Answer:
E
Step-by-step explanation:
We are given:
[tex]\ln(xy)=x-y[/tex]
And we want to find the second derivative at the point (1, 1).
So, we will take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\big[\ln(xy)\big]=\frac{d}{dx}\big[x-y\big][/tex]
Implicitly differentiate. The left will require the chain rule. Hence:
[tex]\displaystyle \frac{1}{xy}\cdot \frac{d}{dx}\big[xy\big]=1-\frac{dy}{dx}[/tex]
Differentiate:
[tex]\displaystyle \frac{1}{xy}\cdot \big( y+x \frac{dy}{dx} \big) =1-\frac{dy}{dx}[/tex]
Distribute:
[tex]\displaystyle \frac{1}{x}+\frac{1}{y}\frac{dy}{dx}=1-\frac{dy}{dx}[/tex]
Isolate the derivative term:
[tex]\displaystyle \frac{dy}{dx}\big(\frac{1}{y}+1\big)=1-\frac{1}{x}[/tex]
Divide:
[tex]\displaystyle \frac{dy}{dx}=\frac{1-\frac{1}{x}}{\frac{1}{y}+1}}[/tex]
Simplify. We can multiply both layers by xy. Hence:
[tex]\displaystyle\begin{aligned} \frac{dy}{dx}&=\frac{1-\frac{1}{x}}{\frac{1}{y}+1}}\cdot\frac{xy}{xy} \\ &=\frac{xy-y}{x+xy} \end{aligned}[/tex]
We can factor. Hence, our derivative is:
[tex]\displaystyle \frac{dy}{dx}=\frac{y(x-1)}{x(y+1)}[/tex]
Differentiate once more to find the second derivative:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{d}{dx}\Big[\frac{y(x-1)}{x(y+1)}\Big][/tex]
Quotient rule:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{\frac{d}{dx}[y(x-1)](x(y+1))-y(x-1)\frac{d}{dx}[x(y+1)]}{(x(y+1))^2}[/tex]
Differentiate using the product rule:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ \big[\frac{dy}{dx}(x-1)+y\big](x(y+1))-y(x-1)\big[(y+1)+x\frac{dy}{dx}\big] }{(x(y+1))^2 }[/tex]
You may choose to simplify, but this is not necessary, as we are only interested in the second derivative at (1, 1).
First, since first derivatives exist in our second derivative, we will find them first. Recall that the first derivative is given by:
[tex]\displaystyle \frac{dy}{dx}=\frac{y(x-1)}{x(y+1)}[/tex]
Therefore, at (1, 1), the first derivative is:
[tex]\displaystyle \frac{dy}{dx}_{(1, 1)}=\frac{1(1-1)}{1(1+1)}=\frac{1(0)}{1(2)}=0[/tex]
So, we will substitute 0 for every dy/dx for our second derivative. Thus:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ \big[(0)(x-1)+y\big](x(y+1))-y(x-1)\big[(y+1)+x(0)\big] }{(x(y+1))^2 }[/tex]
Simplify:
[tex]\displaystyle \frac{d^2y}{dx^2}=\frac{ y(x(y+1))-y(x-1)\big[(y+1)\big] }{(x(y+1))^2 }[/tex]
So, at the point (1, 1), our second derivative is:
[tex]\displaystyle \frac{d^2y}{dx^2}_{(1, 1)}=\frac{1(1(1+1))-1(1-1)(1+1)}{(1(1+1))^2}=\frac{2-0}{4}=\frac{1}{2}[/tex]
Hence, our final answer is E.
HELP Find the value of x
Answer:
90
Step-by-step explanation:
Any two lines coming from the two edges of a diameter when they meet it gives 90
hi, my homework is on khan academy but my screen is ALL broken. cant solve problem, pls dont delete this, need somebodys help. :(
Answer:
Try finding some place with cheap screen fixing prices. If you can't, ask a friend if they know how to do this type of stuff.
Step-by-step explanation:
When P(x) is divided by x-2 the quotient is Q(x) and the remainder is 5.When Q(x) is divided by x^2+2x+4 the remainder is 2x-3.What is remainder when P(x) is divided by x^3-8
Step-by-step explanation:
P(x)
= (x - 2)Q¹(x) + 5
= (x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5.
Since x³ - 8 = (x - 2)(x² + 2x + 4),
(x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5
= (x - 2)(x² + 2x + 4)Q²(x) + (x - 2)(2x - 3) + 5
= (x³ - 8)Q²(x) + (2x² - 7x + 11).
