/x₂ - x₁
⇒ -4 - 1/16 - 15
⇒ -5/1 = -5
Thus, the slope is -5.
Which point will you end at if you start at point b and move 6 right and 6 up coordinates
Find the substitution 2x+3y=-5 and y=-x+5
Answer: x = 20, y = -15
Step-by-step explanation:
Since we already know that [tex]y=-x+5[/tex], we can just substitute in that value of y into the other equation:
[tex]2x+3y=-5\\2x+3(-x+5)=-5\\2x-3x+15=-5\\-x=-5-15\\-x=-20\\x=20[/tex]
with the value of x, we can find the value of y:
[tex]y=-x+5=-20+5=-15[/tex]
pls help me plss!!!!!!
Answer: 9 divided by 5 = 1 and 4/5
Step-by-step explanation:
9 divided by 5 = 1 and 4/5
For the diagram, you will have one box completely full, and another 4/5 full.
A random number Generate is used to select a number from one to 100 what is the probability of selecting a even number
What is the equation of the line through (-2, -3) with a slope of 0
Step-by-step explanation:
Hey there!
The point is; (-2,-3) and slope is 0.
Use one point formula.
(y-y1) = m(x-x1)
Put all values.
(y+3) = 0(X+2)
y+3 = 0
y= -3
Therefore, the equation is y = -3.
Hope it helps...
f(x) = 2x-3 and g(x)=2x+1
Find (f+g) (x)
Answer:
(f + g)(x) = 4x - 2
Step-by-step explanation:
This problem is asking us to find the value of (f + g)(x).
This means that we will need to add the values of f(x) and g(x) together.
Therefore, the values that are defined for these two functions will simply be conjoined by addition.
Steps
Step 1: Place the value of f(x) in parentheses ⇒ (2x - 3). Then, do the same for g(x) ⇒ (2x + 1).
Step 2: Combine any like terms. Start with the terms that are not constants (variables with coefficients) and then combine constants.
Step 3: Simplify as much as possible.
Work Shown
[tex]$\tex$ f(x) = 2x - 3, g(x) = 2x + 1\\\\(f + g)(x) \ $\rightarrow$ \ f(x) + g(x)\\\\(2x - 3) + (2x + 1)\\\\\boxed{(4x - 2)}[/tex]
Therefore, (f + g)(x) = 4x - 2.
Hope this helps!
BD is a perpendicular bisector of AC. The length of BA is 6d + 3, and the length of BC is 10d - 25. What are the lengths of BA and
BC? (1 point)
The length of BA is 30. The length of BC is 50.
The lengths of BA and BC are both 7.
The lengths of BA and BC are both 45.
The length of BA is 40. The length of BC is 50.
The lengths of BA and BC are both 45.
Step-by-step explanation:
Remember For two perpendicular lines, all four angles formed by the two lines are equal to 90° Perpendicular lines are said to be conguent o 45+45=90 thus your answer!
75 less than four times a number is equal to the number. what is the number
Answer:
number = 25
Step-by-step explanation:
❖ First, let's set up the equation.
"75 less than four times a number" means 4x - 75"is equal to the number" means = n (n = number)n = 4n - 75Solving
Step 1: Subtract 4n from both sides
[tex]n-4n=4n-75-4n[/tex] [tex]-3n=-75[/tex]Step 2: Divide both sides by -3.
[tex]-3n/-3=-75/-3[/tex] [tex]n = 25[/tex]Step 3: Check if solution is correct.
[tex]25=4(25)-75[/tex] [tex]25=100-75[/tex] [tex]25=25[/tex]Therefore, the number is 25.
4. The R and D unit at a major auto-makers sampled 36 of the new Model JZ-5 sport cars. They ran each car for one hour on a test track. For the 36 cars the
mean mpg (miles per gallon) was x = 47.8 with a standard deviation of 4.8 mpg.
a. Construct a 98% confidence interval for the mean mpg for the entire year's production of the Model JZ-5.
b. State the meaning of the interval in the context of the problem.
100 points
Answer:
b
Step-by-step explanation:
if u do the math, everything makes sense.
1: what times 2 is 86
2: what times 2 is 32
3: what times 2 is 404
4: what times 1 is 38
Answer:
1=43
2=16
3=202
4=38
Step-by-step explanation:
HOPE THIS HELPED:)
Answer:
1: 43 times 2 is 86
2: 16 times 2 is 32
3: 202 times 2 is 404
4: 38 times 1 is 38
Step-by-step explanation:
For the function f(x) = 6x + 9, find the value of x.so that f(x) = 3.
. Peggy is p years old.
Maggie is 1 year less than ¼ of Peggy’s age. What is Maggie’s age in terms of p?
a. ¼p - 1
b. 1 - ¼p
c. ¼p + 1
d. ¼p
Answer:
Step-by-step explanation:
Peggy is p years old.
¼ of Peggy’s age is ¼p
1 year less than ¼ of Peggy’s age is ¼p - 1
so answer is A
In a survey, 150 people said they prefer shopping online. 75% said they prefer shopping online. How many people were surveyed?
