Laplace transform of f(t) = -1, 0 3 { F(x)
The Laplace transform of f(t) = S(t - 5), 0, 5 - F(3) is F(s) = (1/s) [tex]e^{(-5s)[/tex] - (1/3) [tex]e^{(-15)[/tex].
Laplace transform:The Laplace transform of a function f(t) is given by:
F(s) = ∫[0,∞) e^(-st) f(t) dt
where s is a complex variable.
Using this formula, we can find the Laplace transform of f(t) as follows:
F(s) = ∫[0,∞) e^(-st) f(t) dt
= ∫[0,∞) e^(-st) (-1) dt + ∫[0,∞) e^(-st) (0) dt + ∫[0,∞) e^(-st) (3) dt
= -1/s + 0 + 3/s
= (2/s) - (1/s)
Therefore, the Laplace transform of f(t) = -1, 0, 3 is F(s) = (2/s) - (1/s).
Now, let's move on to the second part of the question.
We need to find the Laplace transform of f(t) = S(t - 5), 0, 5 - F(3).
Here, S(t - 5) is the Heaviside step function, which is defined as:
S(t - 5) = 0, for t < 5
= 1, for t ≥ 5
Using the Laplace transform formula, we can write:
F(s) = ∫[0,∞) e^(-st) S(t - 5) dt
Since S(t - 5) is equal to 0 for t < 5, we can split the integral into two parts:
F(s) = ∫[0,5) [tex]e^(-st)[/tex]S(t - 5) dt + ∫[5,∞) [tex]e^(-st)[/tex] S(t - 5) dt
The first integral is equal to 0, since S(t - 5) is 0 for t < 5.
For the second integral, we can use the fact that S(t - 5) = 1 for t ≥ 5. So, we get:
F(s) = ∫[5,∞) e^(-st) dt
= [-1/s e^(-st)]_[5,∞)
= (1/s) [tex]e^(-5s)[/tex]
Finally, we need to find F(3). Substituting s = 3 in the Laplace transform, we get:
[tex]F(3) = (1/3) e^(-15)[/tex]
Therefore, the Laplace transform of f(t) = S(t - 5), 0, 5 - F(3) is F(s) = (1/s) [tex]e^(-5s) - (1/3) e^(-15).[/tex]
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Find the value of k. Give your answer in degrees ().
k
84°
Not drawn accurately
Step-by-step explanation:
I had to add some assumed portions to your posted picture. See image.
The yellow boxed angle is 84 degrees (upper LEFT) due to alternate interior angles of parallel lines transected by another line.
then, since the triangle is isosceles ....the other (lower LEFT) angle is 84 degrees also....
that means that k= 12 degrees for the triangle interior angles to sum to 180 degrees .
We can calculate the depth � dd of snow, in centimeters, that accumulates in Harper's yard during the first ℎ hh hours of a snowstorm using the equation � = 5 ℎ d=5hd, equals, 5, h. How many hours does it take for 1 11 centimeter of snow to accumulate in Harper's yard? 1/5 hours How many centimeters of snow accumulate per hour?
It takes 1/5 hours or 12 minutes for 1 centimeter of snow to accumulate in Harper's yard.
We are given that the depth of snow that accumulates in Harper's yard during the first h hours of a snowstorm is given by the equation d = 5h.
To find out how many hours it takes for 1 centimeter of snow to accumulate, we need to find the value of h when the depth of snow d is equal to 1 centimeter.
Substituting d = 1 in the equation d = 5h, we get:
1 = 5h
Dividing both sides by 5, we get:
h = 1/5
In summary, the equation d = 5h gives the depth of snow in centimeters that accumulates in Harper's yard during the first h hours of a snowstorm. To find how many hours it takes for 1 centimeter of snow to accumulate, we substitute d = 1 and solve for h, which gives us h = 1/5 hours or 12 minutes.
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Complete question is:
We can calculate the depth d of snow, in centimeters, that accumulates in Harper's yard during the first h hours of a snowstorm using the equation d = 5h. How many hours does it take for 1 centimeter of snow to accumulate in Harper's yard?
The probability that sue will go to mexico in the winter and to france
in the summer is
0. 40
. the probability that she will go to mexico in
the winter is
0. 60
. find the probability that she will go to france this
summer, given that she just returned from her winter vacation in
mexico
The evaluated probability that Sue travel to France this summer is 0.67, under the condition that she just returned from her winter vacation in Mexico.
