Answers
First, rewrite
[tex]x^y=e^{\ln x^y}=e^{y\ln x}[/tex]
[tex]5^{x-y}=e^{\ln5^{x-y}} = e^{\ln(5)(x-y)}[/tex]
Now, differentiate both sides using the chain rule:
[tex]\dfrac{\mathrm d\left(e^{y\ln x}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(e^{\ln(5)(x-y)}\right)}{\mathrm dx}[/tex]
[tex]e^{y\ln x}\dfrac{\mathrm d(y\ln x)}{\mathrm dx}=e^{\ln(5)(x-y)}\dfrac{\mathrm d(\ln(5)(x-y))}{\mathrm dx}[/tex]
[tex]x^y\left(\dfrac{\mathrm dy}{\mathrm dx}\ln x+y\dfrac{\mathrm d(\ln x)}{\mathrm dx}\right)=\ln(5)5^{x-y}\left(\dfrac{\mathrm d(x)}{\mathrm dx}-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]
[tex]x^y\left(\ln x\dfrac{\mathrm dy}{\mathrm dx}+\dfrac yx\right)=\ln(5)5^{x-y}\left(1-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]
[tex]\left(x^y\ln x+\ln(5)5^{x-y}\right)\dfrac{\mathrm dy}{\mathrm dx}=\ln(5)5^{x-y}-yx^{y-1}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\ln(5)5^{x-y}-yx^{y-1}}{x^y\ln x+\ln(5)5^{x-y}}[/tex]
Related Questions
Two sides of a triangle are equal in length. The length of the third side exceeds the length of one of the other sides by 3 centimetres. The perimeter of the triangle is 93 centimetres. Find the length of each side of the triangle
Answers
Answer:
it must be 30, 30, 33
Step-by-step explanation:
first, divide 93 by 3, since a triangle has 3 sides, you would get 31, yet if you took away that three in 93, it'd be 30. For that one that exceeds the others by 3, add the three to one of the thirds, and the other two are just the same, so when it said, "exceeds the length of one of the other sides," It didn't really change anything, because the other side is just as long.
The red-tailed tropic bird, Phaethon rubricauda, is an extremely rare sea bird that nests on several islands of the Queensland coast of Australia. As part of a conservation e ort to manage these endangered birds, every nesting pair was measured and weighed. Below are the body weights of these birds (in kg).
Female 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84
Required:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
b. Determine the mean, variance, and standard deviation for the male weights.
Answers
Answer:
This is a population
a) Female
Mean : 2.432857143kg
Variance: 0.05162040817kg
Standard deviation: 0.2272012504kg
b) Male
Mean : 2.641428571kg
Variance : 0.03432653062kg
Standard deviation: 0.1852742039kg
Step-by-step explanation:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
a) Female: 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Mean
The formula = Sum of term/ Number of terms
Mean = 2.45 + 2.57 + 2.81 + 2.37 + 2.01 + 2.50 + 2.32/7
17.03/7
= 2.432857143kg
Variance
This is a population
Hence: The formula for Population variance =
= (X - Mean)²/N
Where N = Number of terms = 7
= (2.45 - 2.432857143)² + (2.57 -2.432857143)² + (2.81 -2.432857143)² + (2.37- 2.432857143)²+ (2.01 - 2.432857143)²+ (2.50 - 2.432857143)² + (2.32 - 2.432857143)² /7
= 0.0002938775509 + 0.01880816325 + 0.1422367347 + 0.003951020409 + 0.1788081633 + 0.004508163265 + 0.0127367347/7
= 0.3613428572/7
= 0.05162040817kg
Standard Deviation
Formula = √Variance
= √0.05162040817
= 0.2272012504kg
b. Determine the mean, variance, and standard deviation for the male weights
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84
Mean
The formula = Sum of term/ Number of terms
= 2.86 + 2.65 + 2.75 + 2.60 + 2.30 + 2.49 + 2.84/7
= 18.49/7
= 2.641428571 kg
Variance
= ( 2.86 -2.641428571)² + (2.65 - 2.641428571)² + (2.75 -2.641428571)² + (2.60 +2.641428571)² + (2.30 - 2.641428571)² + (2.49+2.641428571)² (2.84 + 2.641428571)²/7
= 0.0477734694 + 0.00007346938775 + 0.01178775511 + 0.001716326531 + 0.1165734694 + 0.02293061224 +! 0.03943061226/7
= 0.2402857143/7
= 0.03432653062kg
Standard Deviation
= √Variance
= √0.03432653062
= 0.1852742039kg
Which is true when you rent?
ОА.
You build equity in your house.
ОВ.
You are responsible for any repairs.
