John’s car runs an average of 30 miles per gallon. At this rate, how many gallons would John use on a 3600-mile trip?

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:

25%

Step-by-step explanation:

the bakery used 25% of butter.

Answer:

240 X 35% = 84

240 + 84 = 324

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

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:

16

Step-by-step explanation:

just turn them all positive and add

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

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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

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:

I think a option is correct

Step-by-step explanation:

because they are point on the graph

V = 1/3 * B * h     /*3

V * 3 = B * h       /B

V * 3 / B = h

h = V * 3 / B

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:

No its not

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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

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

are we suppose to make a story or something

Answer:

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

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

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

Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuseAnswer:

Step-by-step explanation:

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:

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:

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:

the answer is A

Step-by-step explanation:

Answer:

Correct answer is A

Step-by-step explanation:

Answer:

6,500 pennies or $65

Step-by-step explanation:

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

Step-by-step explanation:

Compounded quarterly means n=4