Answers
To make things easier, first rewrite
f(x) = x / (x + 7/x) = x ² / (x ² + 7)
i.e. multiply f by x/x, which is valid because x can't be 0 anyway as it's outside the domain of f.
Now, by the quotient and chain rules, we get
f '(x) = ((x ² + 7) (x ²)' - x ² (x ² + 7)') / (x ² + 7)²
… = (2x (x ² + 7) - x ² (2x)) / (x ² + 7)²
… = (2x ³ + 14x - 2x ³) / (x ² + 7)²
… = 14x / (x ² + 7)²
f ''(x) = ((x ² + 7)² (14x)' - (14x) ((x ² + 7)²)') / ((x ² + 7)²)²
… = (14 (x ² + 7)² - (14x) (2 (x ² + 7)² (x ² + 7)')) / (x ² + 7)⁴
… = (14 (x ² + 7)² - (14x) (2 (2x) (x ² + 7)²)) / (x ² + 7)⁴
… = (14 (x ² + 7)² - 4x (14x) (x ² + 7)²) / (x ² + 7)⁴
… = 14 (x ² + 7)² (1 - 4x) / (x ² + 7)⁴
… = 14 (1 - 4x) / (x ² + 7)²
… = (14 - 56x) / (x ² + 7)²
Related Questions
Triangle GHI is dilated to form new triangle JKL. If angle H is congruent to angle K, what other information would prove that the two triangles are similar by the capital AA similarities postulate?
Answers
Answer: Angle I is congruent to angle L
Step-by-step explanation:
Did da test
To prove ΔGHI and ΔJKL are similar following statements must be true,
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex][tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
What are similar triangles?"Two or more triangles are similar if and only if the corresponding angle measures same and their corresponding side lengths are in proportion.."
What is dilation?"It is a geometric transformation where there is a change in the size of an object without changing its shape.""The size of the object changes on the basis scale factor."For given example,
ΔGHI is dilated to form new ΔJKL.
Also, angle H is congruent to angle K.
To prove ΔGHI and ΔJKL are similar.
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
Therefore, to prove ΔGHI and ΔJKL are similar following statements must be true,
i) angle I and angle L are congruent.
ii) angle G and angle J are congruent
iii) sides of the triangles are in proportion
⇒[tex]\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}[/tex]
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A class of 195 students went on a field trip. They took 19 vehicles, some cars and some buses. If
each car holds 5 students and each bus hold 25 students, how many buses did they take?
Answers
Answer:
1car 8 bus
Step-by-step explanation:
1×5=5
8×25=190
What is the minimum of the sinusoidal function?
Answers
Answer: The minimum is -4.
Step-by-step explanation:
The minimum of a function:
y = f(x)
will be the smallest value of y that the function gives.
such that, if the minimum is y = m
m ≤ f(x) ∀ x
In this case, we can see that the smallest value of y is:
y = -4
Then the minimum of the sinusoidal function is -4.
Question 4 Given that P = 6 and a 2, which yields a quotient greater than -9? O A 3 B 3() c Зр (-2) (-p) (-3)
Answers
Answer:
I think is A or B I don't know
Answer:
a
Step-by-step explanation:
Use the drop down menus to complete the statement to match the information shown by the graph
Answers
Answer:
yes ikow
Step-by-step explanation:
you can do that if you want to buy
Answer:
where the graph?
Step-by-step explanation:
Solve the system of linear equations by elimination. 8x-5y=11 4x-3y=5
Answers
Answer:
(x,y)= ( 5 over 273, - 265 over 273)
Step-by-step explanation:
After solving the obtained equation with the elimination method the obtained value of x and y will be 2 and 1 respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that,
8x-5y=11 ------ (1)
4x-3y=5 --------- (2)
In order to solve the above equation with the elimination method, we have to apply the multiplicative distribution law as,
Multiply by 2 in equation 2
2(4x-3y=5)
8x- 6y = 10 ----- (3)
Subtract equation 3 from equation 1,
(8x- 6y)-(8x-5y) = 10 - 11
8x-8x-6y+5y = -1
-y = -1
y=1
Substitute the value of y in any of the equations 1 to get the value of x
8x-5y=11
8x-5(1)=11
8x-5=11
8x=16
x=2
Thus, after solving the obtained equation with the elimination method the obtained value of x and y will be 2 and 1 respectively.
