Find the volume of the figure below.
6 cm
10 cm
8 cm
7 cm

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

For more such questions on percentage , Visit:

https://brainly.com/question/30744872

#SPJ11

Answer:

14/29

Step-by-step explanation:

16 red + 16 black = 32 total.

remove one black and two red = 32 - 1 - 2 = 29.

there are now 16 - 2 red = 14 red.

P(red) = 14/29

Answer:

Step-by-step explanation:

f(x)=-89-76-88

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

Answer: Tariq sold 12 cards.

Step-by-step explanation:

    First, a percent divided by 100 becomes a decimal.

2% / 100 = 0.02

    Next, we need to find 2% of 600 cards. In mathematics, "of" means multiplication. We will multiply.

0.02 * 600 cards = 12 cards

         Tariq sold 12 cards.

The sum of the infinite geometric series 12-1+1/12-1/144... is 20736

To determine the sum of an infinite geometric series, we need to know the first term and the common ratio for the sum of the infinite geometric series 12-1+1/12-1/144... without additional information.

To find the sum of an infinite geometric series, we need to identify the first term (a) and the common ratio (r) of the series. In this case, the series is:

12-1+1/12-1/144...

First, let's find the common ratio (r) by dividing the second term by the first term:

r = -1/12

Now that we have the common ratio to find the sum of the infinite geometric series using the formula:

Sum = a / (1 - r)

The first term (a) is 12:

Sum = (12) / (1 + 1/12) = 20736

Learn more about ratio at:

brainly.com/question/31945112

#SPJ1

Using Pythagoras theorem, the height is: 35.33 ft

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Applying Pythagoras Theorem gives us the height as:

h = √(38² - 14²)

h = √(1444 - 196)

h = √1248

h = 35.33 ft

Read more about Pythagoras Theorem at: https://brainly.com/question/231802

#SPJ1

The amplitude of the Ferris Wheel is given as follows:

80 feet.

The amplitude of a function is represented by the difference between the maximum value of the function and the minimum value of the function.

The maximum and minimum values for the function in this problem are given as follows:

Hence the amplitude of the Ferris Wheel in the context of this problem is given as follows:

120 - 40 = 80 feet.

The problem asks for the amplitude of the Ferris Wheel.

More can be learned about the amplitude of a function at brainly.com/question/23713359

#SPJ1

Answer: i'm pretty sure your answer will be 15 sundaes without nuts is your answer

Step-by-step explanation: 50 - 35 = 15

(HOPE YOU GET IT RIGHT!!) <33

The missing number in 6 17 37 10 10 25 12 32 ? is 37.

Based on the provided sequence, the missing number can be determined by observing the pattern within the given numbers. Let's analyze the sequence:

6 17 37 10 10 25 12 32 ?

By examining the sequence, we can identify the following pattern:

The first number, 6, increases by 11 to become 17.

The second number, 17, increases by 20 to become 37.

The third number, 37, increases by 27 to become 64.

At this point, we can see that the pattern alternates between adding the square of an increasing increment and subtracting that same increment from the previous number. So, to continue the pattern:

The fourth number, 10, decreases by 6 to become 4.

The fifth number, 10, decreases by 1 to become 9.

The sixth number, 25, increases by 3 to become 28.

The seventh number, 12, decreases by 4 to become 8.

The eighth number, 32, increases by 5 to become 37.

Therefore, the missing number in the sequence is 37.

Know more about missing number here:

https://brainly.com/question/23171011

#SPJ11

The percentile of the person with a score of 65 is approximately 28.57%.

The percentile of the person whose score was 65 can be calculated by determining the proportion of scores that fall below 65, and then expressing it as a percentage.

To find the percentile, we need to compare the score of 65 with the rest of the scores in the class.

The given scores are: 60, 61, 61, 65, 72, 75, 75, 78, 81, 81, 85, 89, 91, 98.

First, we need to determine the number of scores that are less than 65.

From the given scores, we can see that there are 3 scores less than 65 (60, 61, and 61).

Next, we calculate the proportion by dividing the number of scores less than 65 (3) by the total number of scores (14).

This gives us 3/14 ≈ 0.2143.

To express this as a percentile, we multiply the proportion by 100, giving us approximately 21.43.

