Simplify the exponential expression. 2^4⋅3^4

ln(5y) = 4xy

Differentiate both sides with respect to x, taking y = y(x) :

d/dx [ln(5y)] = d/dx [4xy]

1/(5y) d/dx [5y] = 4y + 4x dy/dx

5/(5y) dy/dx = 4y + 4x dy/dx

1/y dy/dx = 4y + 4x dy/dx

(1/y - 4x) dy/dx = 4y

dy/dx = 4y / (1/y - 4x)

Since y = 0 is outside the domain (ln(0) is undefined), we can multiply the right side by y/y :

dy/dx = 4y ² / (1 - 4xy)

To compute the second derivative, differentiate both sides again:

d/dx [dy/dx] = d/dx [4y ² / (1 - 4xy)]

d²y/dx ² = ((1 - 4xy) d/dx [4y ²] - 4y ² d/dx [1 - 4xy]) / (1 - 4xy)²

d²y/dx ² = ((1 - 4xy) 8y dy/dx - 4y ² (0 - 4y - 4x dy/dx)) / (1 - 4xy)²

d²y/dx ² = ((8y - 32xy ²) dy/dx + 16y ³ + 16xy ² dy/dx) / (1 - 4xy)²

d²y/dx ² = ((8y - 16xy ²) dy/dx + 16y ³) / (1 - 4xy)²

Substitute the first derivative founder earlier:

d²y/dx ² = ((8y - 16xy ²) (4y ² / (1 - 4xy)) + 16y ³) / (1 - 4xy)²

d²y/dx ² = ((8y - 16xy ²) 4y ² + 16y ³ (1 - 4xy)) / (1 - 4xy)³

d²y/dx ² = (16y ³ (3 - 8xy)) / (1 - 4xy)³

The second derivative vanishes wherever the numerator vanishes (so long as 4xy ≠ 1) :

16y ³ (3 - 8xy) = 0

16y ³ = 0   or   3 - 8xy = 0

y = 0   or   8xy = 3

As pointed out earlier, y = 0 is outside this function's domain, so we're left with points on the curve

y = 3/(8x)

Substituting this into the original function gives

ln(5 (3/(8x))) = 4x (3/(8x))

ln(15 / (8x)) = 12/8

ln(15) - ln(8x) = 3/2

ln(8x) = ln(15) - 3/2

8x = exp(ln(15) - 3/2)

8x = 15 exp(-3/2)

x = 15/8 exp(-3/2)   →   y = 1/5 exp(3/2)

or approximately (0.4184, 0.8963).

(where exp(x) = e ˣ)

Answer:

3/2

Step-by-step explanation:

Slope = rise / run

Rise: 3

Run: 2

Slope = 3/2

Answer:

Awnser: the slope is y=-3/1

Answer:

6. 8 mi³

7. 72 cm³

Step-by-step explanation:

6. Volume of triangular pyramid = ⅓*A*H

Where,

A = area of triangular base = ½*b*h = ½*3*4 = 6 mi

H = height of pyramid 4 mi

Volume = ⅓*6*4 = 8 mi³

7. Volume of triangular prism = ½*bhl

Where,

b = 3 cm

h = 6 cm

l = 8 cm

Volume = ½*3*6*8 = 72 cm³

Answer: D

Step-by-step explanation:

The volume of the sphere is 12,348 cubic units.

Option B is the correct answer.

It is a three-dimensional figure.

The formula for the volume of a sphere is given by V = (4/3)πr³,

We have,

The formula for the volume of a sphere is given by V = (4/3)πr³,

where r is the radius of the sphere and π is a constant approximately equal to 3.14.

Substituting the value of r = 21 units, we get:

V = (4/3)π(21)³

V = (4/3)π(9261)

V = 154(3)(7²)

V = 22,562π cubic units (using 22/7 as an approximation of π)

Rounding to the nearest whole number, the volume of the sphere is approximately 12,348 cubic units.

Thus,

The volume of the sphere is 12,348 cubic units.

Learn more about Sphere here:

https://brainly.com/question/12390313

#SPJ7

Answer:

m = 6

Step-by-step explanation:

5m - 1 = 4m + 5

5m - 4m = 5 + 1 = 6

m = 6

Answer:

m = 6

Step-by-step explanation:

5 x 6 = 30

30 - 1 = 29

4 x 6 = 24

24 + 5 = 29

29 = 29

V = 1/3 * B * h     /*3

V * 3 = B * h       /B

V * 3 / B = h

h = V * 3 / B

Answer:

I think a option is correct

Step-by-step explanation:

because they are point on the graph

Answer:

No its not

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

the bakery used 25% of butter.

Answer:

240 X 35% = 84

240 + 84 = 324

Step-by-step explanation:

Answer:

In this lesson we learned that inductive reasoning takes information known about a specific scenario and applies it to a large population, while deductive reasoning takes information known about a population and applies it to a specific scenario.

