Use implicit differentiation to find dy/dx.
ln xy + 5x = 30. Please write out the steps.

Answer:

The equation that describes the problem "If 5 is increased to 8, the increase is what percent of the original number?" would be

[tex]x=\frac{8-5}{5}*100%[/tex] where x is the percent of increasing of 5 to 8.

Step-by-step explanation:

Answer:

The property used here is:

Commutative property of addition

Step-by-step explanation:

Commutative property of addition states that if a and b are any two elements

then, a + b = b + a

We are given a equality we have to determine the property used here

5x · (4y + 3x) = 5x · (3x + 4y)

In the above equation, 4y + 3x = 3x + 4y

a= 4y and b= 3x

Then, a+b=b+a

Hence, the property used above is:

Commutative property of addition

Answer:

GH

Step-by-step explanation:

Answer:I hope this helps you

f (-7)=2. (-7)+8

f (-7)= -14+8

f (-7)= -6

Step-by-step explanation:

Let

x-------> the number of hours

y------> the temperature in degrees Fahrenheit

we know that

For [tex]x=0\ hours[/tex]

[tex]y=-10\°\ F[/tex]

For [tex]x=30\ hours[/tex]

[tex]y=30\°\ F[/tex]

The domain of the function is the interval----------> [tex][0,30][/tex]

[tex]0\ hours \leq x\leq 30\ hours[/tex]

The range of the function is the interval----------> [tex][-10,30][/tex]

[tex]-10\°\ F \leq y\leq 30\°\ F[/tex]

therefore

the answer is

The domain is all real numbers 0 through 30

Answer:

width of the rectangular prism is 4.5 inches.

Step-by-step explanation:

Carltren solves for w and writes the equivalent equation as [tex]w=\frac{V}{lh}[/tex]

Now, we have to find the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches.

Thus, we have

V = 138.24 cubic inches

l = 3.2 inches

h = 9.6 inches.

Substituting these values in the above formula to find w

[tex]w=\frac{138.24}{3.2\cdot9.6}[/tex]

On simplifying, we get

[tex]w=4.5[/tex]

Thus, width of the rectangular prism is 4.5 inches.

The figure which is drawn in option D shows a circle with a diameter.

The diameter of a circle is the distance from one point on the surface of a circle to the other point on the circle's surface, which passes through the center.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

According to the given question

We have, some figures of a circle.

In option A there is no any diameter and radius is drawn for the given circle.

In option B, the given line which is drawn in the circle is the radius of the circle not a diameter. Because " radius of a circle is the distance from the center of the circle to any point on it's circumference.

In option C, there is no any diameter and radius is drawn is the given figure or circle.

In option D, the given line which is drawn in the circle is the diameter of the circle because the distance from one point on the surface of a circle to the other point on the circle's surface, which passes through the center is called diameter.

Learn more about the diameter of a circle here:

https://brainly.com/question/266951

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The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.

Thus, the correct answer is b. 2/3 among the provided choices.

To find an equivalent expression for log base 27 of 9, we need to determine the exponent to which 27 must be raised to obtain 9. In other words, we want to find x in the equation 27^x = 9.

Recognizing that 27 is 3^3 (as 3 times 3 times 3 equals 27), we can rewrite the equation as (3^3)^x = 9. Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.

Now, equating the exponents, 3x = 2 since 3^2 equals 9. Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.

Among the provided choices:

a. 1/3

b. 2/3

c. 3/2

d. 0.798

The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.

The question probable may be:

Which of the following is equivalent to log27 9?

answer choices:

a 1/3

b 2/3

c 3/2

d 0.798

The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.

Thus, the correct answer is b. 2/3 among the provided choices.

We must ascertain the exponent to which 27 must be raised in order to

achieve 9 in order to discover an analogous formula for log base 27 of 9.

Put otherwise, we wish to determine x in the formula 27^x = 9.

Since 3 times 3 times 3 is 27, we may express the equation as (3^3)^x = 9 since we know that 27 is 3^3.

Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.

Now, equating the exponents, 3x = 2 since 3^2 equals 9.

Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.

Among the provided choices:

a. 1/3

b. 2/3

c. 3/2

d. 0.798

The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.

Question

Which of the following is equivalent to log27 9?

answer choices:

a 1/3

b 2/3

c 3/2

d 0.798

The option closest to [tex]\( x = 10\sqrt{10} \) and \( y = 200\sqrt{10} \)[/tex] is option D) length = 100 m, width = 20 m. So, the answer is option D.

To minimize the amount of fencing needed, we want to maximize the area of the pen while fulfilling the requirement of 2000 m².

Let's denote the length of the pen as x and the width as y. Since one side of the pen is a river, we only need to fence three sides: two sides of length x and one side of length y. So, the total fencing required is 2x + y.

We're given that the area of the pen should be 2000 m², so we have the equation:

xy = 2000

We want to minimize 2x + y. We can solve the area equation for one variable and substitute it into the expression for the fencing:

[tex]\[ y = \frac{2000}{x} \][/tex]

Substitute this expression for y into the expression for the fencing:

[tex]\[ \text{Fencing} = 2x + \frac{2000}{x} \][/tex]

To minimize this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x.

