y(t)= 3/5[tex]e^{-5.2}[/tex]-3/5esin2t-9/5sin2t when the IVP's is y'+5.2y=19.4sin2t, and y(0)=0 by Laplace transform and partial fraction.
Given that,
We have to solve the IVP's by the Laplace transform.
If necessary we have to use partial fraction expansion for y'+5.2y=19.4sin2t, and y(0)=0
We know that,
y'+5.2y=19.4sin2t, and y(0)=0
L(y(t))= y(s)
L(y'(t)) = sy(s) and
L(sin2t) = s/s²+4 ------->equation(1)
Thus if we take Laplace transform on both sides of the given equation
L(y'+5.2y)=L(19.4sin2t)
sy(s)-y(0)+5.2y(s) = 19.4L(sin2t)
y(s)[s+5.2]=19.4[s/s²+4] (from equation(1))
y(s)= 19.4[s/(s²+4)(s+5.2)]
Breaking left hand side into partial precautions,
y(s) = 3/5(1/s+5.2)-3/5(s/s²+4)-9/5(s/s²+4)
Taking inverse Laplace transform on both sides,
So,
y(t)= 3/5[tex]e^{-5.2}[/tex]-3/5esin2t-9/5sin2t
Therefore, y(t)= 3/5[tex]e^{-5.2}[/tex]-3/5esin2t-9/5sin2t when the IVP's is y'+5.2y=19.4sin2t, and y(0)=0 by Laplace transform and partial fraction.
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Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
Y = x-1
y = 1/2x+1
• A. (-2, 0)
O B. (-4, -3)
O C. (4, 3)
O D. (2, 1)
The solution to the system of equations is (4,3). Option C
What is a system of equations?Generally, To solve this system of equations by graphing, you can start by graphing each equation separately on the same set of axes.
For the first equation, Y = x - 1, you can start by plotting a few points to get a feel for the graph.
, if x = 0, then Y = -1.
If x = 1, then Y = 0.
If x = 2, then Y = 1.
You can continue plotting points like this to get a better idea of what the graph looks like.
For the second equation, y = 1/2x + 1, you can do the same thing. For example,
if x = 0,
then y = 1.
If x = 1,
then y = 1.5.
If x = 2,
then y = 2.
Again, you can plot a few more points to get a better sense of the graph.
Once you have graphed both equations, you can look for the point where the two graphs intersect.
This point will be the solution to the system of equations. In this case, the solution is (4,3), so the correct answer is C.
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2. Jasmine goes to Ben and Jerrys to get ice
cream. Her ice cream costs $8.00. She leaves a
20% tip. How much tip did she leave?
Answer:
$1.60
Step-by-step explanation:
20% of $8.00 is actually 0.20 x 8
0.20 x 8 = 1.60
Answer:
$1.60
Step-by-step explanation:
First, convert the 20% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 20%) by 100%.So, the conversational term "20%" becomes 20% / 100% = 0.20
Second, you need to find out what 20% of your $8.00 meal cost is.This is always done by multiplying 0.20 by $8.00, or
0.20 x $8.00=$1.60.
So, the amount of tip you are going to leave is $1.60.
IF SOMEONE CAN ANSWER BOTH OF THESE QUESTIONS I WILL GIVE YOU 45 points
The value of x is 7.2.
The Perimeter of quadrilateral TWNB is 70.
what is perimeter?
A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.
Given: TWNB ≅ RDHY
NW = 3x,
RD = 5x - 19.6
RY = 2x + 5.6
HD = 5x - 14.4
TW = 3x - 5.2
BN = x + 4.8
We have to find the value of x
As, TWNB ≅ RDHY
⇒ TW ≅ RD, WN ≅ DH, NB ≅ HY, TB ≅ RY
Consider, TW ≅ RD
3x - 5.2 = 5x - 19.6
19.6 - 5.2 = 5x - 3x
14.4 = 2x
x = 7.2
Hence, the value of x is 7.2.
Now to find the perimeter of quadrilateral TWNB.
Perimeter of TWNB = TW + WN + NB + TB
Here,
TW = 3x - 5.2 = 16.4
WN = 3x = 21.6
NB = x + 4.8 = 12
TB = RY = 2x + 5.6 = 20
Hence,
Perimeter of TWNB = 16.4 + 21.6 + 12 + 20 = 70.
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5. Suppose you fill your truck's tank with fuel and begin driving down the highway for a
road trip. Assume that, as you drive, the number of minutes since you filled the tank and
the number of gallons remaining in the tank are related by a linear function. After 40
minutes, you have 28.4 gallons left. An hour after filling up, you have 26.25 gallons left.
