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
James is studying different kinds of weather. Rain has water drops that are larger than 0.02 inch in diameter. Small hailstones are less than 14 inch in diameter. Complete the statement that best represents the different kinds of weather James studied. Select one correct answer from each box to complete the sentence.
Answers
Answer:
wheres the stament
Step-by-step explanation:
Answer:
huh
Step-by-step explanation:
5x + y =7
20x + 2 = y
Answers
Answer:
y = 6
x = 0.2
Step-by-step explanation:
5x + y =7
20x + 2 = y
5x(4) + y(4) = 7(4)
20x + 4y = 28
(20x = 28 - 4y) = (20x = y - 2)
28 - 4y = y - 2
30 - 4y = y
30 = 5y
y = 6
5x + y =7
20x + 2 = y
y = 7 - 5x
7 - 5x = 20x + 2
5 - 5x = 20x
5 = 25x
x = 0.2
f(x) = 23 – 22
g(x) = 4x + 5
Answers
Answer:
23-22=1
5 times 4=20
Step-by-step explanation:
The left and nght page numbers of an open book are two consecutive integers whose sum is 447. Find these page numbers
Answers
Answer:
223 and 224
Step-by-step explanation:
Divide 447 by 2. It gives a decimal of 223.5, but obviously you don't have half pages. So the page number would be 223 and 224.
Answer:
223,224
Step-by-step explanation:
page 1-x
page 2-x+1
2x+1=447
2x=446
x=223
page 1=223
page 2=224
Brainliest is Very Appreciated!
if there are 7 fish and 3 drown how many are left?
Answers
Answer:
7
Step-by-step explanation:
there are 7 left because fish can't drown
1119 divided by 4 and some random stuff cause it aint long enough
Answers
Answer:
29.25 if rounded up it equals 29.3
Step-by-step explanation:
What is the ratio of daises to all the flowers in the vase?
Answers
Answer: Do you have the original ration so we can simplify it then??
Step-by-step explanation:
Aging workers of the Neotropical termite, Neocapritermes taracua, develop blue crystal containing glands ("backpacks") on their backs, When they fight intruding termites and are hampered, these "blue" termites explode, and the glands spew a sticky liquid (Sobotnik et al. 2012). The following data are from an experiment that measured the toxicity of the blue substance. A single drop of the liquid extracted from blue termites was placed on individuals of a second termite species, Labiotermes labralis, and the number that were immobilized (dead or paralyzed) within 60 minutes was recorded. The frequency of this outcome was compared with a control treatment in which liquid from glands of "white" termites lacking the blue crystals was dropped instead.
Is the blue liquid toxic compared to liquid from white termites?
Liquid source Unharmed Immobilized
Blue workers 3 37
White workers 31 9
Answers
Answer:
Yes blue liquid is toxic
Step-by-step explanation:
H0: p1 = p2
H1: p1>p2
For blue
We calculate proportion as
37/40 = 0.925
For white
9/40 = 0.2250
To get p
(X1 + x2)/(n1 + n2)
= 0.5750
After calculating the z as statistic (please check attachment) I got 6.33
P value = 0.0000
We reject null hypothesis and say in conclusion that enough evidence exists for us to say blu liquid is toxic!
Thank you!
The measures of two supplementary angles are in the ratio 1:3. What is the measure, in degrees, of the larger angle?
Answers
Sum of two angles that are supplementary = 180°
Ratios in which they have been given their measurement = 1 : 3
Total number of parts = 1 + 3 = 4
Each part = 180÷4 =
[tex]Each \: part = \: \frac{180}{4} [/tex]
Each part = 45°
Measure of smaller angle = 45 × 1 = 45°
[tex]Measure \: of \ \: the \: smaller \: angle \: = \: 45 \: × \: 1 \: = \: 45°[/tex]
[tex]Measure \: of \: \: the \: larger \: angle \: = \: 3 \: × \: 45 \: = \: 145° \: [/tex]
∴ The measure of the larger angle in degrees = 145° .
plz help, find missing angle.