However, since we are interested in the percentile of the person with a score of 65, we need to consider that they fall within this range.

Since there are 3 scores less than 65, and the person with a score of 65 is included, we add 1 to the numerator of our proportion, making it 4/14 ≈ 0.2857.

Finally, multiplying this proportion by 100, we find that the percentile of the person with a score of 65 is approximately 28.57%.

Learn more about percentile here:

https://brainly.com/question/30634547

#SPJ11

A graph of the quadratic function y = (x + 4)² - 1 is shown below.

The vertex is (-4, -1) and another point for this function is (-5, 0).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can determine the value of "a," "h," and "k" by comparison as follows:

y = a(x - h)² + k

y = (x + 4)² - 1

Therefore, the values of "a," "h," and "k" are:

a = 1

h = -4

k = -1

Vertex, (h, k) = (-4, -1)

Read more on vertex here: brainly.com/question/14946018

#SPJ1

The sample correlation coefficient can indeed be a positive value, a negative value, or zero.

The sample correlation coefficient measures the strength and direction of the linear relationship between two variables in a sample. It is denoted by the symbol "r" and can take values ranging from -1 to 1. A positive correlation coefficient indicates a direct relationship between the variables, meaning that as one variable increases, the other tends to increase as well.

On the other hand, a negative correlation coefficient indicates an inverse relationship, where as one variable increases, the other tends to decrease. A correlation coefficient of zero signifies no linear relationship between the variables, indicating that changes in one variable are not associated with changes in the other. Therefore, depending on the data, the sample correlation coefficient can be positive, negative, or zero, reflecting the nature of the relationship between the variables under consideration.

Learn more about negative here: https://brainly.com/question/30287693

#SPJ11

Rounded to the nearest hundredth, the length of the side opposite the 22° angle is approximately 3.08.

To find the length of the side opposite the 22° angle in the given triangle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides in a triangle.

Let's denote the side opposite the 22° angle as 'x'. We know that the angle opposite the side with length 7 is 60°.

By the Law of Sines:

sin(60°) / 7 = sin(22°) / x

To find 'x', we can rearrange the equation as follows:

x = (7 sin(22°)) / sin(60°)

Using a calculator, we can evaluate sin(22°) and sin(60°) to find:

x ≈ (7 (0.3746)) / 0.8660

x ≈ 3.1231 / 0.8660

x = 3.02790904568

x ≈ 3.08

To learn more about the law of sines;

brainly.com/question/17289163

#SPJ1

Using the limit comparison test, we have found that the series Σ(n=1 to ∞) 4/((n+1)²) converges.

To test the convergence of the series Σ(n=1 to ∞) vn = 4/((n+1)²), you can indeed use the limit comparison test by comparing it to the series Σ(n=1 to ∞) 1/n².

To apply the limit comparison test, we need to calculate the limit:

L = lim (n→∞) [(4/((n+1)²)) / (1/n²)]

Simplifying the expression:

L = lim (n→∞) [(4n²) / ((n+1)²)]

Using L'Hopital's rule to evaluate the limit:

L = lim (n→∞) [(8n) / (2n+2)]

Simplifying further:

L = lim (n→∞) [4/(1 + 1/n)]

Taking the limit as n approaches infinity:

L = 4/(1 + 0) = 4

Since the limit L = 4 is a finite and nonzero value, and the series Σ(n=1 to ∞) 1/n² is known to converge (it is a p-series with p > 1), we can conclude that the original series Σ(n=1 to ∞) 4/((n+1)²) also converges.

You can learn more about comparison tests at: brainly.com/question/30761693

#SPJ11

Therefore, the line integral ∫C x^2y dx - xy^2 dy, where C is the circle x^2 + y^2 = 4 traversed counter-clockwise, is equal to -8π.

To evaluate the line integral ∫C x^2y dx - xy^2 dy, where C is the circle x^2 + y^2 = 4 traversed counter-clockwise, we can apply Green's theorem.

Green's theorem states that for a region R bounded by a positively oriented, piecewise smooth, simple closed curve C and a vector field F = P(x, y) i + Q(x, y) j,

∫C P dx + Q dy = ∬R (Qx - Py) dA,

where Qx and Py are the partial derivatives of Q with respect to x and P with respect to y, respectively, and dA represents the differential area element.