Write this equation in SLOPE INTERCEPT FORM.
The equation that represent the situation in slope intercept form is y = -0.1075x + 32.7.
'
How to represent equation in slope intercept form?Equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptAs you drive, the number of minutes since you filled the tank and the number of gallons remaining in the tank are related by a linear function.
After 40 minutes, you have 28.4 gallons left. An hour after filling up, you have 26.25 gallons left.
Let's find the slope.
(40, 28.4)(60, 26.25)
m = 26.25 - 28.8 / 60 - 40
m = -2.15 / 20
m = - 0.1075
Hence, let's find the y-intercept using (40, 28.4)
y = - 0.1075x + b
where
x = number of minutesy = amount of fuel remainingTherefore,
28.4 = -0.1075(40) + b
28.4 + 4.3 = b
b = 32.7
Therefore, the equation of the line is y = -0.1075x + 32.7
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8) Eugene and Kayla each improved their yards by planting daylilies and shrubs. They bought their
supplies from the same store. Eugene spent $87 on 10 daylilies and 9 shrubs. Kayla spent $60
on 5 daylilies and 10 shrubs. What is the cost of one daylily and the cost of one shrub?
A) daylily: $7, shrub: $1
C) daylily: $3, shrub: $6
12
B) daylily: S6, shrub: $3
D) daylily: $3, shrub: $1
i don't know girl i'm so sorry
fred walks 20 miles toward the north. he turns left and walks 40 miles. he again turns left and walks 20 miles. finally, he walks 20 miles after turning to the left. how far is he from his starting point.
Using vector calculation and analyzing directions, The answer is 20 miles west from the starting point.
What is a vector?An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
What do you mean by vector addition?The process of adding two or more vectors together to create a vector sum is known as vector addition.
20 miles to north and 40 miles left .
Using triangle law of vector addition, Distance from point at the location = [tex]\sqrt{20^2 + 40^2}[/tex]
=[tex]20\sqrt 5[/tex] miles.
Now turns left walks 20miles , Using triangle law of vector addition,
distance from point at the location = [tex]\sqrt{(20\sqrt 5)^2 - 20^2}[/tex]
=40 miles from location.
This location is horizontally same from the start point.
So he turns left and walks 20miles again.
distance from point= 40-20
=20 miles west of start point.
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What is the median of the following set of scores 19 5/12 10 and 14?
The median of this set of scores 19,5/12,10 and 14 is 12.
To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.
In this case, the scores are 5/12, 10, 14, and 19.
After arranging the scores in numerical order, we have 5/12, 10, 14, and 19.
There are four scores in this set, so the median is the average of the two middle scores, which are 10 and 14.
The median of the set is: (10 + 14) / 2 = 12.
The median of this set of scores is 12.
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n a certain wilderness area 1.4 mountain lions are seen each year, on average. what is the probability that in a given year exactly two mountain lions will be seen in this wilderness area? (assume that sightings are independent from each other and that the probability of seeing a mountain lion stays constant.)
Therefore ,the probability that in a given year exactly two mountain lions will be seen in this wilderness area is P =0.2417.
How does probability work?Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. When an event has a probability of 0, it has no possibility of happening, whereas when it has a probability of 1, it is almost certain to happen. When an event has a probability of 0.45 (45%), there are 45 out of 100 chances that it will occur.
Here,
λ=1.2
=> P(X =x) = [tex]\frac{e^{-\lambda} * \lambda^{x} }{x!}[/tex]
=> P(X=2) = [tex]\frac{e^{-1.4} * 1.4^{2} }{2!}[/tex]
=> P(X=2) = 0.2466 * 1.96 /2
=>P(X=2) = 0.2417
Therefore ,the probability that in a given year exactly two mountain lions will be seen in this wilderness area is P =0.2417.
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A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate. Using hospital birth records, she selects a simple random sample of 200 couples who had children within the first 2 years of marriage. Following up on these couples, she finds that 80 couples are divorced within 5 years. Let p= the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years. What is a 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years?Question options:0.402 ± 0.0880.402 ± 0.0670.402 ± 0.0570.402 ± 0.035
The proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years is [tex]0.4\pm 0.057[/tex].
What is a confidence interval?The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value.
A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Given, Out of 200 couples who have children with 2 years, 80 couples had been divorced within 5 years.
Therefore the proportion of couples who have had children and divorce
= (80/200).
= 0.4.
We know the confidence interval for a population proportion is,
[tex]p = p' \pm z_{\frac{\alpha}{2}} \sqrt{\frac{p'(1 - p')}{n}[/tex].
