This is a calculus question please make sure that all steps are shown and that everything is shown clearly i am terrible at calculus so please help .
Thank you
Answers
Answer:
a) [tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]
b) [tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]
Step-by-step explanation:
From the given equations to find, we are differentiating function G with respect to V out. Therefore, we will be only using the equation (6):
[tex]\displaystyle{G=20\log (10V_{\text out})}[/tex]
Here’s a fresh-up reminders for logarithmic differentiation formula:
[tex]\displaystyle{f(V)=a\log_b V \to f'(x)=\dfrac{a\cdot V'}{V\ln b}}[/tex]
Note that V' means to derive or differentiate the V-term
Therefore, in this scenario, our values of term are:
a = 20b = 10 (Since logarithm base is not shown, it’s always assumed to be common logarithm)V = 10V outTherefore, we can apply differentiation formula:
[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot \dfrac{d(10V_{\text out})}{dV_{\text out}}}{10V_{\text out}\ln 10}}[/tex]
Simplify:
[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot 10}{10V_{\text out}\ln 10}}\\\\\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]
And we have finished the part a. On part b, we just differentiate the answer from part a again, the second part is to obtain the second derivative which is to derive the first derivative. Therefore:
[tex]\displaystyle{\dfrac{d^2G}{dV_{\text out}^2} = \dfrac{d\left(\dfrac{20}{V_{\text out}\ln 10}\right)}{dV_{\text out}}}[/tex]
First, separate the constant every time when you have to differentiate a function:
[tex]\displaystyle{\dfrac{20}{\ln 10}\cdot \dfrac{1}{V_{\text out}}}[/tex]
Differentiate 1/V out: recall the formula of fraction:
[tex]\displaystyle{f(V)=\dfrac{1}{V} =V^{-1} \to f'(x)=-V^{-2} = -\dfrac{1}{V^2}[/tex]
The formula above is derived from power rules formula where:
[tex]\displaystyle{f(V)=V^n = nV^{n-1}}[/tex]
Therefore, from the function of V out:
[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(\dfrac{1}{V_\text{out}}\right)'}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (V_\text{out})^{-1}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (-V_\text{out})^{-2}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(-\dfrac{1}{V_\text{out}^2}\right)}[/tex]
Simplify to latest as we get:
[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]
Please let me know if you have any questions!
Related Questions
Match each number with its estimated power of 10
Answers
The matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
What are Exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
We have to match the following terms :
1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵
2) 219,000 = 2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵
3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶
4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵
5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶
Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
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what is (2 x 10 to the power of 5) divided by (4 x 10 to the power of 2)
Answers
500
Explanation:
P(AIB) can be read as "the probability that A occurs given that B has
occurred."
OA. True
OB. False
SUBMIT
Answers
P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.
Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.
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Pls help me thank you
Answers
The value of y is x/2 + c/5
Given,
In the question:
5x - 7y = 3y - 2c
To find the value of y.
Now, According to the question:
The equation is given as:
5x - 7y = 3y - 2c
Combine the like terms:
-7y - 3y = -5x - 2c
Calculate the sum or difference:
-10y = -5x - 2c
y = -5x/-10 - 2c/-10
Calculate the product or quotient :
y = x/2 + c/5
Hence, The value of y is x/2 + c/5
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HELP WHATS 565 divid by 000000.666 x X -k
Answers
Answer:
565/0.666=848.348
Step-by-step explanation:
if you needed variables added to the equation then show a picture and I can answer it.
A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If ( x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
Answers
If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.
Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:
(x, y) → (SFx, SFy) = (0.4x, 0.4y)
Where:
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Complete Question:
A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
answer choices
(0.4x, 0.4y)
(x + 20, y + 20)
(x + 0.4, y + 0.4)
(20x, 20y)
Math help needed (grade 9)
Answers
Step-by-step explanation:
volume = base area × height
= (1/2×12×16)×10
=960cm3
surface area:
1. triangle area = 1/2×12×16=96cm2
2.bottom area = 12×10=120cm2
3.side area = 16×10=160cm2
4.slope area = 10×20=200cm2
5.add everything and remember you have two triangle
surface area= 96×2+120+160+200 =672cm2
Which description matches the graph of the inequality y <|x-2| + 1
Answers
A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
What is inequality?
Inequality is a relationship between two expressions or values that is not equal to each other.
This inequality may be written in two ways:
(a) y < x - 2 + 1
or
y < x - 1
(b) y < -x +2 + 1
or
y < -x + 3
A graph of the inequality is shown below. The shaded region satisfies the inequality.
Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
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Solve the equation or formula for the variable indicated.
X-2y=1
Answers
Answer:
Step-by-step explanation:
-2y = -x -1
2y = x+1
y = 1/2x+1/2
PLEASE HELP ME AND TELL ME HOW YOU DID IT AND THANKS 25 POINTS HELP
Answers
50-36 is 14 and just plug 14 into the blanks to see which one fits.