For the required problem we have to apply Bayes' theorem.
Let us consider that A is the event that Sue goes to France in the summer and B be the event that Sue goes to Mexico in the winter.
Now,
P(A and B) = P(B) × P(A|B)
= 0.40
P(B) = 0.60
Therefore now we have to find P(A|B), which means the probability that Sue traveled to France after coming from Mexico
Applying Bayes' theorem,
P(A|B) = P(B|A) × P(A) / P(B)
It is given that P(B|A) = P(A and B) / P(A), then
P(A|B) = (P(A and B) / P(A)) × P(A) / P(B)
P(A|B) = P(A and B) / P(B)
Staging the values
P(A|B) = 0.40 / 0.60
P(A|B) = 0.67
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The complete question is
The probability that Sue will go to Mexico in the winter and to France in the summer is 0. 40. the probability that she will go to mexico in the winter is 0. 60. find the probability that she will go to France this summer, given that she just returned from her winter vacation in Mexico.
how long is the red ribbon if the blue ribbon is 10 inches?
Is The number of insects feeding on a tree leaf discrete or continious
The number of insects feeding on a tree leaf is a discrete variable.
The number of insects feeding on a tree leaf is a countable variable that can only take on integer values (0, 1, 2, 3, etc.). It cannot take on fractional or continuous values. This is because each insect can either feed on the leaf or not, and there cannot be a fractional or continuous number of insects feeding on the leaf.
Therefore, the number of insects feeding on a tree leaf is a discrete variable. This is in contrast to a continuous variable, which can take on any value within a certain range. For example, the weight of the insects on the leaf would be a continuous variable since it can take on fractional values.
In mathematical terms, the number of insects feeding on a tree leaf can be represented as a discrete random variable X, where X can take on any non-negative integer value.
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Let ∑an be a convergent series, and let S=limsn, where sn is the nth partial sum
The given statement "If ∑an is a convergent series, then S = limsn, where sn is the nth partial sum. " is true. This is because the sum of the series is defined as the limit of the sequence of partial sums.
Given that ∑an is a convergent series, sn is the nth partial sum, S=limsn
To prove limn→∞ an = 0
Since ∑an is convergent, we know that the sequence {an} must be a null sequence, i.e., it converges to 0. This means that for any ε>0, there exists an N such that |an|<ε for all n≥N.
Now, let's consider the partial sums sn. We know that S=limsn, which means that for any ε>0, there exists an N such that |sn−S|<ε for all n≥N.
Using the triangle inequality, we can write:
|an|=|sn−sn−1|≤|sn−S|+|sn−1−S|<2ε
Therefore, we have shown that limn→∞ |an| = 0, which implies limn→∞ an = 0, as required.
Hence, the proof is complete.
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What is the area of the shaded part of the circle?
And also, I am so confused about how to do it so can someone help me pls?
The required area of the shaded part of the circle is 50.24 sq. cm
What is area of a circle?A circle of radius r has an area of r2 in geometry. Here, the Greek letter denotes the constant ratio of a circle's diameter to circumference, which is roughly equivalent to 3.14159.
According to question:Given data:
Radius of small circle = 6/2 = 3 cm
Radius of big circle = 10/2 = 5 cm
then.
Area of shaded part = area of big circle - area of small circle
Area of shaded part = π(5)² - π(3)²
Area of shaded part = 25π - 9π
Area of shaded part = 16π
Area of shaded part = 50.24 sq. cm
Thus, required area of the shaded part of the circle is 50.24 sq. cm
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17. Cylinder A is similar to Cylinder B with a scale
factor of 3:7. If the surface area of Cylinder A
is 153 cm², find the surface area of Cylinder B.
The value of the surface area of Cylinder B is, 357 cm²
We have to given that;
Cylinder A is similar to Cylinder B with a scale factor of 3:7.
And, the surface area of Cylinder A.
Let us assume that,
The value of the surface area of Cylinder B is, y.
Hence, We can formulate;
3x : 7x = 153 : y
By comparing,
3x = 153
x = 51
Thus, The value of the surface area of Cylinder B is,
y = 7x
y = 7 x 51
y = 357 cm²
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Se van a repartir $10000 entre 3 personas de tal forma q la primera recibe $900 mas q la segunda y esta $200 mas q la tercera.La persona más beneficiada recibe en total: a- $4600. b- $4400. c- $4200. d- $4000
Answer:
The answer is A
Step-by-step explanation:
I will give brainlyist to who ever answers it.