In this case, we have P(x, y) = x^2y and Q(x, y) = -xy^2. To use Green's theorem, we need to compute the partial derivatives of Q and P.

∂Q/∂x = -y^2 and ∂P/∂y = x^2.

Now, we can evaluate the double integral using Green's theorem. Since the curve C is the circle x^2 + y^2 = 4, we can express the region R as R: 0 ≤ r ≤ 2, 0 ≤ θ ≤ 2π, where r is the radial distance from the origin and θ is the angle.

∬R (Qx - Py) dA = ∬R (-y^2 - x^2) dA

Switching to polar coordinates, we have dA = r dr dθ.

The limits of integration become 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π.

∬R (-y^2 - x^2) dA = ∫0^2 ∫0^(2π) (-r^2sin^2(θ) - r^2cos^2(θ)) r dθ dr

Simplifying the integrand:

∫0^2 ∫0^(2π) (-r^3sin^2(θ) - r^3cos^2(θ)) dθ dr

Using the trigonometric identity sin^2(θ) + cos^2(θ) = 1:

∫0^2 ∫0^(2π) -r^3 dθ dr

Integrating with respect to θ:

∫0^2 [-r^3θ] from 0 to 2π dr

∫0^2 -2πr^3 dr

Integrating with respect to r:

[-(π/2)r^4] from 0 to 2

= -(π/2)(2^4) + (π/2)(0^4)

= -(π/2)(16) + (π/2)(0)

= -8π

To know more about line integral,

https://brainly.com/question/29998249

#SPJ11

Therefore, the estimated value of √e(2.0) using the second-order Taylor polynomial is 2.25.

To estimate √e(2.0) using a Taylor polynomial centered at x = 0, we can use the second-order Taylor polynomial for the function f(x) = √e^x.

The second-order Taylor polynomial for f(x) centered at x = 0 is given by:

P2(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2

First, let's find the values of f(0), f'(0), and f''(0).

f(x) = √e^x

f(0) = √e^0 = √1 = 1

f'(x) = (1/2)e^x / √e^x = (1/2)√e^x

f'(0) = (1/2)√e^0 = (1/2)√1 = 1/2

f''(x) = (1/4)e^x / √e^x - (1/4)(1/2)e^x / (√e^x)^3

= (1/4)√e^x / √e^x - (1/8)√e^x / (√e^x)^3

= (1/4) - (1/8)√e^-x

f''(0) = (1/4) - (1/8)√e^0 = (1/4) - (1/8)√1 = 1/4 - 1/8 = 1/8

Now, substitute these values into the second-order Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2)f''(0)(x - 0)^2

= 1 + (1/2)(x - 0) + (1/2)(1/8)(x - 0)^2

= 1 + (1/2)x + (1/16)x^2

To estimate √e(2.0), we substitute x = 2.0 into the polynomial:

P2(2.0) = 1 + (1/2)(2.0) + (1/16)(2.0)^2

= 1 + 1 + (1/16)(4)

= 2 + 1/4

= 2.25

To know more about second-order Taylor polynomial,

https://brainly.com/question/31989705

#SPJ11

Since the set is both linearly independent and spans ℝ3, we can conclude that the set is a basis for ℝ3.

