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Pachacha [2.7K]
3 years ago
11

Given that y^x=x^y, wich of the following expressions equal dy/dx?

Mathematics
2 answers:
motikmotik3 years ago
7 0

Answer:

E

Step-by-step explanation:

x^y = y^x

y lnx = x lny

Differentiation both sides with respect to x

(y' × lnx) + (y/x) = lny + x(1/y)y'

y'lnx + y/x = lny + (x/y)y'

y'[lnx - x/y] = lny - y/x

y'[(ylnx - x)/y] = (xlny - y)/x

y' = [y(xlny - y)] ÷ [x(ylnx - x)]

y' = [y(y- xlny)] ÷ [x(x - ylnx)]

patriot [66]3 years ago
6 0

Answer:

E. dy/dx = y (y − x ln y) / (x (x − y ln x))

Step-by-step explanation:

yˣ = xʸ

Take log of both sides.

ln yˣ = ln xʸ

x ln y = y ln x

Implicit derivative (use product rule and chain rule).

x (1/y dy/dx) + ln y (1) = y (1/x) + ln x (dy/dx)

Solve for dy/dx.

x/y dy/dx + ln y = y/x + ln x dy/dx

x² dy/dx + xy ln y = y² + xy ln x dy/dx

(x² − xy ln x) dy/dx = y² − xy ln y

dy/dx = (y² − xy ln y) / (x² − xy ln x)

dy/dx = y (y − x ln y) / (x (x − y ln x))

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prisoha [69]

Answer:

b. You would conclude that the differences in the average scores can be traced to differences in the working memory of the two groups.

Step-by-step explanation:

Though the average scores of the two sets could have lead to various conditions, but retentive ability deminishes with respect to an increase in age. With respect to the age of the elderly people involved, it is expected that some of them would not be able to retain information for a long period of time. Thus, their average score is 72%.

The college students' are younger, so it is expected that they should be able to retain more information. That ability is one of the reasons why their average score is 85%.

It can be concluded from the research that the differences in the average scores is probably due to the working memory of the two groups.

6 0
2 years ago
OPENER: Select all the names for the answers to a polynomial equation
alexira [117]
Roots stems finite solution
6 0
3 years ago
Does anyone know how to do this
Doss [256]

Answer :Plotting the points into the coordinate plane gives us an observation that this quadrilateral with vertices d(0,0), i(5,5) n(8,4) g(7,1) is a KITE, as shown in figure a.

Step-by-step explanation:

Considering the quadrilateral with vertices

d(0,0)

i(5,5)

n(8,4)

g(7,1)

Plotting the points into the coordinate plane gives us an observation that this quadrilateral with vertices d(0,0), i(5,5) n(8,4) g(7,1) is a KITE, as shown in figure a.

From the figure a, it is clear that the quadrilateral has

Two pairs of sides

Each pair having two equal-length sides which are adjacent

The angles being equal where the two pairs meet

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4 0
3 years ago
Colin drew the floor plan of his bedroom shown below. What is the area of his bedroom in square feet?
labwork [276]
512 because multiply each number together
4 0
2 years ago
The volumes of two cubes are 32ft^3 and 1372ft^3
ser-zykov [4K]

Answer:

1) 8 : 343

2) 42.875 or 42 ⅞

3) 4 : 49

4) 16ft²

Step-by-step explanation:

Volume of cube: s³

Surface area of cube: 6s²

_____________________

32ft^3 and 1372ft^3 →

32 : 1372 = 8 : 343

343 / 8 = 42 ⅞ = 42.875

s³ → 6s²

s³ = 8, s = 2, s² = 4.

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These are proportional so it is already in the simplest ratio so it is not necessary to multiply by 6.

s³ → 8 : 343

6s² → 4 : 49

(4 / 49) × 196ft² = 16ft²

4 0
3 years ago
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