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Elena went 60 meters in 15 seconds. Noah went 50 meters in 10 seconds. Elena and Noah both moved at a constant speed. Who went faster?
Answers
Answer:
Noah went faster.
Step-by-step explanation:
Elena: 60 divided by 15 = 4
Noah: 50 divided by 10 = 5.
5 meters per second is greater than 4 meters per second, making Noah faster than Elena.
Write -√-49 as an imaginary number using i.
Represent 4-3i on the graph
Answers
-/-1 * 7 * 7
-7i
4 - 3i
Go to 4 on the x axis (right)
Go to -3i on the y axis (down)
Your coordinate is (4, -3i)
To graph -3i, it is like 0 - 3i
Your coordinate is (0, -3i)
1/2x5/6, as a fraction, because my brain is not remembering rn
Answers
Answer:
5/12
Step-by-step explanation:
you just multiply the numerators and the denominators
Simply
x + 50 × 10 = 150
Answers
Answer:
x + 50 × 10 = 150
x+500=150
x=150-500=-350
Step-by-step explanation:
solution,
here,
given,
x+50*10 = 150
or, x+500=150
or, x= 150 -500
therefore, x= -350
hope this helps u..
Can someone solve this please
Answers
Answers:
11.) 0.25
12.) 3:20
13.) 0.75
14.) 19
Answer:
Question 11: 0.25
Question 12: 3:20
Question 13: 0.75
Question 14: 19
The force acting on a beam was measured 5 times under the same operating conditions. This process was repeated by 3 observers, resulting in 3 sets of data. The standard deviations of these data sets were: Standard Deviation 1= 1.11, Standard Deviation 2= 0.99, Standard Deviation 3= 1.15 The corresponding mean values were: 52.3, 51.5, and 52.7, respectively. Compute the Pooled Standard Deviation for these data sets. (Provide your answer using two decimal places)
Answers
Answer:
The Pooled Standard Deviation for these data sets is 1.09
Step-by-step explanation:
Given that;
Standard Deviation 1 = 1.11
Standard Deviation 2 = 0.99
Standard Deviation 3 = 1.15
pooled standard deviation is given as;
[tex]S_{pooled}[/tex] = (n1 - 1 )s1² + ..... + ( nk - 1 )sk² / n1 + ..... + nk - 1
where n1, n2....., nk are the sample sizes of k groups and s1, s2, ....., sk are the standard deviations of k groups respectively
so for the 3 groups;
[tex]S_{pooled}[/tex]² = (n1 - 1 )s1² + (n2 - 1 )s2² + ( n3 - 1)s3² / n1 + n2 + n3 - 3
we substitute
[tex]S_{pooled}[/tex]² = (5 - 1 )1.11² + (5 - 1 )0.99 ² + ( 5 - 1)1.15² / 5 + 5 + 5 - 3
[tex]S_{pooled}[/tex]² = (4.9284 + 3.9204 + 5.29) / 12
[tex]S_{pooled}[/tex]² = 14.1388 / 12
[tex]S_{pooled}[/tex]² = 1.1782
[tex]S_{pooled}[/tex] = √1.1782
[tex]S_{pooled}[/tex] = 1.08544 ≈ 1.09
Therefore, The Pooled Standard Deviation for these data sets is 1.09
Help me with this one please
Answers
-7
Explanation:
(-3)^2- (-4)^2 =
= 9 - 16 = -7
Complete the table for
y = x/4 -1
Answers
Answer:
X Y
0 -1
2 -0.5
4 0
6 0.5
8 1
Step-by-step explanation:
I hope i got that right
Which statement is true based on the graph ?
Answers
Answer:
C: The speed increases from A to F
Step-by-step explanation:
Check each node A to F including A and F.
B is higher than A, C is higher than B, ...
This is true for all of them, so it is increasing.
The speed of the car is increasing in the time interval from point A to point F. Option C is correct.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
What is the graph?The graph depicts the relationship between the x and y axes through the use of curves.
Here,
The graph shows the speed and time relation of the car,
Where,
The speed of the car is increasing from A to F,
The speed of the car is decreasing from F to G,
The speed of the car is increasing from G to H,
The speed of the car is decreasing from H to K,
Thus, the car's speed increases over the time span from point A to point F. Option C is the right answer.
