Consider again the electric circuit in Problem 21 of Section 7.6. This circuit is described by the system of differential equations ()=(-4,-)(0) a. Show that the eigenvalues are real and equal if L = 4R2C. b. Suppose that R=1.12, C = 1 F, and L = 4 H. Suppose also that I(0) = 1 A and V(0) = 2 V. Find I(t) and V(t).
Answers
The solution of a differential equation to the system is then given by I(t) = (3/4)e-4.48t + (-1/4)e4.48t and V(t) = (3/4)e-4.48t – (2/4)e4.48t.
a. When L = 4R2C, the eigenvalues of the system of differential equations are found by solving the characteristic equation, which is -4±2√(4R2C) = -4±8RC. Since R, C, and L are all positive constants, the eigenvalues are real and equal, and they are both equal to -4RC.
b. Setting R = 1.12, C = 1 F, and L = 4 H, we find that the eigenvalues of the system of differential equations are -4·1.12·1 = -4.48. The solution to the system is then given by I(t) = Ae-4.48t + Be4.48t and V(t) = -4RAe-4.48t + 4RB e4.48t.
Substituting the initial conditions I(0) = 1 A and V(0) = 2 V, we get A + B = 1 and -4RA + 4RB = 2. Solving for A and B, we find that A = 3/4 and B = -1/4.
The solution to the system is then given by I(t) = (3/4)e-4.48t + (-1/4)e4.48t and V(t) = (3/4)e-4.48t – (2/4)e4.48t.
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Related Questions
The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
Answers
\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)
Math time everybody! ALSO,im gonna need points here soon
Answers
Answer:
The Answer is -3
Step-by-step explanation:
perimeter.
6) A quadrilateral can have 2
reflex angles.
Answers
Answer:
False
Step-by-step explanation:
Answer:
A quadrilateral can't have 2 reflex angles
Step-by-step explanation:
A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°
A salesman at J&R Computer World sold a laptop for $1500. His commission was $75. What was his commission rate?
Answers
Answer:
5%
Step-by-step explanation:
1500 * X = 75
X = 75/1500
X = .05 or 5%
When solving the equation below using the quadratic formula, what would be the value inside or under the radical? (Hint: simplify first!)
2x 2 − 10 = 7x
Answers
The values under and inside the radical is 4 and 129 respectively
What is a quadratic equation?A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler.
A quadratic equation is given as ax²+ bx+ c=0
this can be solved using formula x=( -b±√b²-4ac)/2a.
in the equation 2x²-10=7x, it can be Rearranged As 2x²-7x-10= 0
a= 2, b= -7 and c= -10
x= -(-7)±√(-7)²-4×2×-10)/2×2
x= 7±√49+80)/4
x= 7/4 ± √129/4
therefore the values inside and under the radical is 129 and 4
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Obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations. A survey found that 37 of 74 randomly selected women and 47 of 74 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program. Group of answer choices
Answers
Answer:
The 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)
Step-by-step explanation:
The formula for confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
From the question
We have two groups.
Group 1 = For women
A survey found that 37 of 74 randomly selected women
p1 = x/n1
n1 = 74
x1 = 37
p1 = 37/74
p1 = 0.5
Group 2 = For Men
A survey found out that 47 of 74 randomly selected men follow a regular exercise program
p2 = x/n1
n2= 74
x2 = 47
p2 = 47/74
p2 = 0.6351351351 ≈ 0.635
z = z score for 95% Confidence Interval = 1.96
The confidence interval for the difference between the proportions is given as:
p1 - p2 ± z × √p1 (1 - p1)/n1 + p2(1 - p2)/n2
0.5 - 0.635 ± 1.96 × √0.5 (1 - 0.5)/74 + 0.635(1 - 0.635)/74
-0.135 ± 1.96 × √(0.5 × 0.5)/74 + (0.635× 0.365)/74
-0.135 ± 1.96 × 0.08068750209663572
-0.135 ± 0.158147504109406
Hence:
= -0.135 - 0.158147504109406
= -0.2931475041
Approximately = -0.293
= -0.135 + 0.158147504109406
= 0.0231475041
Approximately = 0.023
Therefore, the 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program = ( -0.293, 0.023)
There are 23 students in an MA 206 class at FCC. How many ways are there to select 5 students for a group project?
Answers
Answer:
33649waysStep-by-step explanation:
We are expected to use the combination method to solve for the number of ways
given that
number of students n= 23
number of groups r= 5
the expression for the number of ways is given as
C(n,r)= n!/r!(n-r)!
substituting we have
C(23,5)= 23!/r!(n-r)!
C(23,5)= 23!/5!(23-5)!
C(23,5)= 23!/5!(18)!
C(23,5)= 23*22*21*20*19*18!/5!(18)!
C(23,5)= 23*22*21*20*19/5!
C(23,5)= 23*22*21*20*19/5*4*3*2*1
C(23,5)= 23*22*21*20*19/120
C(23,5)= 4037880/120
33649ways
The distance between the centres of two villages is 8 km.