Answers
Answer:
I don't know the answer because the picture says it's blocked I'm so sorry
Step-by-step explanation:
find the possible factor for the estimated product 5,600
Answers
Question example:
Find the missing angle measures. (2x-3),(8x) and(x+7)
Answers
Answer:
2x-3 = 29
8x = 128
x+7 = 23
Step-by-step explanation:
The sum of the angles of a triangle is 180
2x-3 + 8x+ x+7 = 180
Combine like terms
11x+4 = 180
Subtract 4 from each side
11x+4-4= 180-4
11x = 176
Divide by 11
11x/11 =176/11
x =16
2x-3 = 2*16-3 =32-3 = 29
8x = 8*16 =128
x+7 = 16+7 = 23
What are all the factors of 54? O 1,2, 6, 9, 26, 54 O 1,2, 6, 9, 27, 54 O 1, 2, 3, 6, 9, 18, 26, 54 O1,2, 3, 6, 9, 18, 27, 54.
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┈┈▕▔╱╱╱╱▂▂▂▂▂▂▏
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▔╱┊┈╱▕╲▂▂▂▂▂▂╱┈┈
╱┊┈╱┉▕┉┋╲┈
Answers
Answer:
1 2 3 6 9 18 27 and 54 I hoped this helps
Answer:
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
Step-by-step explanation:
IF YOU ARE REALLY GOOD AT MATH PLEASE HELP ASAP!! Select all the correct answers on the table
Answers
Row2.the first and last one
What is the value to the expression -2.1(4.7+(-7.4))
Answers
write an equation that represent the table
Answers
Answer:
y equals 5x + 20
Pure acid is to be added to a 10% acid solution to obtain 99L of a 20% acid solution. which amounts of each should be used ?
Answers
Answer:
x = amount of 100% acid solution (pure acid, no water)
y = amount of 10% acid solution (acid + water)
both amounts are in liters
Step-by-step explanation:
In a casino in Blackpool there are two slot machines (machine 1 and machine 2): one that pays out 10 % of the time, and one that pays out 20 % of the time. Obviously, you would like to play on the machine that pays out 20% of the time but you do not know which of the two machines is the more generous. You thus adopt the following strategy: you assume initially that the two machines are equally likely to be the generous machine. You then select one of the two machines at random (this turns out to be machine 1) and put a coin into it. Given that you loose that first bet estimate the probability that machine 1 is the more generous of the two machines
What do I know?
What do I want to find out?
What do I expect the answer to be?
How do I go from what I know to what I want to find?
Is the answer consistent with what I expected?
Answers
Answer:
Step-by-step explanation:
From the given information:
We are told that there exist two machines
Machine 1 and Machine 2
Given that machine 1 pays 10% when it is generous, then the probability can be computed as:
P(pays | machine 1 is generous) = 0.10
Also, machine 2 pays 20% when it is generous, then the probability that the machine pays 20% when it is generous is :
P(pays | machine 2 is generous) = 0.20
However, the two machines have an equal chance of being generous.
Therefore, the probability that machine 1 is generous is equal to the probability that machine 2 is also generous.
i.e.
P( machine 1 is generous) = P( machine 2 is generous) = 0.50
The first objective is to find the probability that the machine 1 is generous, given that the player loses the first bet.
i.e. P (machine 1 is generous | but lost)
Thus, we know that the probability that the machine is generous is = 0.5, therefore, the probability that the machine is generous is 50% when he loses the first bet.
Therefore, to find the probability that the machine 1 is generous | but lost, we have:
[tex]\mathbf{P(machine \ 1 \ is \ generous | lost) = \dfrac{P(machine \ 1 \ is \ generous \ \cap lost )}{P(lost)} }[/tex]
Let:
P(lost | machine 1 is generous) = A
P(machine 1 is generous) = B
P (Pays | machine 1 is generous ) = C
P(Pays | machine 2 is generous ) = D
P(machine 2 is generous) = E
[tex]\mathbf{P(machine \ 1 \ is \ generous | lost) = \dfrac{(1 - C) \times B}{ (1 - C) \times B + (1 - D) \times E} }[/tex]
[tex]\mathbf{P(machine \ 1 \ is \ generous | lost) = \dfrac{(1 - 0.10) \times 0.50}{ (1 - 0.10) \times 0.50 + (1 - 0.20) \times 0.50} }[/tex]
[tex]\mathbf{P(machine \ 1 \ is \ generous | lost) = \dfrac{0.45}{0.85}}[/tex]
[tex]\mathbf{P(machine \ 1 \ is \ generous | lost) =0.5294}[/tex]
Thus, the probability that machine 1 loses the first bet but it is generous = 0.5294
Thus, since the answer is close to 0.50, we say that the answer is consistent with what is expected.
if x=3 and y=2 then find the value of 2x²-xy+y²-4x
Answers
Answer:
4Step-by-step explanation:
Put x = 3 and y = 2 to the expression 2x²- xy+y²- 4x:
2(3)² - (3)(2) + 2² - 4(3) use PEMDAS
=2(9) - 6 + 4 - 12
= 18 - 6 + 4 - 12
= (18 + 4) - (6 + 12)
= 22 - 18
= 4
40,984 rounded to the nearest ten thousand
Answers
Hi friend! Hope this helps!