Hence when P(x) is divided by (x³ - 8),
the remainder is 2x² - 7x + 11.
help please will give brainliest
Answer:
B. the slope is 1/4
the y-intercept is (0,3)
Step-by-step explanation:
(-8,1)(0,3)
rise/run
Find the slope of the line.
a. Undefined
b. 0
c. 3/2
d. -1
Answer:
Haven't found the answer but in the comments above me someone said it was D and it was def not D so try anything other than that, I just took the test on Edg2020
Step-by-step explanation:
Alice had x dollars in her account. She spends $35.31 to buy Medicines for her grandmother. If the balance in her account is $161.23, what was the amount in her account before purchase.?
Answer:
Alice started with $196.54 in her account.
Step-by-step explanation:
161.23 + 35.31 = 196.54
find the zeros of the function: f(x)=3x^2-5x+3
Answer:
x = 5 ± i √ 11 /6
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x .
You draw a 52-card deck. Then the card is replaced in the deck, the deck ls shuffled and you draw again. Find the probability of drawing a red card each time
Answer:
we know that the probability of drawing black card is 26/52. Probability of drawing a king is 4/52
Step-by-step explanation:
In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year (a) What will the population be in the year 2033? Population size = (b) In what year will the population have tripled? Year = Note You can earn partial credit on this problem
Answer:
(a) The population in the year 2033 is 18630.
(b) After nearly 36years from the starting population of 11500 we will get our population tripled.
Step-by-step explanation:
In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year
This can be formulated with the compound interest formula, also we can think the given situation as we have 11500 rupees which increases at the rate of 3.1% per year.
we can formulate the given situation using the compound interest formula.
A = P(1 + [tex]\frac{r}{n}[/tex])^n*t
A is the final population
P is the initial population = 11500
r is the rate at which the population increases = 3.1A =% = 0.031
n denotes the number of times the population increases per year = 1
t is the time or year = 1
A = [tex]11500( 1 + 0.031)[/tex]^1*t
(a) The number of years to reach the year 2033 from 2017 is 16years.
so we have the value of t = 16
so the final population in the year 2033 will be
A = 11500(1+0.031)^1*16
= 11500(1.031)^16
= 11500*1.63
A = 18630
Therefore the population size in the year 2033 will be 18630.
(b) We need to find the year in which the population gets tripled. we will triple our population from the population which was in 2017
so the our equation will be
11500*3 = 11500(1+0.031)^1*t
3 = (1.031)^t
upon taking logarithm both sides we get
log(3) = t*log(1.031) ( using the property log(a^b) = blog(a)
0.477 = t*0.133
t = 0.477/0.0133
t = 35.86years
upon taking approximation we will get 36 years.
Therefore after nearly 36years from the starting population of 11500 we will get our population tripled.
Use the graph to find the solution y=x+4 y=-2x-2
Answer:
(-2 , 2)
Step-by-step explanation:
y=x+4
y=-2x-2
x+4=-2x-2
3x=-6
x=-2
y=2
graph attached
[tex]\large\boxed{\boxed{\pink{\bf \leadsto (-2,2) \ is \ the \ solution \ of \ the \ given \ linear \ equations .}}}[/tex]
Step-by-step explanation:Given to equations to us are ,
[tex]\qquad \red{\bullet} \: y = x + 4 \\\\\qquad \red{\bullet} \: y = -2x - 2 [/tex]
And we need to find the solution using graphical method.
So , after plotting the graph of both equations the point where both lines intersect will be the solution of the graph.
And , for plotting we need at least two points .
For equation (1) :-
[tex]\implies y = x + 4 [/tex]
When x = (-4) .
[tex]\implies y = -4+4\\\\\bf\implies y = 0 [/tex]
When x = (-3)
[tex]\implies y = -3+4\\\\\bf\implies y = -1 [/tex]
[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-4) & (-3) \\\cline{1-3} \bf y & 0 & 1 \\\cline{1-3}\end{tabular}}[/tex]
For equation 2 :-
[tex]\implies y = -2x - 2 [/tex]
When x = (-1) .
[tex]\implies y = -2(-1)-2\\\\\bf\implies y = 0 [/tex]
When x = (0)
[tex]\implies y = 0-2\\\\\bf\implies y = -2 [/tex]
[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-1) & 0 \\\cline{1-3} \bf y & 0 & -2 \\\cline{1-3}\end{tabular}}[/tex]
Now , let's plot their graphs. Graph is in attachment. Hence on plotting the graph we see that both the lines Intersect on (-2,2) . Hence x = -2 and y = 2 is the solution of the given linear equation.
Hence (-2,2) is the solution of the given pair of linear equations in two variables.Patrick makes chocolate chip cookies. The recipe calls for 1 3/4 cups of flour. If Patrick triples the recipe, how much flour will he need?
Answer:
21/4 or 5 1/4
Step-by-step explanation:
Answer: 1 1/3 * 3 = 4
What is an equation of the line that passes through the points (4, -2) and (8, – 7)?
