Differentiate the following function with respect to x :

(2x^2+4x+3)^2
_________

Answer:

9, 12,15

Step-by-step explanation:

a^2+b^2=c^2

9^2+12^2=15^2

81+144=225

Step-by-step explanation:

Given

Number of Radio Stations=28

Number of College Radio Stations=12

\(required \: probabilty = \frac{number \: of \: college \: radio \: stations}{total \: number \: of \: radio \: stations} \)

Probability=12/28=3/7

The value of x for a given logarithmic expression is 2 or -4.

What is a logarithmic function?

Logarithmic function is the inverse of an exponential function. It is denoted by using the word, log. For example log 10 = 1.

Solving the given equation: log ₂ ( x² + 2x ) = 3

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

Now, the equation becomes,

log ( x² + 2x ) / log 2 = 3

log ( x² + 2x ) = 3 × log 2

log ( x² + 2x ) = log 2³

log ( x² + 2x ) = log 8

Applying exponent both the sides, we get,

e^[log ( x² + 2x )] = e^[log 8]

x² + 2x = 8

x² + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2 or -4

Hence, the value of x for a given logarithmic expression is 2 or -4.

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Answer:

The slope is \(\frac{3}{2}\)

Step-by-step explanation:

Hi there!

We are given the points (0, 4) and (6, 13)

We want to find the slope of the line containing these two points

Slope (m) is the steepness of the line. When calculating from two points, you use the equation \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

Although we have what we need to find the slope, let's label the values of the points to avoid confusion and mistakes.

\(x_1=0\\y_1=4\\x_2=6\\y_2=13\)

Substitute these values into the equation

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{13-4}{6-0}\)

Subtract

m=\(\frac{9}{6}\)

Simplify

m=\(\frac{3}{2}\)

The slope of the line is 3/2

Hope this helps!

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The particle's velocity at time \(t\) is equal to the first derivative of its position at that time, and acceleration is the second derivative.

We have

\(s(t) = -4\sin(t) - \dfrac t2 + 10 \implies s'(t) = -4\cos(t) - \dfrac12 \implies s''(t) = 4\sin(t)\)

Find when the velocity is zero:

\(s'(t) = -4\cos(t) - \dfrac12 = 0 \implies \cos(t) = -\dfrac18 \implies t = \cos^{-1}\left(-\dfrac18\right) \approx 1.696\)

At this time, the acceleration of the particle is approximately

\(s''(1.696) \approx \boxed{3.969}\)

(B)

Shin splints are a common cause of lower leg pain and can be caused by a variety of factors, such as poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot.

Shin splints is a term used to describe pain that occurs along the shin bone (tibia), which runs down the front of the lower leg. Common causes of shin splints include poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot. Poorly fitting shoes can put excessive pressure on the back of the heel and the front of the foot, leading to inflammation and pain in the shin area. Weak calf muscles can cause the foot to overpronate or roll inward, which can put extra strain on the shin bone and its muscles. Running on uneven terrain can also cause the shin bone to suffer from too much pressure, leading to shin splints. Finally, overpronation of the foot is when the foot rolls inward excessively and puts extra strain on the shin bone and its muscles. Shin splints can cause pain and discomfort and should be treated as soon as possible by rest, stretching, icing, and wearing properly fitting shoes.

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Answer:

4px=20

x=(20/4p)-----(1)

-4px=20--------(2)

putting value of x in epn 2

-4p*20=20*4p

-80p=+80p

Both cut these value are rejected

Checkout the question again bro it might be wrong

Please for my hard work make me brainliest answer

Answer:

400

Step-by-step explanation:

so the question is 20 times 20. This problem means you are doing 20, 20 times. Since you are in 3rd grade I will use the counting meathod. So to do this you need to count starting at 20 by 20 20 times.

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400.

As you can see the answer is 400. I started at 20 and I consistently counted by 20. Also I did it 20 times. I did this because the problem says to do 20, twenty times.