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5. Licorice are 5 cents. How many licorice can you buy
with 10 cents?
Answers
Answer:
2
Step-by-step explanation:
5+5=10
12) Find the zeros of the function:
f(x) = x2 + 5x – 36
IS
Answers
Answer:
x² +5x - 36
= x² - 4x + 9x - 36
= x(x - 4) +9(x - 4)
= (x - 4) (x+9)
so x = 4, - 9
Who can help me with this
Answers
Answer:
Growth
Step-by-step explanation:
Given
[tex]\frac{2}{3}(2.5)^x[/tex]
Required
Growth or decay
The general form is:
[tex]y = ab^x[/tex]
Such that:
[tex]b = rate[/tex]
For b, we have the following conditions:
[tex]b > 1[/tex] ----- Growth
[tex]0<b <1[/tex] --- Decay
[tex]b = 1[/tex] ---- None
Compare [tex]\frac{2}{3}(2.5)^x[/tex] to [tex]y = ab^x[/tex]
[tex]b = 2.5[/tex]
Because 2.5 > 1, then the first condition applies (growth)
f one Canadian dollar is equivalent to US$0.8150, how much do you need in
Canadian funds to buy US$800.00? (2 ma
Answers
Answer:
It will take $ 989.59 in Canadian funds to buy $ 800.
Step-by-step explanation:
If one Canadian dollar is equivalent to US $ 0.8150, in order to determine how much money is needed in Canadian funds to buy US $ 800.00 the following calculation must be performed:
0.8150 = 1
800 = X
(800 x 1) / 0.8150 = X
800 / 0.8150 = X
981.59 = X
Therefore, it will take $ 989.59 in Canadian funds to buy $ 800.
Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided the following data:
Brown Williams Williams Williams Brown
Smith Johnson Williams Smith Miller
Johnson Williams William Johnson Jones
Miller Jones Jones Smith Smith
Miller Johnson Smith Jones Jones
Johnson Smith Brown Smith Johnson
Jones Smith Smith Williams Brown
Johnson Johnson William Smith Brown
Smith Miller Johnson Brown Johnson
Brown Jones Miller Smith Miller
Summarize the data by constructing the following:
A. Relative and percent frequency distributions
B. A bar chart
C. A pie chart
D. Based on these data, what are the three most common last names?
Answers
Answer:
Kindly check attached picture for barchart and piechart distribution
Step-by-step explanation:
Given the name data:
Name ____ freq ___R/Freq ____% frequency
Brown ____7 ______0.14 ______14
Smith ____ 12 -____ 0.24 ______24
Williams__ 8 ______0.16 ______ 16
Miller ____6 ______0.12 ______ 12
Jones ___ 7 ______ 0.14 ______ 14
Johnson _ 10 _____ 0.20 ______20
The three most popular last names are :
Smith, Johnson and Miller
Based on the information given in the bar chart, it should be noted that the most popular last names are Smith, Johnson, and Williams.
Solving the bar chart.It should be noted that the information given in the question is used in solving the bar chart and pie chart.
The name with the least number of people is Miller. On the other hand, the most popular last names are Smith, Johnson, and Williams.
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Write a classification essay to describe two types of animal flight
Answers
One of the two basic types of animal locomotion: powered flight, actual flight, or gliding. Real wings are only found in most bird species, most insect orders, and bats.
What are the categories?A category listing is a list of various product categories, such as children's clothing, women's clothing, and men's clothing. Any form of a category can be simply created
Soaring and gravitational gliding are two distinct types of gliding flight.
In controlled gravitational gliding, a creature propels itself in a precise direction after delaying its descent and relying on the wind for horizontal motion (parachuting).
Adaptations for guided gliding are primarily made to increase glide ratio (the amount of horizontal distance covered per unit descent)
Therefore, powered flight or true flight are the two basic categories of animal locomotion.
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Rachel has 2/3 pound of snack mix. She eats 5/12 of the snack mix.
How much of the snack mix did Rachel eat?