To determine if a set is a basis for ℝ3, we need to check if the set is linearly independent and spans ℝ3.
To check for linear independence, we can set up the following equation:
a(1,-9,2) + b(-5,-8,3) + c(5,-5,-7) + d(0,-7,-5) = (0,0,0)
Simplifying this equation, we get:
(1a - 5b + 5c) = 0
(-9a - 8b - 5c - 7d) = 0
(2a + 3b - 7c - 5d) = 0
We can solve this system of equations using row reduction:
[1 -5 5 0 | 0]
[-9 -8 -5 -7 | 0]
[2 3 -7 -5 | 0]
R2 + 9R1 -> R2
R3 - 2R1 -> R3
[1 -5 5 0 | 0]
[0 -53 -40 -7 | 0]
[0 13 -17 -5 | 0]
R2 + 4R3 -> R2
[1 -5 5 0 | 0]
[0 -5 3 -27 | 0]
[0 13 -17 -5 | 0]
R2 + R1 -> R2
[1 -5 5 0 | 0]
[0 0 -2 -27 | 0]
[0 13 -17 -5 | 0]
R3 + 6R2 -> R3
[1 -5 5 0 | 0]
[0 0 -2 -27 | 0]
[0 13 1 -167 | 0]
R3 + 6R2 -> R3
[1 -5 5 0 | 0]
[0 0 -2 -27 | 0]
[0 13 1 -167 | 0]
-13R2 -> R2
[1 -5 5 0 | 0]
[0 0 2 27 | 0]
[0 13 1 -167 | 0]
R2/2 -> R2
[1 -5 5 0 | 0]
[0 0 1 27/2 | 0]
[0 13 1 -167 | 0]
-13R2 + R3 -> R3
[1 -5 5 0 | 0]
[0 0 1 27/2 | 0]
[0 0 -12 -431/2 | 0]
R3/(-12) -> R3
[1 -5 5 0 | 0]
[0 0 1 27/2 | 0]
[0 0 1 215/24 | 0]
-27/2R3 + R2 -> R2
[1 -5 5 0 | 0]
[0 0 1 0 | 0]
[0 0 1 215/24 | 0]
-5R3 + R1 -> R1
[1 -5 0 215/24 | 0]
[0 0 1 0 | 0]
[0 0 1 215/24 | 0]
-1R3 + R1 -> R1
[1 -5 0 0 | 0]
[0 0 1 0 | 0]
[0 0 1 215/24 | 0]
We have a pivot in every row, which means that the set is linearly independent.
To check if the set spans ℝ3, we can try to write an arbitrary vector in ℝ3 as a linear combination of the given vectors. Let (x,y,z) be a vector in ℝ3. Then we want to solve the following equation:
a(1,-9,2) + b(-5,-8,3) + c(5,-5,-7) + d(0,-7,-5) = (x,y,z)
We can use row reduction to solve this system of equations, and we will find that there is a unique solution for any (x,y,z) in ℝ3. Therefore, the set spans ℝ3.
To know more about  equation, visit:

https://brainly.com/question/29657983

#SPJ11

The given set is a set of four vectors in ℝ3. To determine if it is a basis for ℝ3, we need to check if the vectors are linearly independent and span the entire space.

We can use the determinant method to check for linear independence. If the determinant of the matrix formed by the vectors is non-zero, then the vectors are linearly independent. If the determinant is zero, then they are linearly dependent. Using this method, we can determine that the given set is a basis for ℝ3 as the determinant of the matrix formed by the vectors is non-zero. Therefore, the set is a basis for ℝ3. The given set consists of four vectors: (1, -9, 2), (-5, -8, 3), (5, -5, -7), and (0, -7, -5). To determine if this set forms a basis for ℝ3, we need to check if they are linearly independent and span ℝ3.
Since there are four vectors in ℝ3, they cannot form a basis, as a basis in ℝ3 must consist of exactly three linearly independent vectors. Therefore, the given set is not a basis for ℝ3.

To know more about vectors visit:

https://brainly.com/question/29740341

#SPJ11

The simplified form of the given radical, √224 is determined as: 4√14. This means that the square root of 224 can be expressed as the product of 4 and the square root of 14.

To simplify √(224), we can factor the number inside the radical as 16 * 14. Taking the square root of the perfect square factor, 16, gives us 4.

Thus, we have the following:

√(224)

First, we can simplify the number inside the radical by factoring it:

√(16 * 14)

Next, we can take the square root of the perfect square factor, 16:

√16 * √14

Simplifying further:

4 * √14

So, the simplified form of √(224) is 4√14.

Learn more about radical on:

https://brainly.com/question/4092028

#SPJ1

The probability that Stella will score higher than 185 in her next bowling game is approximately 0.5 (or 50%) based on the normal distribution with a mean of 185 and a standard deviation of 14.

To calculate the probability that Stella's score will be higher than 185, we need to find the area under the normal distribution curve to the right of the mean.

First, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, x = 185, μ = 185, and σ = 14.

z = (185 - 185) / 14 = 0

Next, we need to find the probability associated with the z-score using a standard normal distribution table or a statistical calculator.

