What's the product of (1/3x^2y)*(1/6xy^3)

The log 8(1) = 0Let x = log4(x) Evaluate (1024)We know that the logarithm of a number in a given base is the power to which the base must be raised to get the number.

For example, if the base is 2, then log2(8) = 3 because 23 = 8.

Using this definition, we can justify the statement log8(1) = 0 as follows:log8(1) = 0 because 80 = 1. This means that the power to which 8 must be raised to get 1 is 0.

Therefore, log8(1) = 0.Next, we have:x = log4(x) This means that 4 to the power of x equals x. We can solve for x as follows:4x = x4x - x = 0x(4 - 1) = 0x = 0 or x = 1Plugging in x = 1, we get:log4(1) = 1

This is true because 41 = 1. Finally, we can evaluate (1024) as follows:(1024) = (210)10 = 210·10 = 210+1 = 211This is true because 210 is the base-2 logarithm of 1024. Therefore, (1024) = 211.

Now, we need to write a mathematical equation to justify the statement ln(17) ≈ 2.832. To do this, we need to know the definition of the natural logarithm function, denoted as ln(x).

The natural logarithm of a positive number x is the logarithm of x in the base e, where e is a mathematical constant approximately equal to 2.71828. Therefore, we have ln(17) ≈ 2.832 because e2.832 ≈ 17.

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Answer:

x = 180 -117

x = 63°

y = 90 - 63

y = 27°

Step-by-step explanation:

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer: -1

Explanation: -3 + 5 = 2

2x + 2 = 0

x = -1

Amita can only use one of the possible molds if she wants a rectangular prism with a square base and volume of 28 cubic centimeters.

Let the length, width, and height of the rectangular prism be x, y, and z respectively. Since the volume of the prism is 28 cubic centimeters, we have:

x * y * z = 28

Since x, y, and z are whole numbers, we can find all possible combinations of three factors whose product is 28. These are:

1 * 1 * 28

1 * 2 * 14

1 * 4 * 7

2 * 2 * 7

Therefore, there are four different molds that Amita can make.

If Amita wants the mold to have a square base, then the length and width of the base must be equal. We can see that only one of the above combinations has equal length and width, which is:

2 * 2 * 7

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Answer:

Lea messed up on line one when you flip a fraction the exponents become negative hers haven't changed

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x+7)/2= -8

x + 7 = -16

x= -23

(y + 1)/2 = -9

y + 1 = -18

y = -19

(-23, -19)

The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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Answer:

yes

Step-by-step explanation:

The positive integers are the numbers 1, 2, 3, ...

given the function

A) the value when Shiyun bought the car (t=0)

the value when Shiyun bought the car was 25000 USD

b) calculate the Value of the car 3 years after Shiyun bought it (t=3)

then the Value of the car 3 years after Shiyun bought it was 19601.32 USD

c)calculate time when V is half the value when Shiyun bought it

since the started value is 25000

half of that value is 12500

then

Solving for t

then t when v=12500 is

t=8.55

Answer:

\(3b^{4} + 5b^{3} + b^{2} + 5b\)

Step-by-step explanation:

\( {b}^{4} + 2 {b}^{4} + 8 {b}^{3} - 3 {b}^{3} + {b}^{2} + 5b\)

Answer:

8

Step-by-step explanation:

SW and UW are equal because they are at the midpoint . A midpoint is a point on a line segment that divides it into two congruent segments.

If "r" is an odd function, "s" is an even function , then the function "s(x) × s(x)" will be an (a) Even Function .

A function is considered as Even Function if it satisfies : f(x) = f(-x) for all x in its domain, and

A function is considered as Odd Function if it satisfies : f(x) = -f(-x) for all x in its domain.

The product of two even functions is even, because if f(x) and g(x) are both even, then

⇒ (f(x) × g(x)) = (f(-x)) × (g(-x)) = f(-x) × g(-x) = f(x)g(x),

So, f(x)g(x) is also even.

In this case, since the function "s" is an even function, So , "s(x) × s(x)" is also Even .

The given question is incomplete , the complete question is

Assume that "r" is an odd function, "s" is an even function, and both "r" and "s" are defined on the entire real line R. Are the following functions even or odd?