Answer:
y = -1.25x + 3
Step-by-step explanation:
To see if the coordinate pairs are on this line, plug x into the equation above.
y = -5 + 3
y = -2, so (4, -2) is on that line.
y = -1.25(8) + 3
y = -10 + 3
y = -7, so (8, -7) is also on that line.
Answer:
y = -1.25x + 3
Step-by-step explanation:
i got it right
Answer correct plz if u steal points ill report
Answer:
I think it might be y= x+2
Step-by-step explanation: because it is going up times 2 every time
OWO
Select all the correct answers.
Which expressions below are equal to each other?
3 × (4 + 2)
3 + (4 × 2)
(3 × 4) × 2
(3 × 4) + 2
(3 + 4) + 2
3 × (4 × 2)
Answer:
Answers 3 ((3x4)x2) and 6 (3x(4x2)) are equal to eachother.
Step-by-step explanation:
1. 3(4+2)=18
2. 3+(4x2)=11
3. (3x4)x2=24
4. (3x4)+2=14
5. (3+4)+2=9
6. 3x(4x2)=24
3. and 6. are the only two answers that have the same outcome, therefore equaling eachother.
Y=7/8x-3/2
Y=-8/7x-3/2
Y=-3/2x+7/8
Y=-7/8x-3/2
Answer:
second option
Step-by-step explanation:
Jason buys 8 colored markers at the art store. He handed the cashier $15. The cashier gave him back $1. How much did each marker cost?
Answer:
2.25
Step-by-step explanation:
i think though
Each colored marker costs $1.75.
What is Unit Rate?The amount of one quantity in another single quantity is termed as the unit rate of that quantity.
For example, speed is a unit rate in terms of distance and speed.
Number of colored markers Jason bought = 8
Cash that Jason gives the cashier = $15
Cash that cashier gives back = $1
Price of 8 colored markers = 15 - 1
= $14
We have to find the unit rate of the colored marker, that is the price of one colored marker.
Let x be the cost of the one colored marker.
Using proportion,
8 : 14 = 1 : x
8/14 = 1/x
Doing cross multiplication,
8x = 14
x = 14/8
x = 1.75
Hence the unit rate of the colored marker or the cost of one colored marker is $1.75.
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Of the 200 students in school 90 volunteered to work the book sale. what percent of students volunteered?
Answer:
45%
Step-by-step explanation:
90/200 = 0.45
0.45 = 45%
noob
What is the equation of the line that passes through the points (-3, -2) and (1, 6)?
Answer:
y = 2x +4
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~
(1, 6)
(- 3, - 2)
m = 2
y - 6 = 2 ( x - 1 ) <------ ( point-slope form )
y = 2x + 4 <------- ( slope-intercept form )
2x - y = - 4 <------ ( standard form )
Determine the equation of the line that passes through the given points (if you have a graphing calculator, you can use the table feature to confirm that the coordinates of both satisfy your equation.
(0, 6) and (-10, 0)
a. y = -0. 6x + 6
b. y = 0. 6x 6
c. y = 6x + 0.6
s. y = -0. 6x -6
Answer:
b. y=0.6x+6
Step-by-step explanation:
First, find the slope using the slope formula, [tex]\frac{0-6}{-10-0}[/tex]. This is 6/10, which simplifies to 3/5 or 0.6. Then you need to find the y-intercept, however, this is already given to you. Remember that the y-intercept is when x=0, so (0,6) must be the y-intercept. Therefore the equation is y=0.6+6.
Please help me I need to turn in tomorrow please!!!!
I think of a number,i added 4 to the number, the result is 20
Answer:
i exactly didnt understand what you meant but if that was a question on what was the number it was 16.
Step-by-step explanation:
cause 16+4=20
Write an equation of the line that passes through a pair of points: (2, 3), (4, -2)
a. y = -5/2 x -1/8
b. y = -5/2x -8
c. y = -5/2x +8
d. y = 5/2x +8
Answer:
C. y = -5/2x +8
Step-by-step explanation:
To solve first find the slope using the slope formula which is m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. To find the slope simply plug in the points, [tex]\frac{-2-3}{4-2}[/tex] which equals -5/2. Next, put the equation into slope-point form, which is [tex]y-y_{1} = m(x-x_{1})[/tex]. I will use the point (2,3). y-3=-5/2(x-2), then solve for y which equals y=-5/2+8.
A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans.
Answer:
[0.184, 0.266]
Step-by-step explanation:
Given:
Number of survey n =280
Number of veterans = 63
Confidence interval = 90%
Computation:
Probability of veterans = 63/280
Probability of veterans =0.225
a=0.1
Z(0.05) = 1.645 (from distribution table)
Confidence interval = 90%
So,
p ± Z*√[p(1-p)/n]
0.225 ± 1.645√(0.225(1-0.225)/280)
[0.184, 0.266]
At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a randomly selected loan agent closes on a randomly selected day has the probability distribution below.x 1 2 3 4 5 6 7p(x) 0.05 0.10 0.22 0.30 0.18 0.12 0.03 At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let YY represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true?A. The mean of X is less than the mean of Y. B. The standard deviation of Y is approximately $71. C. The mean daily salary is greater than $350 per day. D. The standard deviation of X is less than the standard deviation of Y. E. The shape of the probability distribution of Y is unimodal and roughly symmetric.