Ос.
You pay fewer up-front costs.
Answers
You are responsible for any repairs.
please answer....writing assignment for math
Answers
Answer:
This information tells me that f equals a number and 3 multiplied by the number that f equals is 16.
Could I please have Brainliest?
PLEASE HELP! 6TH GRADE MATH please write done what number you're doing
Answers
Answer:
# 10 is 4/3 or 1 and 1/3
#11 is 4/10 or 2/5
#12 is 2 and 3/4
#13 is 36/12 or 3 and 1/12
Step-by-step explanation:
i am not 100% sure on #13 btw
hope this helped!
p.s it would be cool if you gave me brainliest.
Answer:
Hey your answers on there are correct.
Step-by-step explanation:
List the numbers in order from least to greatest.
-4,8,-15,-8,4,1
The numbers in order from least to greater Are
Answers
Answer: -15, -8, -4, 1, 4, 8
One box of pencils costs rupees 28 . What is the cost of 509 boxes
Answers
One box of pencils costs rupees 28 . What is the cost of 509 boxes
Given:1 pencil costs=₹281 pencil costs=₹28No. of boxes=509We know:Costs of total no. of pencil boxes
=1 pencil box's costs×No. of boxes
=509×28
=14252✓
Can you guys help me with this angle problem for Geometry tysm
Answers
Answer:
You need to solve for x
Step-by-step explanation:
3x + 5 + 10x - 7 = 180
13x + 5 - 7 = 180
13x - 7 = 175
13x = 182
x = 14
Plug in x
3(14) + 5 for QRT and 10(14) - 7 for TRS
QRT = 47 and TRS = 133
Answer:
QRT = 47
TRS = 133
Step-by-step explanation:
The two angles form a straight line so they add to 180
3x+5 + 10x-7 = 180
13x-2 =180
Add 2 to each side
13x-2+2 =180+2
13x= 182
Divide by 13
13x/13 = 182/13
x =14
We want QRT = 3x+5 = 3*14+5 = 42+5 = 47
TRS = 10x-7 = 10*14-7 = 140-7 = 133
Brandon enters bike race. He bikes 9 1/2 miles every 1/2 hour
Answers
Hope this helps:)
Multiply. Do not round your answer.
2.48x8.62 =?
Answers
Answer:
21.3776
Step-by-step explanation:
Answer: 21.3776
This is what I got for the answer hope it helps.
Write the equation of the line parallel to the given line and through the given
point. y=2x - 8 through (3.10)
Answers
Answer:
y-2x -8
Step-by-step explanation:
your jus gonna right it back because it's parallel which means it's the same thing.
I need help on math
Answers
PLZ HURRY IT'S URGENT!!!
Write the equation of a line with a slope of -2 and a y-intercept of 3.
options:
y=3x−2
y=−3x+2
y=2x−3
y=−2x+3
Answers
Answer:
y=-2x+3
Step-by-step explanation:
Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value between 29.0 and 55.0. Use Table IV in Appendix C to compute the probabilities. Round your answer to four decimal places.
Answers
Answer:
i think it is between 22 and 35
Step-by-step explanation:
What is 5/8 of $16 restaurant bill=
What is the answer
Answers
Answer:
$10
Step-by-step explanation:
16 * 5 / 8 = 16 * 0.625 = $10
Graph the line that represents the equation
Answers
Answer:
In the attachment.Step-by-step explanation:
We need only two points.
Choose any two values of x. Put them to the equation and calculate the value of y:
[tex]y=-\dfrac{2}{3}x+1\\\\\text{for}\ x=0\\\\y=-\dfrac{2}{3}\cdot0+1=0+1=1\to A(0;\ 1)\\\\\text{for}\ x=3\\\\y=-\dfrac{2}{3}\cdot3+1=-2+1=-1\to B(3;\ -1)[/tex]
I’m not well with percentages lol. Can someone help me with solving it and answer
Answers
Answer:
1. Dracula Answer: D) 12.5%
2. Jack-O-Lantern Answer: D) 40%
Step-by-step explanation:
1. 54 - 48 = 6
6/48 = 0.125 x 100 = 12.5%
2. $20 - $12 = 8
8/20 = 0.4 x 100 = 40%
can anyone help me
Answers
Answer:
A
Step-by-step explanation:
A scale drawing of a building needs to be made using the scale 1 in = 230 ft. How tall will the building in the scale drawing be if the building is 1380 ft tall?
Answers
-
y=2/3x + 2 and passes through the point (12, 6).