A family with travel 475 miles on the Road trip which inequality can be used to find all possible values of T the time it would take to reach their destination if they travel in an average speed of at least in miles per hour
The inequality that can be used to find all possible values of T, the time it would take to reach their destination if they travel at an average speed of at least "r" miles per hour, can be expressed as:
T ≤ 475 / r
This inequality states that the time taken (T) should be less than or equal to the distance traveled (475 miles) divided by the average speed (r miles per hour). By dividing the total distance by the average speed, we obtain the maximum time it would take to reach the destination. Any time less than or equal to this value would satisfy the condition of traveling at an average speed of at least "r" miles per hour.
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What is 30 players for 10 sports expressed as a rate
The rate can be expressed as "3 players per sport"
What is rate?A rate is a ratio that compares two quantities with different units. In this case, we have 30 players and 10 sports. To express this as a rate, we want to compare the number of players to the number of sports. We can write this as:
30 players / 10 sports
To simplify this ratio, we can divide both the numerator (30 players) and denominator (10 sports) by the same factor to get an equivalent ratio. In this case, we can divide both by 10:
(30 players / 10) / (10 sports / 10)
This simplifies to:
3 players / 1 sport
So the rate can be expressed as "3 players per sport" or "3:1" (read as "three to one"). This means that for every one sport, there are three players.
Alternatively, we can express the rate as a fraction or decimal by dividing the number of players by the number of sports:
30 players / 10 sports = 3 players/sport = 3/1 = 3 or 3.0 (as a decimal)
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If a circle has a circumference of 40π and a chord of the circle is 24 units, then the chord is ____ units from the center of the circle
A circle with a circumference of 40π and a chord of the circle is 24 units, then the chord is 16 units from the center of the circle,
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Here, we are given that the circumference is 40π. That is
40π = 2πr
Dividing both sides by 2π, we get:
r = 20
Now, we need to find the distance between the chord and the center of the circle. Let O be the center of the circle, and let AB be the chord. We know that the perpendicular bisector of a chord passes through the center of the circle. Let P be the midpoint of AB, and let OP = x.
By the Pythagorean Theorem,
x^2 + 12^2 = 20^2
Simplifying,
x^2 + 144 = 400
x^2 = 256
x = ±16
Since OP is a distance, it must be positive. Therefore, x = 16, and the chord is 16 units from the center of the circle.
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Fertilizer: A new type of fertilizer is being tested on a plot of land in an orange grove, to see whether it increases the amount of fruit produced. The mean number of pounds of fruit on this plot of land with the old fertilizer was 403 pounds. Agriculture scientists believe that the new fertilizer may decrease the yield. State the appropriate null and alternate hypotheses
Alternative hypothesis can also be written to reflect an increase in yield if the researchers believed that was a possibility.
Why Alternative hypothesis reflect an increase in yield?In hypothesis testing, the null hypothesis is a statement that assumes there is no difference or no effect between two variables.
The alternative hypothesis, on the other hand, assumes that there is a difference or an effect between the variables being tested.
In this scenario, the null hypothesis would be that the new fertilizer has no effect on the yield of the orange grove. The alternative hypothesis would be that the new fertilizer decreases the yield of the orange grove.
So, the appropriate null and alternative hypotheses for this scenario can be stated as follows:
Null hypothesis (H0): The new fertilizer has no effect on the yield of the orange grove.
Alternative hypothesis (Ha): The new fertilizer decreases the yield of the orange grove.
It is important to note that the alternative hypothesis can also be written to reflect an increase in yield if the researchers believed that was a possibility.
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Joe started a tutoring job and earns $40 per week tutoring his classmates. He bought a new iPad to help with his tutoring job for $150. Write a linear equation that represents Joe's money, y, after x amount of weeks.
Solve the equation. 2 = \dfrac{f}{8}2= 8
f
2, equals, start fraction, f, divided by, 8, end fraction
f =\,f=f, equals
The solution to the equation is f = 16. The value of f can be found by multiplying both sides of the equation by 8.
How we solve the equation: 2 = f/8 for f?To solve the equation 2 = f/8 for f, we aim to isolate f on one side of the equation.