Answer:5.97

Step-by-step explanation.  

you have to look at the question.

you have to look around the question

The very last step is you have to answer it  

The average rate of change between x=2 and x=6 is 23. To find the net change between x=2 and x=6, we need to find the difference between f(6) and f(2).

f(6) = 3(6)² - 6 = 108 - 6 = 102

f(2) = 3(2)² - 2 = 12 - 2 = 10

The net change is therefore: f(6) - f(2) = 102 - 10 = 92.

To find the average rate of change between x=2 and x=6, we need to find the slope of the line connecting the points (2, f(2)) and (6, f(6)).

The slope of this line can be found using the slope formula:

slope = (f(6) - f(2)) / (6 - 2) = 92/4 = 23

Therefore, the average rate of change between x=2 and x=6 is 23.

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The area if base x height

8 x height = 96

Divide both sides by 8 to find the base size:

96 / 8 = base

base = 12

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Answer:

1. x= -1 & x= -13

2. x= -3 & x= -4

3. x= -3 & x= -5

4. x= -6 & x= -2

5. x= -5 & x= -2

8. x= -7 & x= -3

9. x= -8 & x= -2

10. x= -3 & x= -3

11. x= -5 & x= -4

12. x= -2 & x= -2

13. x= -6 & x= -7

14. x= -6 & x= -3

15. x= -10 & x= -7

The following equation represents the function g in function notation,

g(x) = 3x - 14 [Option (A)]

Definition of a Function

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.

Given equation is,

y -3x = -14

⇒ y = -14 + 3x

or y = 3x - 14

Here, y stands for or represents the function g(x) which is a function of independent variable x.

Thus, the correct function notation is as follows,

g(x) = 3x - 14

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Answer:

We know P(x<$180,000)=.25 and P(x>$320,000)=.25

Using the formula for normal distributions, we can find the mean and standard deviation (z = (x-mean)/SD) using the given info. Then you'll have two equations with two unknowns.

Finally when finding part a, make sure to do a continuity correction [P(x<$200,000) = P(x≤$200,000.5) = ?]

Step-by-step explanation:

Answer:

anything to the power of zero is 1 so assuming thats a dash and not a negative its B

Step-by-step explanation:

Answer:

D. 3•(x - 9) = 15

Step-by-step explanation:

Three times the difference of x and 9 is 15

        3                               (x - 9)            = 15

3(x - 9) = 15

Answer:

1/2

Step-by-step explanation:

1/2 is bigger then 1/3 and 1/4.

Answer:

After that, the 3X + 1 problem has appeared in various forms. It is one of the most infamous unsolved puzzles in the word. Prizes have been offered for its solution for more than forty years, but no one has completely and successfully solved it [5].

Step-by-step explanation:

The sum of all the angles that are labeled in the given vertex is 294°

In a single vertex, the three angles around the vertex are given as 55°, 64°, and 175°

We have to find the sum of all the angles that are labeled in the given single vertex.

A vertex is a point two or more lines meets.

It is the corner of a geometrical shape.

Example:

A square has 4 corners so it has 4 vertexes.

A cube has 8 corners so it has 8 vertexes.

We will add all the different angles in the single vertex as shown in the figure below.

Let,

Angle A = 55°

Angle B = 64°

Angle C = 175°

The sum of all the angles that are labeled is:

= Angle A + Angle B + Angle C

= 55° + 64° + 175°

= 294°

The sum of all the angles that are labeled in the given vertex is 294°

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Answer:

y = -x -2

Step-by-step explanation:

-1 is the slope

-2 is the y-intercept

slope = \(\frac{-4-1}{2-(-3)}\) = \(\frac{-5}{5}\) = \(\frac{-1}{1}\) = -1

Answer:

Step-by-step explanation:

Dhddhhfjvjvmx,sfkiritifkflf,gjgi*jfckblhog

Answer:

3.25lbs in the last 4 months

Step-by-step explanation:

Answer:

Step-by-step explanation:

The standard deviation for the given sample data is 2.83.

To calculate the standard deviation, we first need to calculate the mean of the sample data:

Next, we calculate the deviation of each data point from the mean:

Then, we square each deviation:

Next, we calculate the sum of squared deviations:

To calculate the variance, we divide the sum of squared deviations by the sample size minus one:

Finally, we calculate the standard deviation by taking the square root of the variance:

Therefore, the standard deviation for the given sample data is 2.83. This tells us how spread out the data points are from the mean, with most data points being within 2.83 units of the mean.