A. 300
B. 225
C.200
D. 125
Find the area of the square
Solution:
[tex]\text{Area of square = L}^{2} \ \ \ \ \ \text{(L = Side)}[/tex]
[tex]\rightarrow \text{Area of square} = (3x^{2} - 5)^{2}[/tex]
Using the formula "(a + b)² = a² + 2ab + b²"
[tex]\rightarrow \text{Area of square} = (3x^{2} )^{2} - 2(3x^{2} )(-5) + 5^{2}[/tex]
Simplifying the LHS:
[tex]\rightarrow \text{Area of square} = (3x^{2} )(3x^{2} ) +(30x^{2} ) + 25[/tex]
[tex]\rightarrow \boxed{\text{Area of square} = 9x^{4} +30x^{2} + 25}[/tex]
which ratio is different from the other three A.8/20 B.12/30 C.6/10 D.14/35
A museum charges $12.50 for a one-day youth admission and $17.50 for a one-day adult admission. One Friday, the museum collected $1485 from a total of 106
youths and adults. How many admissions of each type were sold?
UZE
Answer:
number of youth admissions sold (x) = 74
number of adult admissions sold (y) = 32
Step-by-step explanation:
Let x = number of youth admissions
Let y = number of adult admissions
Given:
total number of admissions sold = 106⇒ x + y = 106
Given:
cost of youth admission = $12.50cost of adult admission = $17.50total amount collected = $1485⇒ 12.5x + 17.5y = 1485
Rewrite x + y = 106 to make y the subject:
⇒ y = 106 - x
Substitute y = 106 - x into 12.5x + 17.5y = 1485 and solve for x:
⇒ 12.5x + 17.5(106 - x) = 1485
⇒ 12.5x + 1855 - 17.5x = 1485
⇒ 5x = 370
⇒ x = 74
Substitute found value of x into y = 106 - x to find y:
⇒ y = 106 - 74
⇒ y = 32
In the graphic below, one palr of vertical angles is?
Answer:
1 and 6
Step-by-step explanation:
vertical angles = angles across diagonally which can either be 1 + 6 or 2 + 5, but only 1 + 6 is available
A publisher ships magazines in cube-shaped boxes. These boxes are placed into a larger box that measures 6 ft long, [Math Processing Error] ft wide, and 12 ft tall. The edge length of each cube-shaped box is [Math Processing Error] ft.
How many cube-shaped boxes can fit into the larger box?
648 boxes
9,216 boxes
10,368 boxes
36,864 boxes
Please hurry!! 30 Points!!!
Answer: I am pretty sure that 648 boxes is the answer.
Step-by-step explanation:
What is the relationship between the lines with the following equations? 6x+4y=−12 y=−3/2x−5 The lines are perpendicular. The lines are the same. The lines are neither parallel nor perpendicular. The lines are parallel.
Answer:
I think the answer is "The lines are parallel."
Step-by-step explanation:
Cam wants to find 509-106. Which steps can he use to find the difference
Answer:
Standard addition
509
-106
9-6=3
509
-106
------
3
0-0=0
509
-106
-------
03
5-1=4
509
-106
-------
403
403 is your answer and to check it you can add 403+106=509
Please mark brainly!! Have a great day!
(a)
Rewrite the decimal in the sentence below as a percentage.
The value had decreased to 0.02 of the purchase price.
Answer:
2%
Step-by-step explanation:
We can multiply a decimal by 100 to turn it into a percent.
0.02 * 100 = 2%
A car undergoing uniform acceleration from rest moves 25 meters in 7.5 seconds. What is the acceleration of the car?
Ok, so Jay has a goal of saving money to buy a handheld game console. Jay has reached 10% of his goal and saved $12. complete the bar
Answer:
if he reaches 20% he will make 22
It takes 0.5 gallon of cream to make 1 pound of butter How much butter could you make with 0.25 gallons of cream
Answer:
half a pound of butter
Step-by-step explanation:
The GCF of 28 and 64 is blank
Answer:
4
Step-by-step explanation:
the greatest common factor is 4 (maybe brainliest?)
Answer: 4
Step-by-step explanation:
The factors of 64 are 64, 32, 16, 8, 4, 2, 1
The factors of 28 are 1, 2, 4, 7, 14 and 28
Therefore the GCF is 4
Hope This Helps!
please help. please it's due soon
factor 20mn-15m show work
Answer:
hello
20 mn - 15 m
= 5 m ( 4 n - 3 )
Step-by-step explanation:
80 POINTS BRAINLIES !!!
PHOTO ATTACHED
ANSWER A THROUGH J
a) Which country had the lowest number of overall medals among the ten countries?
b) Which country/countries competed in the least number of games?
c) What is the mode in the number of games countries participated in?
d) What is the range between the gold medals awarded to the 10 countries?
e) How many countries got more silver medals than bronze medals?
f) Apart from the United States, which country/countries got more gold medals, more silver medals and more bronze medals than Great Britain?
g) In comparing the number of games a country participated in and the overall number medals received, which country did the best (ie highest number of metals recived per game )?
