If x^(y)=5^(x-y) then dy/dx=
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]
Plz help Plz help
Ella played a math game and had the five cards shown.
7 0 -4 -10
Her score was the sum of the numbers on these five cards. What was Ella’s score?
3
⊝
23
−5
⊝
Not here
Answer:
-7 (Not here)
Step-by-step explanation:
1. A negative plus a negative equals a negative/ a negative minus a positive equals a negative so: -10 -4 = -14
2. -14 + 7 = -7 so your answer is -7 and it's not an answer choice so you would select "Not here"
1) 2,340/9=
What’s the answer
Answer:
260
Step-by-step explanation:
i can do it mentally
15,614+?=68,025
What is the total
Answer:
52411 that's the answer
Hello, I wanted to leave you this photograph of mathematics that I think will be very useful to some of you, observe it
Answer:
yes
Step-by-step explanation:
Answer:
thank you
Step-by-step explanation:
:)
What operation is happening in an additive pattern??
Multiplication
Subtraction
Addition
Division
Answer:
Addition
Step-by-step explanation:
If it has the word "add" in it it's probably addition.
Answer:
The answer is addition.
Step-by-step explanation:
a bag contains 12 blue marbles and 8 blue what is the ratio of blue to red
Answer:12:8 or 12 to 8 or u could do it in fraction form
is 60 : 45 and 4 : 3 equlvalent ratios?
Answer:
Yes
Step-by-step explanation:
If you divide 60 and 45 by 15 you get 4 and 3.
Answer:
yes they are infact equivalent
Consider the function f(x) = 3.x2 + 7x + 2.
what is the value of the discriminat?
Answer:
The Discriminant is 25
Step-by-step explanation:
For this case, the discriminant will be given by
b ^ 2 - 4 * a * c
Where
b = 7
a = 3
c = 2
substituting
b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25
Therefore the value of the discriminant is 25.
How many x-intercepts does this function have?
It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,
3x2 + 7x + 2 = 0
The results will be the interceptions with x.
What are the number of zeros for this function?
The number of zeros for this function is
two real number solutions
Because it is a quadratic function.
Typically, your car gets 32 mpg on the highway, how many gallons of gas did you use if you
traveled 1760 miles?
Answer:
13 gallons
Step-by-step explanation:
A large hamburger (e.g., Whopper®) sandwich contains 628 kcal and 36 grams of fat. Approximately what percentage of the total energy is contributed by fat?
Answer:
Step-by-step explanation:
Total energy of the sandwich = 628kcal
Mass of fat contained = 36grams
Convert gram to kcal
1gram = 9kcal
36 grams = x
x = 36×9
x = 324kcal
Hence the fat contains 324kcal
%fat contained = fat(in kcal)/total calorie × 100%
%fat contained = 324/628 × 100%
%fat contained = 1/2 × 100%
%fat contained = 50%
Hence approximately 50% of the total energy is contributed by fat.
can anyone help me
Answer:
A
Step-by-step explanation:
Which of the following in NOT an equation of a line parallel to the line with equation y=1/2x-6 *
y = 2/4x + 6
y = 0.5x - 3
y = 1/2x + 1
y = 2x - 4
9514 1404 393
Answer:
y = 2x - 4
Step-by-step explanation:
You want an equation with an x-coefficient that is not 1/2.
2/4 = 0.5 = 1/2
so, the first three answer choices don't meet problem requirements.
The line with equation ...
y = 2x -4
is not parallel to y = 1/2x -6.
help asap!! answer
Plz help nothing to big but hard for me
Answer: Which question?
Step-by-step explanation:
What is the slope of the line that passes through the coordinate points: (0,3)
and (5, 96)?
Answer:
93/5
Step-by-step explanation:
How do I solve this?
Answer:
Step-by-step explanation:
Slope= -3/1
plot from point (-2,4)
Answer:
Step-by-step explanation:
Just so that we have something to work with, the length of the longest day (June 22) in Acron Ohio is 15 hours 8 minutes and 9 seconds on the 20th of June of this year. The number we get won't be this accurate, but it will tell us if we have done it correctly. The tricky part is when to use the radians.
cos(0.1309 H) = -0.4336 tan (40o 46 minutes) I have assumed this is in radians. It won't work any other way. The measurement cannot be in degrees which will give a negative tan from the minus sign out in front. The cos being minus will make things even worse.
cos(0.1309 H) = -0.4336 tan (40 46/60 )
cos(0.1309 H) = -0.4336 tan (40.766666667)
cos(0.1309 H) = -0.4336 * -0.074173405
cos(0.1309 H) = 0.032161588
0.1309 H = cos-1(0.032161588)
0.1309 H = 1.538629191
H = 1.538629191 / 0.1309
H = 11.754 which is no where near 15 hours, but it is what the numbers give.