A line passes through the point
(8, 7) and has a slope of 4
Write an equation in slope-intercept form for this line.
Answers
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 4}(x-\stackrel{x_1}{8}) \\\\\\ y-7=4x-32\implies {\Large \begin{array}{llll} y=4x-25 \end{array}}[/tex]
Answer:
y = 4x -25
Step-by-step explanation:
y = 4x + b
we must find the y intercept
plug in the point
7 = 4(8) + b
7 = 32 + b
subtract 32 from both sides
-25 = b
the y intercept is -25
plug in -25 for b
y = 4x - 25
Each month, kaisorn deposits $50. 00 onto her public transportation card. It costs her $2. 50 per trip to ride the subway. Thom deposits $40. 00 on his public transportation card. It costs him $2. 00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2. 5x = y 40 − 2x = y 50 + 2. 5x = y 40 + 2x = y 50 − 2. 5y = x 40 − 2y = x 50 + 2. 5y = x 40 + 2y = x.
Answers
The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
The correct option is (A)
Given,
In the question:
Kaisorn deposits $50. 00 onto her public transportation card.
It costs her $2. 50 per trip to ride the subway.
Thom deposits $40. 00 on his public transportation card.
It costs him $2. 00 per trip to ride the subway.
Now, According to the question:
x → represents the number of trips
y → represents the amount remaining in each account
According to the given condition:
The system of equations represents their transportation costs is :
50 − 2. 5x = y
40 − 2x = y
Hence, The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
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Please help pleaseee
Answers
According to the Pythagoras theorem, the value of x is 13.76
Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.
Given,
Here we have the triangle with the side values.
Now, we have to find the value of x through this given values.
In order to calculate the value of x,
First, we need the value of the side KM.
Let us consider the value of KM is y.
Then according to the concept of Pythagoras theorem,
The value of y is calculated as,
=> (12.3)² = y² + (5.4)²
=> 151.29 = y² + 29.16
=> y² = 122.13
=> y = 11.05
Therefore, the value of the hypotenuse x is calculated as,
=> x² = (11.05)² + (8.2)²
=> x² = 122.13 + 67.24
=> x² = 189.37
=> x = 13.76
Therefore, the value of x is 13.76.
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A robot can complete 4 tasks in hour. Each task takes the same amount of time.
5/6
a. It takes the robot
(Simplify your answer.)
-
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
hour(s) to complete one task.
Answers
1 task will complete in 12.5 minutes
The robot can complete 9.6 task in 1 hour
Given,
Number of task a robot can complete = 4
Time taken by robot = 5/6 of 1 hour
5/6 of 1 hour = 5/6 × 60 minutes
= 300/6
= 50 minutes
Then,
4 task takes 50 minutes
1 task = 50 minutes / 4 task
= 12.5 minutes
So,
1 task = 12.5 minutes
x task = 60 minutes
1 : 12.5 = x : 60
1/12.5 = x / 60
1*60 = 12.5*x
60 = 12.5x
x = 60/12.5 = 4.8
x= 4.8
Therefore,
The robot can complete 4.8 task in 1 hour
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about 310 000 t of atlantic cod were caught in 1991. in 2001 the mass of the cod caught was 87% less. HOw much cod was caught in 2001
Answers
Number of Atlantic cods caught in the year 2001 is; 40300 t
How to solve percentage word problems?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;
Percentage = (value / total value) * 100%
Now, we are told that;
Number of Atlantic cods caught in 1991 = 310000 t
We are told that in the year 2001, there were 87% less caught. Thus;
Number by which it was reduced = 310000 * 87% = 269700
Thus;
Number of Atlantic cods caught in the year 2001 = 310000 - 269700
Number of Atlantic cods caught in the year 2001 = 40300 t
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In the following figure, AD is the bisector of ZBAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that AAEG = AAFG by the AAS congruence postulate. Do you agree or disagree? Explain.
Answers
I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent
The AAS have it that the two triangles being compared should have their two angles and the side not included being equal
The Angle - Angle - Side = AAS, here include
< FA,G - < AFG - AG
< EAG - < AEG - AG
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there is a line whose slope is 1 and whose y-intercept is -9, what is its equation in slope-intercept form?
Answers
Choose the equation that represents the graph shown
Answers
Answer:
[tex]y=|x|-4[/tex]
Step-by-step explanation:
The vertex of the graph is at (4, 0).
This eliminates all of the options except for [tex]y=|x|-4[/tex].
Evaluate the expression for the given value of the variable. 52+1/5(-1/2)
Answers
The simplified form of the expression 52 + 1/5(-1/2) is [tex]\frac{519}{10}[/tex]
What is a fraction?A fraction is a ratio of two integers.
The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.