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Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

Given the functions in the question;

To evaluate f + g, replace the function designators in f + g with the actual functions and simplify

( f + g )(x) = f(x) + g(x)

( f + g )(x) = (4x + 1) + (x + 5)

Remove the parenthesis and collect like terms

( f + g )(x) = (4x + 1) + (x + 5)

( f + g )(x) = 4x + 1 + x + 5  

( f + g )(x) = 4x + x + 5  + 1

( f + g )(x) = 5x + 6  

Given the functions f(x) = 4x + 1 and  g(x) = x + 5, the function operation ( f + g )(x) is 5x + 6.

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Bianca is the first to reach the finish line with her speed.

What is speed?

Alberto runs faster in the beginning of the race.

For the first hour of the race, Alberto keeps a 50 km/h pace.

Bianca's running pace is exponential in the meantime.

Bianca is the first to reach the finish line with her speed.

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Answer:  Initially,

Alberto

Albertostart  runs faster.

Alberto maintains a speed of

20km/h during the first hour of the race.

Meanwhile, Bianca's running speed is increasing

The first person to cross the finish line is Bianca

Step-by-step explanation:

A, K, and α are all positive, the expression in parentheses is always negative, and therefore the second derivative is still negative. This implies that the marginal product of labor decreases as L is raised when K is set.

The production function of a company is Q(L;K)=ALαK1−α where A>0 and 0<α<1. We are required to demonstrate that the marginal product of labor is good and that it is a declining function of L when K is set.  We can calculate the marginal product of labor as follows:

Marginal product of labor = dQ/dL = AαK1−α(1-α)L−α

= AαK1−α(1-α)/L1-α

As L is raised, we find that the marginal product of labor is positive because A>0 and α, K, and (1-α) are all positive. Similarly, since α<1, the marginal product of labor is a decreasing function of L, which we can see from the fact that the exponent α of L is negative.

When K is kept fixed, we can use calculus to demonstrate that the marginal product of labor is decreasing as L increases. We first find the second derivative of the production function with respect to L, which is as follows:

d2Q/dL2 = AαK1−α(1-α)(1-α-Lα-1)

Since A, K, and α are all positive, the expression in parentheses is always negative, and hence the second derivative is always negative. This means that the marginal product of labor is decreasing when L is raised while K is set.


The production function of a company is Q(L;K) = ALαK1−α where A>0 and 0<α<1. We have to show that the marginal product of labor is good, and that it is a declining function of L when K is set.

The marginal product of labor is:

Marginal product of labor = dQ/dL = AαK1−α(1-α)L−α

= AαK1−α(1-α)/L1-α

As L is increased, we find that the marginal product of labor is positive since A>0 and α, K, and (1-α) are all positive. Similarly, because α<1, the marginal product of labor is a decreasing function of L, as the exponent α of L is negative.

When K is kept fixed, we can use calculus to show that the marginal product of labor is declining as L rises. The second derivative of the production function with respect to L is found first:

d2Q/dL2 = AαK1−α(1-α) (1-α-Lα-1)

Since A, K, and α are all positive, the expression in parentheses is always negative, and therefore the second derivative is still negative. This implies that the marginal product of labor decreases as L is raised when K is set.


When K is kept fixed, the marginal product of labor is a decreasing function of L. This means that the company must hire fewer workers to achieve the same amount of output if it already has a large number of workers.

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Prevalence rates are a measure of how common a disease is in a population.

To calculate the prevalence rate, you would divide the number of current cases of the disease by the total population at risk of the disease. This can give you an idea of the overall burden of the disease in a given population. It's important to note that prevalence rates can vary depending on factors such as age, gender, geographic location, and other demographic or health-related factors. Additionally, prevalence rates can change over time as new cases are identified and as treatments or prevention strategies are implemented. Overall, understanding the prevalence of a disease can help public health officials and healthcare providers identify areas of need and develop targeted interventions to reduce the impact of the disease on affected populations.

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Answer:

it's D

Step-by-step explanation:

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