Answer:
C. The mean daily salary is greater than $350 per day
Step-by-step explanation:
The computation is shown below:
Y = a + bX
where,
Y = money made by a random selected
a = $150
b = $50
X = number of loan
Now
E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)
= 3.94
Now
E(y) = $150 + ($50 × 3.94)
= $347
hence, the option C is not correct
The mean daily salary is greater than $350 per day and this can be determined by using the given data.
Given :
At a certain company, loan agents are paid based on the number of loans they close in a day.
The computation is given by:
Y = a + bX
where Y is the money made by randomly selected, a is $150, b is $50, and X is the number of loans.
Now, the value of E(x) is given by:
[tex]\rm E(x) = (1\times 0.5)+(2\times 0.1)+(3\times 0.22)+(4\times 0.3)+(5\times 0.18)+(6\times 0.12)+(7\times 0.03)[/tex]
[tex]\rm E(x) = 3.94[/tex]
Now, the value of E(y) is given by:
[tex]\rm E(y) = 150+(50\times 3394)[/tex]
E(y) = $347
So, the correct option is given by C) The mean daily salary is greater than $350 per day.
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Which of the following are true statements?
Check all that apply
Answer:
a and d
Step-by-step explanation:
Imma try again
Can someone link me a website or pdf explaining how to solve this?
I'm sure it is easy but I just haven't been taught this
hi can you send me the formula...let me teach you
Answer:
B. BD = 67Step-by-step explanation:
ABCD is a square.
BD and AC are diagonals and they have equal length.
We have AC = 7x + 18 and BD = 10x - 3
Since AC = BD, we substitute their values and solve for x:
7x + 18 = 10x - 310x - 7x = 18 + 33x = 21x = 21/3x = 7Then find the length of BD:
BD = 7x + 18 = 7*7 + 18 = 49 + 18 = 67Correct option is B. BD = 67
Which of the following best describes the slope of line that passes through the points (-3,8) and (-3,11)?
⭕️increasing
⭕️decreasing
⭕️zero
⭕️undefined
Answer:
undefined
Step-by-step explanation:
when x has the same number is undefined
but when y has the same is zero
Using the inverse trig functions, find the measure of angle A to the nearest degree.
1. 43 degrees
2. 37 degrees
3. 90 degrees
4. 53 degrees
X-3y=-12 and 4x+6y=-12 substitution
Answer:
x = -6
y = 2
Step-by-step explanation:
1. Approach
x - 3y = -12
4x + 6y = -12
In this problem, it would likely be easier to use elimination, but since the problem specifically says that one must use substitution, substitution will be used. Substitution is when one solves one of the equations for a variable, similar to solving a literal equation. The one will substitute in the value of the variable into the other equation and solve for the other varibale. Then one will finally back substitute in that value of the other variable to find the value of the first variable, hence solving the equation.
2. Solve equation 1
x - 3y = -12
Solve the literal equation with inverse operations;
x - 3y = -12
+3y + 3y
x = 3y - 12
3. Substitute the answer into the second equation
4x + 6y = -12
x = 3y - 12
4 ( 3y - 12 ) + 6y = -12
Distribute;
12y - 48 + 6y = -12
Simplify;
12y - 48 + 6y = -12
18y - 48 = -12
Inverse operations;
18y - 48 = -12
+48 +48
18y = 36
/18 /18
y = 2
4. Backsolve for x
Substitute the value for y back into the equation for x and solve
x = 3y - 12
y = 2
x = 3(2) - 12
x = 6 - 12
x = -6
Sabrina has 54 ballon to arrange in bunches. She want to put the same numberof ballon on each bunch .list all the different ways can sabrina arrange the ballon
Answer:
54 groups of 1, 27 groups of 2, 18 groups of 3, 9 groups of 6, and repeat vice versa (6 groups of 9, etc).
Step-by-step explanation:
Total number of ways are 8 to arrange the balloon,
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
Given that,
Total number of balloon Sabrina has = 54,
The number of ways Sabrina can arrange the balloon are:
1 group of 54 balloons,
2 groups of 27 balloons,
3 groups of 18 balloons,
6 groups of 9 balloons,
9 groups of 6 balloons,
18 groups of 3 balloons,
27 groups of 2 balloons,
54 groups of 1 balloon,
There are total 8 different ways Sabrina can arrange the balloons.
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