I would suggest that you go to your instructor for the other two. Work this one out until you get somewhere near 11.7 hours.
The other two cities should come to something near this answer.
What integers are the closest to the square root of 11
Answer:
-3, 3.
Step-by-step explanation:
3^2 = 9 and 4^2 = 16.
Also -3 and -4 give the same results.
Since 9 is closer to 11 than 16 the answer is 3 and -3.
Arachnophobia is the fear of spiders. People with arachnophobia suffer to different degrees, but they tend to react intensely to visible signs of the presence of spiders, such as webs. The director of a clinic decides to investigate different treatment types for arachnophobia. She gathers three groups of clients: One group receives in vivo flooding, which involves prolonged or repeated exposure to the actual anxiety-producing stimuli. The second group receives imaginal flooding, which involves the same techniques as in vivo flooding, except the exposure occurs in the client’s imagination. The third group receives no treatment. The results come in, and a statistician conducts an analysis of variance.
The ___________ is that there is no difference between the population means (in other words, there is no treatment effect).
The ___________is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
Answer:
1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).
2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
Step-by-step explanation:
In a statistical analysis, the statistician shares his participants into several groups and administers treatments to them. After administering the treatment, he might want to compare the values obtained to see if there is a difference. If he accepts the null hypothesis as true, that means that there was no difference between the population means. This can also be taken to mean that the result had no difference among the groups.
But if the alternative hypothesis was true, that means that the population means were not all equal and so, there was an effect from the treatment administered.
Answer:
1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).
2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
What is the sign of the product (3)(−25)(7)(−24)?
A. Positive, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is positive
B. Positive, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is positive
C. Negative, because the products (3)(−25) and (7)(−24) are negative, and the product of two negative numbers is negative
D. Negative, because the products (3)(−25) and (7)(−24) are positive, and the product of two positive numbers is negative
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).
Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Required:
Approximate the mean and standard deviation for temperature.
Answer:
The mean is [tex]\= x = 79.7 [/tex]
The standard deviation [tex]\sigma =7.81[/tex]
Step-by-step explanation:
From the question we are told that
The data given is
Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Generally the average of each limit is evaluated as
Temperature Lower Limit Upper Limit Average[tex](x_i)[/tex] Days[tex](f_i)[/tex]
50-59 50 59 ( 50 + 59 )/2 =54.5 2
60-69 60 69 (60+69)/2 = 64.5 313
70-79 70 79 (70+79)/2 =74.5 1419
80-89 80 89 (80+89)/2 =84.5 1503
90-99 90 99 (90+99)/2 = 94.5 319
100-109 100 109 (100+109)/2 = 104.5 9
Generally the mean is evaluated as
[tex]\mu = \frac{\sum x_i f_i}{\sum f_i}[/tex]
=> [tex]\mu = \frac{ (54.5 * 2) + (64.5 * 313) +\cdots +(104.5 * 9)}{2 + 313 +\cdots + 9}[/tex]
=> [tex]\= x = 79.7 [/tex]
Generally the standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum[ f_i * ( x_i^2 - \= x^2)] }{\sum f_i}}[/tex]
=> [tex]\sigma =\sqrt{ \frac{[2 * [(54.5)^2) - 79.7^2 ]]+[313 *[ (64.5)^2)-79.7^2] +\cdots +[9 *[ (104.5)^2)- 79.7^2] }{2 + 313 +\cdots + 9}}[/tex]
=> [tex]\sigma =7.81[/tex]
The mean and Standard deviation for the given data would be as follows:
μ [tex]= 79.7[/tex]
б [tex]= 7.81[/tex]
Frequency DistributionGiven that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i}[/tex])
[tex]( 50 + 59 )/2 =54.5[/tex]
[tex](60+69)/2 = 64.5[/tex]
[tex](70+79)/2 =74.5[/tex]
[tex](80+89)/2 =84.5[/tex]
[tex](90+99)/2 = 94.5[/tex]
[tex](100+109)/2 = 104.5[/tex]
As we know,
Mean (μ) [tex]=[/tex] ∑[tex](x_{i} f_{i}) /[/tex]∑[tex]f_{i}[/tex]
[tex]= [(54.5[/tex] × [tex]2) + (64.5[/tex] ×[tex]313)+....(104.5[/tex]× [tex]9)][/tex][tex]/(2 + 313 + 1419 + ....9)[/tex]
∵ μ [tex]= 79.7[/tex]
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{f_{i} }}}[/tex]
by putting the values, we get
∵ б [tex]= 7.81[/tex]
Thus, μ [tex]= 79.7[/tex] and б [tex]= 7.81[/tex] are the correct answers.