To do so, we can multiply both sides of the equation by 8, as this will cancel out the denominator of f/8.
By multiplying 2 by 8, we obtain 16 on the left side of the equation.
On the right side, the 8 in the denominator cancels out with the 8 we multiplied, leaving us with just f.
we find that f = 16 is the solution to the equation.
This means that if we substitute f with 16 in the equation, we will have a true statement: 2 = 16/8, which simplifies to 2 = 2.
f = 16 satisfies the original equation and is the solution.
It's important to note that when solving equations, we perform the same operation on both sides to maintain equality.
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(0,1),(5,2),(2,-3),(-3,-3),(-5,3) range and domain
The domain of the set of points {(0,1),(5,2),(2,-3),(-3,-3),(-5,3)} is {0, 5, 2, -3, -5}, and the range is {-3, 1, 2, 3}.
What is the range and domain of the relation?Given the relations in the question:
(0,1), (5,2), (2,-3), (-3,-3), (-5,3)
To determine the domain and range of a set of points, we need to look at the x-coordinates of the points to determine the domain, and the y-coordinates of the points to determine the range.
{(0,1),(5,2),(2,-3),(-3,-3),(-5,3)}
The x-coordinates of these points are: 0, 5, 2, -3, and -5.
Therefore, the domain of this set of points is:
Domain = {0, 5, 2, -3, -5}
The y-coordinates of these points are: 1, 2, -3, and 3.
Therefore, the range of this set of points is:
Range = {-3, 1, 2, 3}
Therefore, the domain is {0, 5, 2, -3, -5}, and the range is {-3, 1, 2, 3}.
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Jasmine creates a map of her town on the coordinate plane. The unit on the coordinate plane is one block.
The locations of the school, post office, and library are given. school (-4,1)
post office (2,1)
library (2,-4)
Move the points of each building to its correct location on the coordinate plane. Jasmine walks from the school to the post office and then to the library.
What is the total distance, in blocks, of her walk?
Jasmine walks from the school to the post office, which is a distance of $2 - (-4) = 6$ blocks horizontally and 0 blocks vertically, so the distance is 6 blocks. Then she walks from the post office to the library, which is a distance of $2 - 2 = 0$ blocks horizontally and $-4 - 1 = -5$ blocks vertically, so the distance is 5 blocks.
The total distance of Jasmine's walk is the sum of the distances of each leg of her journey, which is $6 + 5 = 11$ blocks. Therefore, Jasmine walks 11 blocks in total.
Write as a logarithm with a base of 4.
2
To express the number 2 as a logarithm with a base of 4, you would write it as log₄(16). This is because 4² = 16.
In general, the logarithm function is the inverse of exponentiation. When we write logₐ(b) = c, it means that a raised to the power of c equals b.
In your example, you want to find the logarithm of 2 with a base of 4, which means you are looking for the exponent to which 4 must be raised to obtain 2.
So, log₄(2) represents the exponent c such that 4 raised to the power of c equals 2.
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A park maintenance person stands 16 m from a circular monument. Assume that her lines of sight form tangents to the monument and make an angle of 56°. What is the measure of the arc of the monument that her lines of sight intersect?
The measure of the angle of the near arc of the monument that her lines of sight intersect with is 124°
What is the angle of an arc of a circle?The angle of an arc of a circle is the angle formed by the two radii of the circle that intersects with the boundaries of the arc
The distance the park maintenance person stands from the monument = 16 m
The angle the lines of sight from the maintenance person that are tangent with the monument make where they intersect = 56°
Whereby the tangent lines from the monument to the maintenance person intersect and form an angle of 56°, we get that the tangent lines form two right triangles, please see the attached figure which is created with MS Excel;
The right triangles ΔABO and ΔACO are congruent by Leg Hypotenuse, LH, congruence rule
Therefore; ∠OAC ≅ ∠OBC
m∠OAC = m∠OBC (Definition of congruent angles)
Similarly, m∠BOA = m∠COA
However, m∠BAC = m∠OAC + m∠OBC (Angle addition postulate)
m∠BAC = 2 × m∠OAC = 56°
m∠OAC = 56° ÷ 2 = 28°
m∠BOA = 90° - m∠OBC (Acute angles of a right triangle)
m∠BOA = 90° - 28° = 62°
Therefore, m∠BOA = m∠COA = 62°
The angle at the center = m∠BOC = m∠BOA + m∠COA
m∠BOC = 62° + 62° = 124°
Angle formed at the center of the monument, m∠BOC = 124°
The arc angle of a circle = The angle the radius of the arc forms at the center of the circle.