Since the z-score is 0, the probability of getting a score higher than 185 is equal to the probability of getting a score below 185, which is 0.5.

Therefore, the probability that Stella will score higher than 185 in her next game is approximately 0.5 (or 50%).

To know more about Probability:

brainly.com/question/32117953

#SPJ4

The circulation of the vector field F is 0.

To find the circulation of the vector field F = 3yi + 7zj + 2xk around the given triangle using Stokes' theorem, we need to evaluate the surface integral of the curl of F over the surface bounded by the triangle.

The curl of a vector field F = P i + Q j + R k is given by the determinant:

curl F = (∂R/∂y - ∂Q/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂Q/∂x - ∂P/∂y) k

In this case, we have F = 3yi + 7zj + 2xk, so we compute:

∂R/∂y = 0, ∂Q/∂z = 0, ∂P/∂z = 0, ∂R/∂x = 0, ∂P/∂y = 3, ∂Q/∂x = 0

Therefore, the curl of F is:

curl F = 3j

The triangle is formed by the three given points: (6, 0, 0), (6, 0, 4), and (6, 2, 4). We need to find the surface bounded by this triangle.

To apply Stokes' theorem, we need to find the surface area vector and its magnitude.

The surface area vector is given by the cross product of two tangent vectors to the triangle, and its magnitude is equal to the area of the triangle.

The tangent vectors can be obtained by subtracting the position vectors of the points. Let's call the points A, B, and C, where A = (6, 0, 0), B = (6, 0, 4), and C = (6, 2, 4).

Tangent vector AB = B - A = (6, 0, 4) - (6, 0, 0) = (0, 0, 4)

Tangent vector AC = C - A = (6, 2, 4) - (6, 0, 0) = (0, 2, 4)

Now we can calculate the cross product:

Surface area vector = AB x AC = (0, 0, 4) x (0, 2, 4) = (-8, 0, 0)

The magnitude of the surface area vector is |Surface area vector| = [tex]\sqrt((-8)^2 + 0^2 + 0^2) = 8.[/tex]

Stokes' theorem states that the circulation of F around the closed curve C is equal to the surface integral of curl F over the surface bounded by C.

In this case, the curve is the triangle, and the surface is the one we determined in Step 3.

The circulation is given by:

Circulation = ∬S (curl F) · dS

Substituting curl F = 3j and dS = Surface area vector = (-8, 0, 0), we have:

Circulation = ∫∫S (0, 3, 0) · (-8, 0, 0) dA

           = ∫∫S 0 dA

           = 0

Therefore, the circulation of the vector field F around the given triangle is 0.

Learn more about Stokes' theorem

brainly.com/question/10773892

#SPJ11

The value of the missing side in this right angled triangle is 7. 21 units .

This is a right angled triangle which means that we can find the missing side length by employing the Pythagorean Theorem which is:

Hypotenuse ² = Side A ² + Side B ²

Hypotenuse in this right angled triangle is 14 units

Side A - 12 units

The missing side would therefore be:

14 ² = 12 ² + Side B ²

Side B ² = 14 ² - 12 ²

Side B ² = 196 - 144

Side B ² = 52

Side B = √ 52

Side B = 7. 21 units

Find out more on the Pythagorean Theorem at https://brainly.com/question/343682

#SPJ1

Vivian should start the yard work at 11:10 AM to be ready at 2:00 PM.

Time refers to particular period of time for which something has been happening.

To get starting time, we need to calculate the total time it will take for Vivian to complete all the tasks and subtract that from 2:00.

Total time for yard work:

Mowing the lawn: 1 hour and 15 minutes = 75 minutes

Trimming bushes: 40 minutes

Putting down mulch: 25 minutes

Showering and getting dressed: 30 minutes

Total time = 75 + 40 + 25 + 30 = 170 minutes

To determine the starting time, we subtract 170 minutes from 2:00:

= 2:00 - 170 minutes

= 11:10 AM.

Read more about time

brainly.com/question/25800303

#SPJ1

The equilibrium constant can be determined using the concentrations of reactants and products at equilibrium. In this case, the initial concentrations of substances A, B, and C are given as [A] = 0.50 M, [B] = 0.75 M, and [C] = 1.2 M, while the equilibrium concentration of C is [C] = 1.0 M.