A map on which they are shown has a scale of 1:50000.
Calculate the distance between the centres of the two villages on the map. Give your answer in centimetres.
Answers
The distance between the centres of the two villages on the map is 16cm. The solution is obtained using the concept of unit conversion.
What is unit conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles. Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.
Now, we are given the scale of a map as 1 : 50000 and that two villages are 8km apart on the map.
The scale of a map is given as 1 : 50000.
=> 1 cm on map = 50,000 cm on actual
We know that 1 km = 1,00,000cm
So,
=> 8km = 8,00,000 cm
So, The distance on the map is
800000 / 50000
= 80/5
= 16 cm
Hence, the actual distance between them is 16cm.
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What is the rate of the trains in mph?
Answers
Rearrange g
=
fr to make f the subject.
Answers
Answer:
f=g/rStep-by-step explanation:
divide by R
Car Survey In a survey of 2,200 people who owned a certain type of car, 1,320 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
Percentage is expressed in terms of 100. We were told that out of 2200 people that were surveyed, 1,320 said they would buy that type of car again. This means that 1320 people were satisfied. Thus, the percent of the people surveyed were satisfied with the car would be
1320/2200 x 100
= 60%
60 percent of the people surveyed were satisfied with the car
2 dived by 49 with a remainder
Answers
Answer:
The answer is 24 with remainder of 1
Step-by-step explanation:
First, solve the problem by seeing what number gives you 4 when multiplied by 2. That would be 2 (2x2=4)
you subtract 4 by 4 to get zero and bring down the nine
Then you see which number would get you close to nine without overlapping when multiplied by two. That would be 4 (2x4=8)
your answer would be 24 then you subtract 9 by 8 to get a remainder of 1
Joey is flying his Cesna due Northwest at 188mph. Unfortunately, a wind traveling.
60mph due 150 bearing. Find Joey's actual Speed and direction.
Answers
Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.
Given that Joey's aircraft speed: 188 mph
Wind speed: 60 mph
Wind direction: 150 degrees (measured clockwise from due north)
We can consider the wind as a vector, which has both magnitude (speed) and direction.
The wind vector can be represented as follows:
Wind vector = 60 mph at 150 degrees
We convert the wind direction from degrees to a compass bearing.
Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.
Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)
Wind vector = 60 mph at 210 degrees
To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.
Converting the wind vector into its x and y components:
Wind vector (x component) = 60 mph × cos(210 degrees)
= -48.98 mph (negative because it opposes the aircraft's motion)
Wind vector (y component) = 60 mph×sin(210 degrees)
= -31.18 mph (negative because it opposes the aircraft's motion)
Now, we can add the x and y components of the two vectors to find the resulting velocity vector:
Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph
Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph
Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)
= 143.59 mph
Direction = arctan((-31.18 mph) / 139.02 mph)
= -12.80 degrees
The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.
The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.
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Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. Explain the steps that Lana could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5,2) into the point-slope formula. B) C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5,2) into the point-slope formula. Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5,2) into the point-slope formula. Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula. D)
Answers
3x + 2y = 15
Make y the subject of the formula to make it in the slope-intercept form
\(\begin{gathered} 2y=-3x+15 \\ \text{divide through all elements by 2} \\ \frac{2y}{2}=-\frac{3x}{2}+\frac{15}{2} \\ y=-1.5x+7.5 \end{gathered}\)The gradient of a line & the one parallel to it are equal:
Express the equation in general form
0.1 × 0.1 represent
Answers
Answer:
0.01
Step-by-step explanation:
0.1 x 0.1 = 0.01
HOPE IT HELPS YOU
Let R be the shaded region bounded by the graphs of y = e^x, y = -1, x = 1, and the y-axis. R is the base of a solid with cross sections perpendicular to the x-axis as squares. Find the volume of the solid.
Answers
Answer:
get a graphing caculator and type the numbers in the rectangle and see what you get
Step-by-step explanation:
In the equation Y+2/y+1 + 2y^2-y+3/y^2-1 = y-2/y-1 the value of a is: a)2 b)1 c)4
Answers
Answer:
2
Step-by-step explanation:
hope that helped
the value of a is 1. Correct answer is A
To find the value of 'a' in the equation (y+2)/(y+1) + (2y²-y+3)/(y²-1) = (y-2)/(y-1), we can simplify and solve for 'a'.
First, we need to simplify the equation by finding a common denominator for all the fractions. The common denominator is (y+1)(y-1), which is the same as y²-1.
Multiplying each term by the common denominator, we get:
(y+2)(y-1) + (2y²-y+3) = (y-2)(y+1)
Expanding the terms, we have:
(y²+y-2) + (2y²-y+3) = (y²-y-2)
Combining like terms:
3y² + 2 = y² - y - 2
Now, let's move all the terms to one side of the equation:
3y² - y² + y + y + 2 + 2 = 0
2y² + 2y + 4 = 0
Dividing through by 2:
y² + y + 2 = 0
Comparing the equation to the quadratic form y² + y + 2 = 0, we can see that a = 1, b = 1, and c = 2.