Show your work
h) Using the given Data, give TWO likely reasons why a country like Jamaica does not feature in the top 10 medals even though it does very well in athletics.
i) Using the given information, determine the medal category in which the United states far outperformed its closest competitor.
Show your work.
j) Which 3 countries had the most evenly distributed number of goals. Silver and bronze medals (i.e. least smallest range)?
Show your work.
PLEASE HELP DUE TODAY!! THANK YOU.
a) Hungary had the lowest total medal count at 491
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b) It's a tie between China and the Soviet Union with 10 games per country.
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c) The mode is 27 since it is the most frequent value in the "total games" column. The mode is not necessarily the largest or smallest value. It's simply the value that shows up the most. It is possible to have more than one mode, but in this case 27 shows up the most times and no other value ties it. The value 27 shows up three times with the countries Italy, Sweden, and the United States
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d) The range is 875. To find the range, subtract the largest value (max) and the smallest value (min). So we have range = max - min = 1022 - 147 = 875.
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e) Answer: 4
List of countries that got more silver than bronze = {China, Great Britain, Soviet Union, United States}
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f)
List of countries that got more gold, silver, and bronze compared to Great Britain
{Germany, Soviet Union}
So only two other countries fit the criteria
------------------------------------------------------------------------------
g)
Answer: The Soviet Union had the most medals per game (around 112 medals per game)
Work Shown:
For each row, divide the total medal count (in column F) by the number of games (in column B)
Australia = 497/26 = 19.1154 China = 543/10 = 54.3 France = 713/28 = 25.4643 Germany = 937/24 = 39.0417 Great Britain = 847/28 = 30.25 Hungary = 491/26 = 18.8846 Italy = 577/27 = 21.3704 Soviet Union = 1122/10 = 112.2 Sweden = 494/27 = 18.2963 United States = 2520/27 = 93.3333------------------------------------------------------------------------------
h)
The country is likely not large enough to participate in enough games, especially when compared to larger countries. They may be specialized in just one or two events, or one or two categories of events.
------------------------------------------------------------------------------
i)
Answer: Gold Medal (vs Soviet Union)
The United States has a total medal count of 2520. The closest competitor is the Soviet Union at 1122
To compare which category (gold, silver, bronze) the US did better at, we'll divide each corresponding medal count for the two countries. We'll have the Soviet Union's count as the numerator and the US as the denominator.
Gold = 440/1022 = 0.4305
Silver = 357/794 = 0.4496
Bronze = 325/704 = 0.4616
The lowest result is one where the US performed best at. The gold percentage is 43.05% meaning the Soviet Union's gold count is roughly 43.05% of the US gold count
------------------------------------------------------------------------------
j)
Answer: Hungary, Italy, Sweden
Explanation:
You'll subtract the min and max for each row to get the range for each country. Sort the ranges from smallest to largest to see the top three countries that have the smallest range.
For example, Australia's highest medal count is at 187 (bronze) and lowest medal count at 147 (gold) so the range here is 187-147 = 40.
The various answers for each of the sections are answered below;
A) Looking at the table on the seventh column, we see that the lowest number of overall medals is 491 and it is gotten by the country Hungary.
B) Looking at the third column of the table, the least number of games a country participated is 10 and there are two countries with that number namely China and the Soviet Union.
C) Mode simply means the most frequently occurring number or event. In this case, under the third column, the most occurring number is 27 games.
D) Formula for range is;
Range = Highest value - Least Value
Under the Gold Medal Column, highest value is 1022 and least value is 147. Thus;
Range = 1022 - 147
Range = 875.
E) Comparing the Silver and Gold gotten by each country, we can see that the countries that got more silver than bronze medals are; China, Great Britain, Soviet Union, United States. This is a total of 4 Countries.
F) Looking at the table, the only countries that got more gold, silver, and bronze respectively than Great Britain are Germany and Soviet Union.
G) For each country, to get their medals per game rate, we will just divide their medal total by the number of games in which they participated. Thus;
Australia = 497/26 ≈ 19
China = 543/10 ≈ 54
France = 713/28 ≈ 25
Germany = 937/24 ≈ 39
Great Britain = 847/28 ≈ 30
Hungary = 491/26 ≈ 19
Italy = 577/27 ≈ 21
Soviet Union = 1122/10 ≈ 112
Sweden = 494/27 ≈ 18
United States = 2520/27≈ 93
Country with most medals per game is Soviet Union with approximately 112 medals per game
H) Two reasons why a country like Jamaica that is very good in athletics does not feature on the table is because;
- The country is not big enough to participate in many events
- The number of medals in Athletics is nowhere near the total for other events in the Olympic games.
I) The medal category in which the united states far outperformed its closest competitor is in the Gold medal category because the united states had a gold medal count of 2520 while the soviet union had 440 and thus the difference between both Gold medal counts will produce the highest range.
J) The 3 countries had the most evenly distributed number of Gold, Silver and bronze medals are;
Italy with a range of 13
Hungary with a range of 14
Great Britain with a range of 23
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