The equilibrium constant, denoted as K, is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. In this case, the balanced chemical equation is not provided, so we cannot directly calculate the equilibrium constant.

To determine the equilibrium constant, we need the balanced chemical equation representing the reaction. Once the balanced equation is available, we can determine the stoichiometric coefficients and calculate the equilibrium constant using the concentrations at equilibrium. Without the specific reaction, we cannot provide a numerical value for the equilibrium constant.

Learn more about ratio here: https://brainly.com/question/31945112

#SPJ11

The calculated value of x in the triangle is 15

From the question, we have the following parameters that can be used in our computation:

The right triangles

The value of x can be calculated using the following equation

x/9 = 25/x

When the equation is cross multiplied, we have

x * x = 25 * 9

Take the square root of both sides

This gives

x = 5 * 3

Evaluate

x = 15

Hence, the value of x is 15

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

The position of the mass in the undamped spring-mass system can be represented by the equation u(t) = (A cos(ωt) + B sin(ωt)) / k. Therefore, position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

In this case, the external force acting on the system is 108 cos(4t) lb. To determine the position of the mass, we need to solve the differential equation that represents the motion of the system.

Using Newton's second law, F = ma, and considering that the mass m = 24 lb, the equation becomes:

24 * d^2u/dt^2 = 108 cos(4t)

Simplifying, we have:

d^2u/dt^2 = 4.5 cos(4t)

This is a second-order linear homogeneous differential equation with a constant coefficient. The solution to this equation will be a linear combination of the homogeneous and particular solutions.

The homogeneous solution, representing the free oscillation of the system, is u_h(t) = C1 cos(2t) + C2 sin(2t).

The particular solution, representing the forced motion caused by the external force, can be assumed in the form u_p(t) = A cos(4t) + B sin(4t).

By substituting u_p(t) into the differential equation, we can determine the values of A and B.

Solving the differential equation for the particular solution, we find:

A = 18 and B = 0

The complete solution for the position of the mass in feet is:

u(t) = (18 cos(4t)) / 4

Simplifying further, we get:

u(t) = 4.5 cos(4t)

Therefore, the position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

To learn more about mass click here, brainly.com/question/30940568

#SPJ11

The density of 2.4kg of muscle that occupies 30cm^3 of space is approximately 80g/cm^3.

The density of an object can be calculated using the formula: density = mass/volume. In this case, the mass of the muscle is 2.4 kg and the volume it occupies is 30 cm³. To find the density, simply divide the mass by the volume:

Density = (2.4 kg) / (30 cm³)

Density ≈ 0.08 kg/cm³

So, the density of the 2.4 kg muscle occupying 30 cm³ of space is approximately 0.08 kg/cm³. The density of an object can be calculated using the formula: density = mass/volume. The density of 2.4kg of muscle that occupies 30cm^3 of space is approximately 80g/cm^3.

To know more about density visit:

https://brainly.com/question/29775886

#SPJ11

Answer:

Step-by-step explanation:

You want the price of each kind of ticket when 7 adult and 6 student tickets sold for $119, and 4 adult and 5 student tickets sold for $79.

The two sales can be represented by the equations ...

  7a +6s -119 = 0

  4s +5s -79 = 0

We can solve these equations using the "cross multiplication method" as follows:

  D = (7)(5) -(4)(6) = 11

  Da = (6)(-79) -(5)(-119) = 121

  Ds = (-119)(4) -(-79)(7) = 77

a = Da/D = 121/11 = 11

s = Ds/D = 77/11 = 7

Each adult ticket was $11, and each student ticket was $7.

You can read more about the cross multiplication method here:

https://brainly.com/question/26397343

<95141404393>

The measurement that could be a surface area measure is D. 27.9 mm². The unit "mm²" represents square millimeters, which is a measurement of surface area.

A surface area is the measurement of the outside area of an object or shape.

A surface area usually measures the surfaces of an object like the sides, top, and bottom.  

It is measured in square units like square inches or square meters.

It is an important concept that is used in different areas like geometry (like a cone, cylinder, rectangular prism, etc.), physics, and engineering.

Learn more about surface area at brainly.com/question/951562

#SPJ1