Therefore, the value of a is 1. Correct answer is A
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What is the explicit formula for this sequence?
60, 30, 15, 7.5, ...
A. an = 60.
(9)
OB. an= = (1.60
OC. an = 60.
• (+)-
OD. an=3.2(n-1)
60(n-1)
(n-1)
Answers
i beilive this is unknown
Find the unknown side of the triangle. Urgent
Answers
Answer:
13 in
Step-by-step explanation:
It’s a right triangle, so use the Pythagorean Theorem.
12²+5²=c²
144+25=c²
169=c²
√169=c
13=c
If the odometer is reading 20,000 miles, how many miles have you actually traveled?
Answers
Answer:
22,256
Step-by-step explanation:
If the speedometer reading is 60, your actual speed is miles. miles per hour. Since the value of k = 1.1128 for the two tires in comparison, 1.1128 (20,000) = 22,256 miles (actual) and 1.1128 (60) = 66.768 miles per hour (actual). The percent error is 11.28% for both readings.
The slope of the line shown below is 3/2. What is the value of a? 2, 3, 5, 6
Answers
The solution is Option D.
The value of a from the equation of slope is a = 6
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second poin
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the value to be determined be = a
Now , the slope of the line be = m
The value of m = 3/2
So , Slope m = 3/2
And , the value of a is calculated by
Slope = rise / run
Slope = y/x
Since , the value of x = 4
3/2 = y/4
Multiply by 4 on both sides of the equation , we get
y = 3 x 2
y = 6
Therefore , the value of a = 6
Hence , The value of a from the equation of slope is a = 6
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substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place.
Answers
The value of the height is 17
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
Volume, V = 1/3πr²h
Volume= 1138.8,
π=3.14
r= 8
h= 3V/πr²
h= 3* (1138.8)/3.14* 8*8
h=3416.4/200.96
h=17
Hence, the value of height is 17
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Simplify 3\(\sqrt\)2-√2
Answers
Answer: (√2)(2) = 2√2
Step-by-step explanation:
To simplify the expression 3√2 - √2, you can factor out the common term √2:
3√2 - √2 = (√2)(3 - 1)
Now, subtract the numbers in parentheses:
(3 - 1) = 2
(√2)(2) = 2√2
A skier IS skiing down a slope on the mountain.
Is the mechanical energy conserved? Why or why not?
Answers
Answer:
The mechanical energy isn't conserved.
Step-by-step explanation:
Honeslty I think you should Start cheatin on your Hw
Answer:
The mechanical energy is not conserved
Step-by-step explanation:
Recall that the law of conservation of energy states that in an isolated system (no external forces acting on it), the mechanical energy is conserved.
A skier skiing down a slope is not an isolated system in this case because the friction of the snow causes some of the mechanical energy to convert to thermal energy.
There was a country concert held at the park. For every 3 men there were 5 women that went to the concert. If 30 more women attended the concert than men, how men and how many women attended the concert.
Answers
Answer:
3m == 5w, that means for such unit, there is a 2 person difference
30 person difference = 30/2 = 15units
and again one unit means 3m and 5w
so 15*3men, and 15*5women
and you can check the difference is 30
A statistical question produces data that varies. Which question below will produce data that varies?
A. how many days are in a leap year
B. How many quarts are in a gallon
C. How many senses are there
D. How many students are in each class
Answers
Explanation: this is the only statistical question that would have data that varies. The other answer choices are all questions with one answer that are factual. But there can be any amount of students in a class and there are numerous types of classes so there is lots of data to be produced from this one question.
PLEASE HELP A bike wheel has a radius of 25 cm. a)How far (rounded to a tenth of unit) does the bike wheel travel in 1 rotation? b)10 rotations? c)Write an equation relating the distance the bike travels in cm, (d), to the number of wheel rotations (x)? d) How many rotations does the bike wheel make when the bike travels 1 kilometer? Explain or show your reasoning.?
Answers
your mom
Step-by-step explanation:
Which equation represents g(x)
Answers
Answer:
Option D. is the correct option
Step-by-step explanation:
The graph of g(x) is the translation of y = ∛x, which passes through origin (0, 0).
The graph in the figure is showing a shift of 1.5 units downwards.
Therefore, the new translated function g(x) will be represented by
g(x) = ∛x - 1.5
This graph can create a confusion of being shifted on x-axis but when we plug in the values of x in the options A and B, parent graph gets changed.
Therefore, option D. is the answer
Since 1 inch is equal to 2.54 centimeters what does 1 centimeter equal to In inches
Answers
Answer:
one centimeter is 0.393701 inches
Step-by-step explanation:
Find the measure of the indicated angle in each triangle
The choices are
A=180
B=156
C=103
D=360
Answers
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
⇢∠V + ∠T = ∠x
⇢53° + 103° = 156°
⇢∠VUX = 156°
Hence , option b is the correct answer.
Answer:
B) 156 is correct
Hope it helps