52 + 1/5(-1/2)
Multiply out the fraction
we have
52 + (-1/10)
52 - 1/10
to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes
520/10 - 1/10
simplifying the numerator we have,
[tex]\frac{520 - 1}{10}[/tex] = [tex]\frac{519}{10}[/tex]
In conclusion the solution to 52+1/5(-1/2) is [tex]\frac{519}{10}[/tex]
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
7, 7/1
Step-by-step explanation:
The ratio 7:49 can be simplified to 1:7.
A rectangle is 25 cm on one side and 6 cm on another side. What is the perimeter?
Answers
Answer:
31
Step-by-step explanation:
If you roll a die three times, how many different sequences are possible? a. 6 cubed = 216 b. 3 superscript 6 baseline = 216 c. 3 superscript 6 baseline = 729 d. 6 cubed = 729
Answers
Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex] =216
What is outcome of an event?
Suppose an event is happening. The result of the event is called outcome of the event.
For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die
Number of outcomes of rolling a die first time = 6
Number of outcomes of rolling the die second time = 6
Number of outcomes in rolling a die third time = 6
Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]
= [tex]6^3[/tex]
= 216
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The scatterplot shows the relationship between the length of a pendulum and the time it takes to complete one full swing.
Which transformations would linearize these data using a power model? Check all that apply.
ln(Length), ln(Time)
ln(Length), Time
log(Length), log(Time)
Length, log(Time)
Length, Time2
Answers
Answer:
a) ln(Length), ln(Time)
c)log(Length), log(Time)
e)Length, Time²
Step-by-step explanation:
Answer:
the person above me is correct!
Step-by-step explanation:
a coin is flipped eight times. each result is either a heads or a tails. how many possible outcomes contain at least 33 tails ?
Answers
The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.
The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:
[tex]\frac{8!}{3!5!} + \frac{8!}{4!4!} + \frac{8!}{5!3!} + \frac{8!}{6!2!} + \frac{8!}{7!1!} + \frac{8!}{8!0!}[/tex]56 + 70 + 56 + 28 + 8 + 1= 219Hence, the possible outcomes that contain at least three tails are 219.
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wilma can mow a lawn in 120 minutes. vanessa can mow the same lawn in 80 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
Answers
Working together, they can mow the yard in 48 minutes.
Given data;
A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?
Let 't' is their time in minutes working together.
Add their rates of working to get their rate working together,
Wilma's rate: [ 1 lawn ] / [ 120 min ]
Vanessa's rate: [ 1 lawn ] / [ 80 min ]
Rate working together: [ 1 lawn ] / [ t min ]
1/120 + 1/80 = 1/t
Multiply both sides by 240t;
2t + 3t = 240
5t = 240
t = 48
It takes them 48 min to mow the lawn working together.
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necesito saber como se resuelve
Answers
La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.
¿Cómo resolver un ecuación exponencial?
Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.
Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:
f(x) = 9ˣ⁺¹ - 28.3ˣ - 3
g(x) = 0
La solución es todo punto tal que f(x) = g(x).
A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.
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There are 100 items in a garage sale. 30% of the items are sold during the first hour of the sale. If 10 items are sold during the second hour, what percent of the items have not been sold?
Answers
The percentage of items that have not been sold is: 60%
In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.
Percent in itself stands for out of 100.
Let the total number of items= i
Let the percentage be represented as= p
Then,
i=100 (Given in the question)
Let the number of items sold in the first hour be= a
Let the number of items sold in the second-hour be= b
Since,
p= Given Value/Total value x100
thus,
a/100x100=30%
The hundreds cancel out.
Thus, a=30 -(i)
The number of items sold in the second hour= b
b=10 (provided in the question) -(ii)
Let the total number of items sold be=T
The total number of items sold= a+b
From (i) and (ii)
Total number of items sold=30+10
Thus,
Total number of items sold=40 -(iii)
Number of items that have not been sold(n)=100-(a+b)
=100-T
= 100-40
From (iii)
n = 60 -(iv)
Then,
Percentage of items that have not been sold = n/100x100
From -(iv)
= 60/100x100
Canceling hundred by hundred
= 60%
Thus,
Answer: The percentage of items that have not been sold is: 60%
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Type the missing number to complete the proportion.
18 orders in 2 days = 9 orders in
days
Answers
Answer:
18 orders in 2 days 9 orders in 1 day
Answer:
Step-by-step explanation:
9x2=18 which is 2 days so 9x1= 9 which is one day
order the sides DEF from shortest to longest
Answers
From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.
Triangle:
The polygon with three edges known as sides and three vertices are known as triangle.
Given,
Here we have the triangle with their corresponding angle.
Now, we have to order the sides from shortest to longest.
Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.
By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.
In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.
From values, the shortest to longest the order is written as DE, DF and EF.
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Select the type of cross section formed when a triangular pyramid is cut parallel to its
base.