The measure of the arc close to the park maintenance person is 124°
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6 cm
4.4 cm
2 cm
determine the total surface area of the figure.
The total surface area of the given cuboid is 94.4 square centimeter.
Given that, the dimensions of box are length=4.4 cm, breadth=2 cm and Hight=6 cm.
We know that, the total surface area of cuboid = 2(lb+bh+lh)
= 2(4.4×2+2×6+4.4×6)
= 2×47.2
= 94.4 square centimeter
Therefore, the total surface area of the given cuboid is 94.4 square centimeter.
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Out of a sample of 760 people, 367 own their homes. Construct a 95% confidence interval for the population mean of people in the world that own their homes. CI = (45. 31%, 51. 27%) CI = (43. 62%, 52. 96%) CI = (44. 74%, 51. 84%) CI = (46. 87%, 52. 56%)
The correct confidence interval for the population mean of people in the world who own their homes is CI ≈ (45.3%, 51.3%).
To construct a confidence interval for the population mean of people in the world who own their homes, we can use the sample data and calculate the margin of error. The confidence interval will provide an estimated range within which the true population mean is likely to fall.
Given the sample size of 760 people and 367 individuals who own their homes, we can calculate the sample proportion of individuals who own their homes as follows:
Sample proportion (p-hat) = Number of individuals who own their homes / Sample size
p-hat = 367 / 760 ≈ 0.483
To construct the confidence interval, we can use the formula:
CI = p-hat ± Z * sqrt((p-hat * (1 - p-hat)) / n)
Where:
CI = Confidence Interval
p-hat = Sample proportion
Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)
n = Sample size
Plugging in the values, we get:
CI ≈ 0.483 ± 1.96 * sqrt((0.483 * (1 - 0.483)) / 760)
Calculating the expression inside the square root:
sqrt((0.483 * (1 - 0.483)) / 760) ≈ 0.0153
Substituting back into the confidence interval formula:
CI ≈ 0.483 ± 1.96 * 0.0153
CI ≈ (0.483 - 0.0300, 0.483 + 0.0300)
CI ≈ (0.453, 0.513)
Therefore, the correct confidence interval for the population mean of people in the world who own their homes is CI ≈ (45.3%, 51.3%). None of the provided answer choices match the correct confidence interval.
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If a card never cost to ask what the first minimum payment would be for $3000 balance transfer at 4. 99% there is currently no balance on the account and the fee is 4% the minimum payment would be what
The first minimum payment would be $62.40 as it is higher than $25.
To determine the first minimum payment for a $3000 balance transfer at 4.99% with a 4% fee, you need to first calculate the balance transfer fee and add it to the initial balance. Then, you'll need to determine the minimum payment based on the credit card issuer's policy.
1. Calculate the balance transfer fee: $3000 * 4% = $120
2. Add the balance transfer fee to the initial balance: $3000 + $120 = $3120
3. The minimum payment depends on the credit card issuer's policy. Typically, the minimum payment is a percentage of the balance or a fixed amount, whichever is higher. For example, if the issuer requires a minimum payment of 2% of the balance or $25, whichever is higher:
- Calculate 2% of the balance: $3120 * 2% = $62.40
- Since $62.40 is higher than $25, the first minimum payment would be $62.40.
Please note that the actual minimum payment may vary depending on the specific credit card issuer's policy.
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Use the Mean Value Theorem to show that if * > 0, then sin* < x.
According to the Mean Value Theorem, if a function is continuous on the interval [a, b] and differentiable on the open interval (a, b), there exists a point c in (a, b) such that the derivative at c equals the average rate of change between a and b.
To use the Mean Value Theorem to show that if * > 0, then sin* < x, we first need to apply the theorem to the function f(x) = sin x on the interval [0, *].
According to the Mean Value Theorem, there exists a number c in the interval (0, *) such that:
f(c) = (f(*) - f(0)) / (* - 0)
where f(*) = sin* and f(0) = sin 0 = 0.