Is "s(x) × s(x)" even or odd ?

(a) even function

(b) odd function

(c) neither

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Step-by-step explanation:

4.1  X 10^2    is    4.1  X 100   =   410

We can actually deduce here that the biggest advantage of correlational research is: The use of important variables in a real-world setting.

A correlational research is actually known to be the research that investigates relationships between two variables or more. It does this without the researcher trying to manipulate or control any of the variables.

Correlational research is known to be a non-experimental type of quantitative research. In this research, the researcher assesses the statistical relationship that exists between the variables.

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Answer: 51.4

Step-by-step explanation:

Rule:

The sum of all the exterier angles of any shape is 360

Heptagon has 7 sides

Solution:

sides = 360/7 =  51.4

The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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Answer: 3v+15

Step-by-step explanation:

Using distribution, you simply multiply everything in the brackets by the three. This gets you 3v+15.

Answer:

(3v + 15)

Step-by-step explanation:

If you use the distributive property, you times 3 x v = 3v

and you multiply 3 x 5 = 15

Put those together and you have your answer!

Kim can arrange the 10 identical lamps on the 3 identical tables in 66 different ways.

Number of lamps= 10

Number of tables=3

For identical objects we have the following formula;

(n + r - 1)C(r - 1) (r - 1)

We thus have;

n + r - 1 = 10 + 3 - 1

            = 12

r - 1 = 3 - 1

      = 2

Thus,

(n + r - 1)C(r - 1) = ¹²C₂

Apply the following combination formula:

ⁿCr = n!/((n - r)!r!)

So, we have:

¹²C₂ = 12!/((12 - 2)! * 2!)

¹²C₂ = 12!/(10! * 2!)

¹²C₂ = 12 * 11 * 10!/(10! * 2!)

¹²C₂ = 132/2

       = 66

Therefore, there are 66 ways to put all the lamps on the tables.

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So the total surface area of the composite figure is 138 square inches.

To find the surface area of the composite figure, we need to add the areas of all the faces of the figure.

The square has an area of 6 * 6 = 36 square inches.

The green rectangular prism has a base with an area of 6 * 3 = 18 square inches. It also has four lateral faces, each with an area of 3 * 7 = 21 square inches. The total area of the lateral faces is 4 * 21 = 84 square inches.

So the total surface area of the composite figure is 36 + 18 + 84 = 138 square inches.

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Answer:

there is no answer, absolute value always > 0

To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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Answer:

Step-by-step explanation:

$4.64

Answer:

x=51/5

Step-by-step explanation:

Add 61 on both sides

You'll have 5x=51

So now 51/5 is your answer.

Answer:

16/5

Step-by-step explanation:

|5x - 6| = -10

5x -6 = 10

5x = 10+6 = 16

x = 16/5

Step-by-step explanation:

please mark me as brainlist please

Answer:

Uhmm you need to know the radius too to find the area...

To determine the complex exponential Fourier series representation for each of the given signals, we can use the formula:

X(t) = ∑[n=-∞ to ∞] Cn * e^(jnω0*t)

where Cn represents the complex Fourier coefficients and ω0 is the fundamental frequency.

X(t) = cos(ωt):

The complex exponential Fourier series representation for X(t) = cos(ωt) is:

X(t) = C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j*(-1)ω0t)

= C0 + C1 * e^(jω0t) + C(-1) * e^(-jω0t)

x(t) = -cos(0.5 * ωt):

The complex exponential Fourier series representation for x(t) = -cos(0.5 * ωt) is:

x(t) = C0 * e^(j0ω0t) + C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j(-1)ω0t)

= C0 + C0 + C1 * e^(j0.5ω0t) + C(-1) * e^(-j0.5ω0t)

x(t) = cos(2t + 1):

The complex exponential Fourier series representation for x(t) = cos(2t + 1) is:

x(t) = C0 * e^(j0ω0t) + C2 * e^(j2ω0t) + C(-2) * e^(j*(-2)ω0t)

= C0 + C2 * e^(j2ω0t) + C(-2) * e^(-j2ω0t)

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