Enter your answer in the box as a fraction in simplest form.
pound
Basic
Answers
Answer:
[tex]\frac{5}{18} pound of snack mix is eaten by Rachel.[/tex]
Step-by-step explanation:
Given
Total snack mix with Rachel [tex]\frac{2}{3}[/tex] Pounds
Snack mix eaten by Rachel [tex]= \frac{5}{12}[/tex] of the total snack mix
[tex]\frac{5}{12}[/tex] of the total snack mix accounts for
[tex]\frac{5}{12} * \frac{2}{3} = \frac{5}{18}[/tex] Pound
all vertical and horizontal cross-sections of any Cube are all the same size and shape what about vertical and horizontal cross-sections of a pyramid are they all the same size are they all the same shape discuss why or why not
Answers
Answer:
All the horizontal sections are the same shape like their base, but have different sizes.
All vertical sections through top are triangles, size are different.
The vertical sections not cut through top are 4 sided shapes, sizes are different.
Step-by-step explanation:
If f(x) = x3+ x2and g(x) = x4+ x2+ x, what is the value of f(x) –g(x) when x = 1?
A) -2
B) -1
C) 1
D) 5
Answers
Answer:
B) -1Step-by-step explanation:
[tex]f(x)=x^3+x^2\\\\g(x)=x^4+x^2+x[/tex]
METHOD 1[tex]f(x)-g(x)=(x^3+x^2)-(x^4+x^2+x)=x^3+x^2-x^4-x^2-x\\\\=-x^4+x^3-x\\\\x=1\\\\-1^4+1^3-1=-1+1-1=-1[/tex]
METHOD 2[tex]x=1\\\\f(1)=1^3+1^2=1+1=2\\\\g(1)=1^4+1^2+1=1+1+1=3\\\\f(1)-g(1)=2-3=-1[/tex]
The price of Stock A at 9 A.M. was $12.21. Since then, the price has been increasing at the rate of $0.11 each hour. At noon the price of Stock B was $12.71. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
Answer:
mildiu usa so lapuaña kqyiq iwguiq oga oga. apphq. kgaoa
Step-by-step explanation:
suost. oaabqj the ksysa
Sheila rolled a number cube numbered 1 through 6 and tossed a coin for heads, H, or tails, T.
Which list represents all the possible outcomes of rolling the numbercube and tossing the
coin?
Answers
Kamala has 2 liter of soup. he pours it into 4 bowls. each bowl gets an equal amount. how many millilitres of soup are in each bowl?
Answers
Answer:
500ml
Step-by-step explanation:
[tex]2000 \div 4 = 500[/tex]
Answer:
500 ml
Step-by-step explanation:
2 litres= 2000 millilitres divided into 4 bowls=2000÷4=500 millilitres
The rectangle can be made into a hollow cylinder with height 40cm and radius 1.910cm.
a) calculate the volume of this cylinder.
Answers
Answer:
458.45 cm³
Step-by-step explanation:
Volume of a cylinder is A = πr²h.
A = π(1.910)²(40)
A = 458.43 cm³
Multiply and divide decimals.
One pound of chocolate chip cookies cost $3.79. David buys exactly 5 pounds of chocolate chip cookies. How much will the cookies cost?
State Your answer. Give Details. Explain what you did and justify Your steps.
And also, you'll get brain if u do these directions. :)
Answers
Answer:
5 pounds of chocolate chip cookies cost $18.95.
Step-by-step explanation:
If one pound of chocolate chip cookies cost $3.79, then 5 pounds of chocolate chip cookies will cost 3.79 times 5 dollars, which is equal to $18.95.
Hope this helps!
A profit of a football club after a takeover is modeled by p(t) = t3 - 14t2 + 20t + 120, which t is the number of years after the takeover. In which years was the club making loss?
Answers
p(t) = t^3 - 14t^2 + 20t + 120
Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10
Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)
0 = 3t - 2
2 = 3t
2/3 = t
Plug 2/3 into original equation, this is a maximum. We want the minimum:
0 = t - 5
5 = t
Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5
The club losses during the years 4.89 years<t<11.29 years.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
Profit of a football club after a takeover is modeled by p(t) = t³ - 14t² + 20t + 120,
t is the number of years after the takeover
We need to find in which years was the club making loss
p(t) = t³ - 14t² + 20t + 120,
the profit is negative when the club is in loss.
Plot the cubic equation
The profit p(t) is negative in the interval (4.89,11.29)
The number of years t cannot be a negative number
Hence the club lost during the years 4.89 years<t<11.29 years.
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