Find an equation perpendicular to the line
A. y=-3/2x + 21
B. y=-3/2x +24
C. y= 2/3x + 14
D. y= 2/3x + 8
Answers
Answer:
B. y = -3/2x + 24
Step-by-step explanation:
The perpendicular slope is -3/2x to find the y-intercept use the point given
Plug in
6 = -3/2(12) + b (b = y-intercept)
6 = -18 + b (add 18 on both sides)
24 = b (so)
y = -3/2x + 24
pls help meeeeeeeeeeee!!
Answers
Answer:
45 with a remainder of 27.
Step-by-step explanation:
Hope this helps you! Good luck! <3
The variables x and y are related proportionally. When x = 8, y = 20. Find y when x = 80.
Answers
Answer:
y = 200
Step-by-step explanation:
Use the equation y = kx, where k is a constant.
Plug in the given x and y values, then solve for k:
y = kx
20 = k(8)
2.5 = k
Then, plug in k and the given x value, and find y:
y = 2.5x
y = 2.5(80)
y = 200
So, y = 200 when x = 80
Carrie has $500 in her bank account. She plans to add $245 a week to her account. Jose has $710 in his bank account. He plans to add $230 a week. How many weeks will it take untill carrie & jose have an equal ammount of money saved up is neither of them spent any of their savings?
Answers
Answer:
14 weeks
Step-by-step explanation:
14 times 245= 3430+ 500=3930 (carrie)
14 times 230= 3220+ 710= 3930 (jose)
Write 1/8% as a decimal number Enter your number in the box
Answers
Answer:
it is 0.125
Step-by-step explanation:
......................
What is the measure of ZRIA?
R
PA
N
999
.
A. 55
B. 30°
O C. 95°
D. 60°
Answers
The measure of angle RIA is 55 degrees, option A is correct.
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the measure of angle RIA
The opposite angle of RIA is LIK
Let us find the measure of LIK
∠FIL+∠LIK+∠KIN=180
30+∠LIK+95=180
∠LIK + 125 =180
Subtract 125 from both sides
∠LIK = 180 - 125
=55 degrees
∠LIK is equal to ∠RIA
∠RIA = 55 degrees
Hence, the measure of angle RIA is 55 degrees, option A is correct.
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
#SPJ5
Solve for x.
x-4/5= -1/3
Answers
Answer:
x = 1 2/15
Step-by-step explanation:
An investigation of wages paid to its employees by a large company was undertaken as a result of an allegation of discrimination. Data was collected for 1000 randomly selected employees. The data included employee ID, gender, race, annual wages in dollars (Salary), whether the employee had full-time status or part-time status (Full_Part), number of years of education (Ed), and number of years with the company (Tenure). The first two rows of data in the worksheet are displayed below.
1 Gender Race Salary Full_Part Ed Tenure
2 Female Caucasian 32196 Full 14 2
3 Male Black 62385 Full 16 10
How many cases does this data set contain?
How many variables does this data set contain? (3 p)
How many quantitative variables does this data set contain, and what are they? How many qualitative variables does this data set contain, and what are they?
Answers
Answer:
Step-by-step explanation:
First, the data set is:
Gender Race Salary WorkTimeStatus Education Tenure
1. Female Caucasian 32196 Full Time 14yrs 2 yrs
2. Male Black 62385 Full Time 16yrs 10yrs
Now to the questions:
(A) This data set contains 2 cases; 1 for the first employee (the female caucasian) and 2 for the second employee (the male black).
(B) This data set contains 6 variables;
1. Gender 2. Race 3. Salary 4. Work time status 5. Years of education
6. Number of years in/with the company
(C) Out of these 6 variables, the quantitative ones (those that can be measured or weighted numerically) are:
3. Salary 5. Years of education 6. Years with the company
Altogether, 3 in number
(D) The qualitative variables are:
1. Gender 2. Race 4. Work Time Status
Altogether that's 3 variables
adult men weights mean of 190 30 3 random men mean weight
Answers
Answer:
is this the question ?
Step-by-step explanation:
Assemble the proof by dragging tiles to the statements and reasons columns
Answers
Answer:
Here, I did the assignment. I wish you good luck!
The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?
Answers
Answer:
21 sheets of paper
Step-by-step explanation:
If its basically 6 tickets to a piece of paper then you just divide 125 tickets by 6 and get 20.833.... Then your round to the nearest sheet which is 21.
Hope this helps!
Answer:
Approx. 21 sheets of paper
Step-by-step explanation:
1 sheet of paper is used to make 6 tickets
6 tickets = 1 sheet
If 1 sheet is used to make 6 tickets. The number of sheets used to make 125 tickets will more.
if
6 tickets = 1 sheet
125 tickets = (125÷6) × 1
= 20.83333333333