40,000.
What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58
Answers
Answer:
5.08
Step-by-step explanation:
5 8/100
Since there are 2 zero's in 100, we need two numbers in the top
Replace 8 with 08 which is the same number
5 08/100
Now write as a decimal
5.08
Answer:
B. 5.08
Step-by-step explanation:
[tex]5\frac{8}{100} = \frac{508}{100}[/tex] 508 ÷ 100 = 5.08I hope this helps!
what is the rate of change of y=7x+9
Answers
A restaurant will select 1 card from a bowl to win a free lunch. Jo puts 5 cards in the bowl. The bowl has 100 cards. What are the odds of jo winning a free lunch?
A)1/5
B)1/10
C)1/20
D) 1/500
Answers
Answer:
1/20
Step-by-step explanation:
Part B
Complete the table for the clementines in units of pounds and cost.
В І о
Font Sizes
А
А -
Pounds Cost
II
O
Answers
Answer:
Pounds Cost
3 $5
6 $10
9 $15
Step-by-step explanation:
I just did this one, and this was the answer.
Which of the following is a rational number?
Square root of 15, square root of 16, square root of 21, square root of 22
Answers
Answer:
square root of 16
Step-by-step explanation:
4x4=16
Cliff needs 6 meters of wood for a building project. He already has 3
meters of wood.
Approximately how many feet of wood does Cliff need? (One meter
is approximately 3.3 feet.)
1 foot
3 feet
6 feet
10 feet
Answers
letter B 3 feet
Step-by-step explanation:
he needs three more to get 6 meters of wood
find x (x+y) 30 24 2x
Answers
Answer:
vfvgyfygj
Step-by-step explanation:
gvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvdyu so yeah
12 apples to 8 oranges
Answers
Suppose that the weight of navel oranges is normally distributed with a mean µµ = 8 ounces, and a standard deviation σσ = 1.5 ounces. a. What percent of oranges weigh more than 11.5 ounces? b. What percent of oranges weigh less than 8.7 ounces? c. If you randomly select a navel orange, what is the probability that it weighs between
Answers
Answer:
Hello some parts of your question is missing below is the missing part
c. If you randomly select a navel orange, what is the probability that it weighs between6.2 and 7 ounces
Answer: A) 0.0099
B) 0.6796
C) 0.13956
Step-by-step explanation:
weight of Navel oranges evenly distributed
mean ( u ) = 8 ounces
std ( б )= 1.5
navel oranges = X
A ) percentage of oranges weighing more than 11.5 ounces
P( x > 11.5 ) = [tex]P ( \frac{x - u}{ std} > \frac{11.5-8}{1.5} )[/tex]
= P ( Z > 2.33 ) = 0.0099
= 0.9%
B) percentage of oranges weighing less than 8.7 ounces
P( x < 8.7 ) = [tex]P ( \frac{x - u}{ std} > \frac{8.7-8}{1.5} )[/tex]
= P ( Z < 0.4667 ) = 0.6796
= 67.96%
C ) probability of orange selected weighing between 6.2 and 7 ounces?
P ( 6.2 < X < 7 ) = [tex]P (\frac{6.2-8}{1.5} < \frac{x - u}{ std} < \frac{7-8}{1.5} )[/tex]
= P ( -1.2 < Z < -0.66 )
= Ф ( -0.66 ) - Ф(-1.2) = 0.13956
What is the y-intercept of the line with equation 3y - 4x = 9?
Answers
Answer: (0, 3)
Step-by-step explanation: To find the y-intercept, we can plug a 0 in for x.
So we have 3y - 4(0) = 9.
This simplifies to 3y = 9.
Dividing both sides by 3, we find that y = 3.
So our y-intercept is 3 which we can write as the ordered pair (0, 3).