Learn more about "Temperature" here:
brainly.com/question/7510619
Over the past few years, there has been a strong positive correlation between the annual consumption of diet soda drinks and the number of traffic accidents.
(a) Do you think increasing consumption of diet soda drinks causes traffic accidents? Explain your answer.
No. A strong correlation implies causation.
No. A strong correlation does not imply causation.
Yes. A strong correlation does not imply causation.
Yes. A strong correlation implies causation.
(b) What lurking variables might be causing the increase in one or both of the variables? Explain your answer.
Answer:No. A strong correlation does not imply causation.
Step-by-step explanation:
Cause and effect relationship is not explained by correlations. A cause and effect relationship can only be established by carrying out carefully controlled experiments.
Hence, a strong correlation between the the intake of soda and accidents does not necessarily imply that soda intake causes accident.
A lurking variable in this study may be the speed of the drivers. A lurking variable is not controlled but significantly impacts results obtained from the study.
Since the speed of the drivers is not strictly controlled, it may just be a lurking variable.
Are these questions different at all? And if so whats the answer to them?
Answer:
i think u got it
Step-by-step explanation:
PLSSSS PLSSS HELPPPP MEEEEE ASAPPPPP I WILLLLL GIVE BRAINLIEST!!!!!!!
Answer:
40 ft
Step-by-step explanation:
1. Emma’s average in math increased from an 80 to an 84. By what percentage did her average increase?
Answer:
82
Step-by-step explanation:
PLEASE HELP FAST!!!! THIS IS URGENT!!!
For the following set of triangles, fill in the blanks with the correct measure. Enter your answers as number only.
1) m∠A = _____˚
2) m∠B = _____˚
3) m∠C = _____˚
4) m∠X = _____˚
5) m∠Y = _____˚
6) m∠Z = _____˚
7) Segment AB = ___ units
8) Segment BC = ___ units
9) Segment AC = ___ units
10) Segment XY = ___ units
11) Segment YZ = ___ units
12) Segment XZ = ___ units
Answer:
a=53, b=90, c=37, x=53, y=90, z=37
segment ab=3, segment bc=4, segment ac=5
pretty sure these are the answers but sorry if not
Step-by-step explanation:
Drag the operator to the correct location on the image. Which operation results in a trinomial?
Answer:
-
Step-by-step explanation:
I took the test
The correct operator that enters a circle is a subtraction sign.
Given the expressions
[tex](4x^5-8x) ()(3x^2-8x+9)[/tex]
We need to know which sign goes into the bracket that will give a trinomial when simplified.
A trinomial is a function containing 3-terms.
Using the subtraction sign.
[tex](4x^5-8x) - (3x^2-8x+9)[/tex]
Expand
[tex]= 4x^5-8x - 3x^2+8x-9\\= 4x^5-3x^2-8x+8x-9\\=4x^5-3x^2+0-9\\=4x^5-3x^2-9[/tex]
Since the resulting term is a trinomial (3 terms), hence the correct operator that enters a circle is a subtraction sign.
Learn more here: https://brainly.com/question/1320408
A jewelry store is having a 45% off sale for all necklaces. During this sale, what is the cost of a necklace that regularly costs $59.98?
Answer:
32.99
Step-by-step explanation:
59.98(45%)=26.99
59.98-26.99=32.99
Answer:
$32.99, the discount took off $26.99.
Step-by-step explanation:
Good luck!
4cm
2cm
6cm
Find the area please
Step-by-step explanation:
ummm where is the pic? like bruh
Answer:
48 cm
Step-by-step explanation:
Multiply 4x2x6 and get the answer of 48 cm.
How can you use a number line to find the sum of -8 and 9?
Answer:
The answer is 1
Step-by-step explanation:
If you look at the number line and start counting from -8 and count 9 to the right then the number that you end on is the answer.