Simplifying this equation, we get:
sin c = sin* / *
Now, since * > 0, we have sin* > 0 (since sin x is positive in the first quadrant). Therefore, dividing both sides of the equation by sin*, we get:
1 / sin c = * / sin*
Rearranging this inequality, we have:
sin* / * > sin c / c
But c is in the interval (0, *), so we have:
0 < c < *
Since sin x is a decreasing function in the interval (0, π/2), we have:
sin* > sin c
Combining this inequality with the earlier inequality, we get:
sin* / * > sin c / c < sin* / *
Therefore, we have shown that if * > 0, then sin* < x.
I understand that you'd like to use the Mean Value Theorem to show that if x > 0, then sin(x) < x. Here's the answer:
According to the Mean Value Theorem, if a function is continuous on the interval [a, b] and differentiable on the open interval (a, b), there exists a point c in (a, b) such that the derivative at c equals the average rate of change between a and b.
Let's consider the function f(x) = x - sin(x) on the interval [0, x] with x > 0. This function is continuous and differentiable on this interval. Now, we can apply the Mean Value Theorem to find a point c in the interval (0, x) such that:
f'(c) = (f(x) - f(0)) / (x - 0)
The derivative of f(x) is f'(x) = 1 - cos(x). Now, we can rewrite the equation:
1 - cos(c) = (x - sin(x) - 0) / x
Since 0 < c < x and cos(c) ≤ 1, we have:
1 - cos(c) ≥ 0
Thus, we can conclude that:
x - sin(x) ≥ 0
Which simplifies to:
sin(x) < x
This result is consistent with the Mean Value Theorem, showing that if x > 0, then sin(x) < x.
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7) Compute the derivative of the function m(x) = -5xğ · V(x2 – 9)3. =
The answer for the derivative of m(x) is:
m'(x) = -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)
This is the final result after applying the product rule and the chain rule.
By use the product rule and the chain rule how we find the derivative?We can use the product rule and the chain rule to find the derivative of the function
First, let's break down the function as follows:
[tex]m(x) = -5x^2 · V(x^2 – 9)^3[/tex][tex]= -5x^2 · (x^2 – 9)^3/2[/tex]
Using the product rule, we have:
[tex]m'(x) = [-5x^2]' · (x^2 – 9)^3/2 + (-5x^2) · [(x^2 – 9)^3/2]'[/tex]Taking the derivative of the first term:
[tex][-5x^2]' = -10x[/tex]Taking the derivative of the second term using the chain rule:
[tex][(x^2 – 9)^3/2]' = (3/2)(x^2 – 9)^(3/2-1) · 2x[/tex][tex]= 3x(x^2 – 9)^(1/2)[/tex]
Putting it all together:
[tex]m'(x) = -10x · (x^2 – 9)^(3/2) + (-5x^2) · 3x(x^2 – 9)^(1/2)[/tex][tex]= -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)[/tex]
To compute the derivative of a function, we need to apply the rules of differentiation, which include the product rule and the chain rule. In this case, we have a product of two functions, [tex]-5x^2[/tex] and [tex]V(x^2 – 9)^3[/tex], where V represents the square root. We apply the product rule to differentiate the two functions.
The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product, u(x) · v(x), is given by u'(x) · v(x) + u(x) · v'(x). We use this rule to differentiate the two terms in the product.For the first term, [tex]-5x^2[/tex], the derivative is straightforward and is simply -10x.
For the second term, [tex]V(x^2 – 9)^3[/tex], we need to use the chain rule because the function inside the square root is not a simple polynomial. The chain rule states that if we have a function g(u(x)), where u(x) is a function of x, then the derivative of g(u(x)) is given by g'(u(x)) · u'(x). In this case, we have [tex]g(u(x)) = V(u(x))^3[/tex], where [tex]u(x) = x^2 – 9[/tex]. We need to apply the chain rule with [tex]g(u) = V(u)^3[/tex] and [tex]u(x) = x^2 – 9[/tex].
To apply the chain rule, we first take the derivative of the function [tex]g(u) = V(u)^3[/tex] with respect to u. The derivative of [tex]V(u) = u^(1/2[/tex]) is [tex]1/(2u^(1/2))[/tex].