Deductive reasoning

To answer this question, we must understand the clear distinction that exists between inductive and deductive reasoning.

Inductive reasoning is the process of reasoning that involves making specific observations and drawing a general conclusion from those observations

That is, the observations are narrower than the conclusion.

Deductive reasoning is the process of reasoning that applies the observations made from a general population to a specific case. That is, making specific conclusions from general observations

Therefore, the illustration given in this exercise is an example of a deductive reasoning.

Learn more here: https://brainly.com/question/4163182

Answer:

We have the system:

y < -3*x - 2

y > -3*x + 8

The solution set of this system will be the intersection between the solution sets of both inequalities.

First, to find each set of solutions, we need to find the line:

y = -3*x - 2

Because we have the symbol <, the solution set will be all the points below this line, and the line will be a dashed line (meaning that the points on the line are not solutions).

For the other line we have the same approach.

First we need to find the line:

y = -3*x + 8

Now because we used the symbol >, we need to shade the region above the line, and again the line must be a shaded line.

The graph of this system can be seen below.

Where we can see that there is no intersection of the two solution sets, meaning that the system of inequalities has no solutions.

Answer:

Know what? You need to add more to your question (:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

Correct answer is A

Step-by-step explanation:

are we suppose to make a story or something

Answer:

This question makes 0 sense! how do i even answer?

Answer:

Thomas is 14  because 19-5=14

Step-by-step explanation:

brailiest please

Answer:

7

Step-by-step explanation:

19-5=14

14/2=7

Answer:

Any ratio that can be simplified to 1:3

Step-by-step explanation:

Any ratio would work for this answer, but the ratio would have to simplify back to 1 to 3.

Here are some examples you could use:

2:6 = 1:3

3:9 = 1:3

4:12 = 1:3

6:18 = 1:3

7:21 = 1:3

10:30 = 1:3

Answer:

x = 2

Step-by-step explanation:

=============================================================

Explanation:

The tickmarks tell us which sides are the same length. This in turn tells us that points N and O are midpoints of LJ and LK respectively (since midpoints cut a segment in half). We consider segment NO to be a midsegment.

Recall that midsegments are half as long as the side they are parallel to. That means segment NO is half as long as JK. This reverses to segment JK being twice as long as segment NO.

-------------

JK = 2*(NO)

2x+8 = 2*(12)

2x+8 = 24

2x+8-8 = 24-8 .... subtract 8 from both sides

2x = 16

2x/2 = 16/2 ...... divide both sides by 2

x = 8

If x = 8, then 2x+8 = 2*8+8 = 16+8 = 24. This shows that segment JK is 24 units long which is double that of midsegment NO being 12 units long. This confirms we have the correct x value.

Answer:

6,500 pennies or $65

Step-by-step explanation:

Step-by-step explanation:

Compounded quarterly means n=4

Answer:

10 feet

Step-by-step explanation:

Find the hypotenuse

a^2 + b^2 = c^2

6^2 + 8^2 =c^2

36+ 64 = c^2

100=c^2

(square root) 100 = 10

c=10

Answer:

c = 8

Step-by-step explanation:

Given the following data;

Slope, m = -2

Points (x, y) = (5, -2)

To find the intercept, c;

Equation of a straight line is given by the formula: y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

Substituting the values in order to find the intercept, we have;

-2 = -2(5) + c

-2 = -10 + c

c = 10 - 2

c = 8

Therefore, the y-intercept is 8.

Answer:

31 units ²

Step-by-step explanation:

Area of a rectangle = length × width

Length = 8 units

Width = 5 units

Area of a rectangle = length × width

= 8 units × 5 units

= 40 units ²

Area of of the blue square = length ²

Length = 3 units

Area of of the blue square = length ²

= (3 units) ²

= 9 units ²

Area of the orange colored part of the figure = Area of a rectangle - Area of of the blue square

= 40 units ² - 9 units ²

= 31 units ²

Area of the orange colored part of the figure = 31 units ²

9514 1404 393

Answer:

  A = (-5, -5)

Step-by-step explanation:

Solving ...

  M = (A +B)/2

for A, you find ...

  A = 2M -B

  A = 2(1/2, -2) -(6, 1) = (1-6, -4-1)

  A = (-5, -5)

Answer:

16

Step-by-step explanation:

just turn them all positive and add

Answer:

It is -3/4

Step-by-step explanation:

Coefficient : the number multiplied by d² in the equation

so it's ans is -3/4

Answer:

x= 2

Step-by-step explanation:

Divide each term in

6

x

=

12

by

6

.

6

x

6

=

12

6

Cancel the common factor of

6

.

Tap for more steps...

x

=

12

6

Divide

12

by

6

.

x

=

2