[tex]\[ \frac{d}{dx}(2x + \frac{2000}{x}) = 2 - \frac{2000}{x^2} = 0 \][/tex]

[tex]\[ 2 = \frac{2000}{x^2} \][/tex]

[tex]\[ x^2 = \frac{2000}{2} = 1000 \][/tex]

[tex]\[ x = \sqrt{1000} = 10\sqrt{10} \][/tex]

Once we find x, we can find y using the area equation:

[tex]\[ y = \frac{2000}{x} = \frac{2000}{10\sqrt{10}} = 200\sqrt{10} \][/tex]

Now, we need to choose the option closest to x and y.

Checking the options:

A) length = 43 m, width = 46 m

B) length = 50 m, width = 40 m

C) length = 63 m, width = 32 m

D) length = 100 m, width = 20 m

The option closest to [tex]\( x = 10\sqrt{10} \) and \( y = 200\sqrt{10} \)[/tex] is option D) length = 100 m, width = 20 m.

So, the answer is option D.

The three consecutive odd integers are [tex]-11, -9,[/tex] and [tex]-7[/tex].

To find three consecutive odd integers whose sum is -27, let's define the three integers as follows:

According to the problem, the sum of these integers is -27. We can write this as an equation:

[tex]x + (x + 2) + (x + 4) = -27[/tex]

Now, let's simplify and solve the equation step-by-step:

Combine like terms on the left-hand side of the equation:
[tex]x + x + 2 + x + 4 = -27[/tex]
[tex]3x + 6 = -27[/tex]

Subtract 6 from both sides to isolate the term with [tex]x[/tex]:
[tex]3x + 6 - 6 = -27 - 6[/tex]
[tex]3x = -33[/tex]

Divide both sides by 3 to solve for [tex]x[/tex]:
[tex]x = \frac{-33}{3}[/tex]
[tex]x = -11[/tex]

So, the first consecutive odd integer is [tex]-11[/tex].

Find the second consecutive odd integer:
[tex]-11 + 2 = -9[/tex]

Find the third consecutive odd integer:
[tex]-11 + 4 = -7[/tex]

Final answer:

The height of a can holding three tennis balls is 20.1 cm, while the circumference of the lid is approximately 21.02 cm. Hence, the circumference of the can's lid is slightly larger than its height.

Explanation:

The question is comparing two different measurements of a can that holds tennis balls. One measurement is the height of the can, and the other is the circumference of the can's lid. In a standard can of tennis balls, three tennis balls are stacked on top of each other perfectly. Knowing that the diameter of a standard tennis ball is approximately 6.7 cm, we can calculate the height of the can by multiplying the diameter of one tennis ball by three (since the diameter is the same as the height for a ball stacked in such a can).

Height of can = Diameter of tennis ball × number of balls
= 6.7 cm × 3
= 20.1 cm.

To determine the circumference of the can's lid, we first need to find the radius of the lid which would be half the diameter of a tennis ball:

Radius of lid = Diameter of tennis ball / 2
= 6.7 cm / 2
= 3.35 cm.

Then, we use the formula for the circumference of a circle, which is C = 2πr:

Circumference of lid = 2π × Radius of lid
= 2π × 3.35 cm
≈ 21.02 cm.

The circumference of the lid is slightly larger than the height of the can. Therefore, the circumference of the can's lid is larger than the height of the can of tennis balls.

The correct set of equations based on the information given about the pricing of apples, bananas, and coconuts by Old MacDonald is: a + 5b + c = 14, 3a + 3b + 3c = 18, and a + 2b + 3c = 14.

The student is asking which set of equations corresponds to the problem given, involving prices for apples, bananas, and coconuts. In the context of this problem, variables a, b, and c represent the price of an apple, a banana, and a coconut, respectively. By analyzing the problem's given information, we can deduce the following equations:

These equations reflect the costs of different combinations of fruit based on the prices provided by Old MacDonald. To solve for the variables a, b, and c, we could use a system of linear equations.

Answer:

The answer is 30.

Step-by-step explanation:

Answer:

The distance CC' is [tex]\sqrt5units[/tex]

Step-by-step explanation:

Given the transformation T:  (x, y) (x + 2, y + 1)

we have to find the distance CC'

Let coordinate of C are (a,b).

Now, by using transformation T the coordinates of C' are (a+2,a+1)

By using distance formula,

[tex]CC'=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\= \sqrt{(a+2-a)^2+(b+1-b)^2}\\\\=\sqrt{4+1}=\sqrt5 units[/tex]

Hence, the distance CC' is [tex]\sqrt5units[/tex]

Answer: The correct option is,

A. <

Step-by-step explanation:

Given,

[tex]8=x+y-----(1)[/tex]

Also,

[tex]y > 0[/tex]

Adding x on both sides ( additive property of inequality )

[tex]x+y>x+0[/tex]

[tex]x+y>x[/tex]

From equation (1),

[tex]8>x[/tex]

Hence, x is less than 8,

We use < sign for less than,

⇒ x is '<' 8

Option A is correct.

Answer:

6, 3, 10 and 11

A, C, D and E are correct options.

Step-by-step explanation:

The given inequality is 11x < 132

Now, divide both sides by 11.

x < 12

Now, from the given options we check, the numbers that are less than 12. All those number should lie in the given solution set.

The numbers 6, 3, 10 and 11 are less than 12.

Hence, the numbers 6, 3, 10 and 11 belongs to the solution set of the given inequality.

A, C, D and E are correct options.