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During 2022, each of the assets was removed from service. The machinery was retired on January 1. The forklift was sold on June 30 for $13,000. The truck was discarded on December 31. Journalize all entries required on the above dates, including entries to update depreciation, where applicable, on disposed assets. The company uses straight-line depreciation. All depreciation was up to date as of December 31, 2021
Loss on disposal of plant assets = $46400 - $32550
Loss on disposal of plant assets = $13850
How to solveDate Account titles and Explanation Debit Credit
Jan. 01 Accumulated depreciation-Equipment $81000
Equipment $81000
June 30 Depreciation expense (1) $4000
Accumulated depreciation-Equipment $4000
(To record depreciation expense on forklift)
June 30 Cash $13000
Accumulated depreciation-Equipment (2) $28000
Equipment $40000
Gain on disposal of plant assets (3) $1000
(To record sale of forklift)
Dec. 31 Depreciation expense (4) $5425
Accumulated depreciation-Equipment $5425
(To record depreciation expense on truck)
Dec. 31 Accumulated depreciation-Equipment (5) $32550
Loss on disposal of plant assets (6) $13850
Equipment $46400
(To record sale of truck)
Calculations :
(1)
Depreciation expense = (Book value - Salvage value) / Useful life
Depreciation expense = ($40000 - $0) / 5 = $8000 per year
So, for half year = $8000 * 6/12 = $4000
(2)
From Jan. 1, 2019 to June 30, 2022 i.e 3.5 years.
Accumulated depreciation = $8000 * 3.5 years = $28000
(3)
Gain on disposal of plant assets = Sale value + Accumulated depreciation - Book value
Gain on disposal of plant assets = $13000 + $28000 - $40000
Gain on disposal of plant assets = $1000
(4)
Depreciation expense = (Book value - Salvage value) / Useful life
Depreciation expense = ($46400 - $3000) / 8
Depreciation expense = $5425 per year
(5)
From Jan. 1, 2017 to Dec. 31, 2022 i.e 6 years.
Accumulated depreciation = $5425 * 6 years = $32550
(6)
Loss on disposal of plant assets = Book value - Accumulated depreciation
Loss on disposal of plant assets = $46400 - $32550
Loss on disposal of plant assets = $13850
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Solve for x. Assume that lines which appear tangent are tangent.
Multiply (x-4)(x+5) Show your work in the box and enter your answer in the spot below: (No work loses points)
The solution to the expression is x² + x - 20
How to calculate the expression?(x-4)(x+5)
open the bracket
x² + 5x - 4x - 20
x² + x - 20
Hence the solution to the expression leads to quadratic equation which is written is x² + x -20
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Kimi wants to teach her puppy 4 new tricks. in how many different orders can the puppy learn the tricks?
Answer:
3! = 6
Step-by-step explanation:
Once she teaches the puppy one trick there are 3 possible tricks left. After teaching the second trick there are 2 and after the third there is 1. Therefore, we multiply these numbers together to get 3(2)(1)=6 which is 3!.
8
Violet is taking a computer-adaptive test, where each time she answers a question correctly, the computer gjves
her a more difficult question. Let Q be the number of questions Violet answers correctly before she misses one.
What type of variable is Q?
None of them.
Geometric
ОООО
Binomial
Algebraic
The variable Q, representing the number of questions Violet answers correctly before she misses one in a computer-adaptive test, is a Geometric variable.
This is because a geometric distribution models the number of trials needed for the first success in a series of Bernoulli trials with a constant probability of success.
Where as all aspects of a logarithmic articulation that is isolated by a short or in addition to sign is known as the term of the algebraic expression and an algebraicexpression with two non-zero terms is called a binomial.
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What is the probability of selecting an Ace, not replacing it, and then selecting a King?
The probability of selecting an Ace, not replacing it, and then selecting a King is 4/663 or approximately 0.006 or 0.6%.
The probability of selecting an Ace, not replacing it, and then selecting a King can be calculated using the rules of conditional probability.
First, we need to determine the probability of selecting an Ace from a standard deck of 52 cards. There are four Aces in the deck, so the probability of selecting an Ace is 4/52, which can be simplified to 1/13.
Next, we need to consider the fact that the Ace is not replaced before selecting the King. This means that the deck now contains 51 cards, with only three remaining Aces. Therefore, the probability of selecting a King after selecting an Ace without replacement is 4/51.
To determine the overall probability of selecting an Ace and then a King, we multiply the probability of selecting an Ace (1/13) by the probability of selecting a King after selecting an Ace without replacement (4/51).
The calculation is as follows:
(1/13) x (4/51) = 4/663
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