Now, [tex]z_{\frac{\alpha}{2}[/tex] at 90% confidence interval is 1.645 and n = 200.
Therefore, [tex]p = 0.4\pm 1.645} \sqrt{\frac{0.4'(1 - 0.4)}{200}[/tex].
[tex]p = 0.4\pm 1.645} \sqrt{\frac{0.4\times0.6}{200}[/tex].
[tex]p = 0.4\pm 1.645\times0.0346[/tex].
[tex]p = 0.4\pm 0.057[/tex].
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At what point on the graph is the rate of reaction the greatest?
The instantaneous rate at the beginning of a reaction, or when t = 0, is known as the starting rate of the reaction.
What is rate of Reaction ?The rate at the beginning of the reaction may be determined using the graph of change in product over time or change in reactant over time. The highest rate on the curve is the beginning rate. Since the reactants are concentrated at their highest at the beginning, the most collisions are occurring.
Rates of response can be depicted in graphs. To depict the pace of reaction, we may create a graph of product (or reactant) against time. The pace of reaction will be the gradient of the graph. The pace of response increases with increasing gradient steepness.
The instantaneous rate at the beginning of a reaction, or when t = 0, is known as the starting rate of the reaction. The beginning rate is equal to the slope of the reactant concentration versus time curve at time zero, which is negative.
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Can the sides of a triangle have lengths 2, 18, and 20?
Answer: No triangle lengths have to add all three length together to equal 180 like 60 60 60 or 90 80 10
Step-by-step explanation:
graph the following features Y-intercept = 2 Slope = -5/4
The equation of the line in intercept form will be x / 1.6 + y / 2 = 1. Then the graph of the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is negative 5/4 and the y-intercept of the line is 2. Then the equation of the line is given as,
y = -(5/4)x + 2
Convert the equations into intercept form. Then we have
y = -(5/4)x + 2
4y = -5x + 8
5x + 4y = 8
x / 1.6 + y / 2 = 1
The condition of the line in the capture structure will be x/1.6 + y/2 = 1. Then, at that point, the diagram of the line is drawn underneath.
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I need help just on #6 please!
The two column proof is written as follows
Statement Reason
h || g given
j || g given
< 2 ≅ < 1 Alternate angle theorem
< 1 ≅ < 3 Corresponding angle theorem
< 1 ≅ < 3 Transitive property
What is transitive property?According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."
hence if < 2 ≅ < 1 and < 1 ≅ < 3, then < 1 ≅ < 3
What are alternate angles postulate?According to the alternate angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.
What are congruent angles?Two angles are said to be congruent when they are equal to each
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Which of thee i equal to co 47°?
Repone
A in 43°in 43°
B co 133°co 133°
C tan 43°tan 43°
D co 43°
Option (A) cos 47° is equal to sin 43°.
What is cos in trigonometry ?
The cos meaning in trigonometry defines the cosine of an angle. This angle is an acute angle in a right angled triangle, which is considered to find the ratios. Thus, cosine of an angle, in a right-triangle, is equal to the ratio of adjacent side of that angle and hypotenuse of the triangle.
What is sin in trigonometry ?
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
Have given,
cos 47°,
We know that cos x = sin (90 - x),
Thus cos 47° = sin (90 - 47)
cos 47° = sin 43°
Therefore, cos 47° is equal to sin 43°.
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cos 47°,
We know that cos x = sin (90 - x),
Thus cos 47° = sin (90 - 47)
cos 47° = sin 43°
Therefore, cos 47° is equal to sin 43°.
En el experimento de la clase de Física, se pone a calentar agua durante 3 minutos y se registra la temperatura. Posteriormente, aumenta la masa del agua, se pone a calentar durante 3 minutos en las mismas condiciones, se observa que la temperatura disminuye. ¿Qué relación existe entre la masa de agua y la temperatura?.
La masa del sistema es inversamente proporcional a la temperatura del mismo. Existe una relación de proporcionalidad inversa.
¿Cuál es la relación entre la temperatura y la masa de un sistema?
En este problema tenemos dos casos de calentamiento sensible en dos muestras de agua, cuya fórmula se describe a continuación:
Q' · Δt = m · c · ΔT
Donde:
Q' - Tasa de transferencia de calor.Δt - Tiempo de calentamiento, en minutos. m - Masa del sistema.c - Calor específico del agua.ΔT - Cambio en la temperatura del sistema.A partir de esta fórmula comprobamos que la masa del sistema es inversamente proporcional al cambio de la temperatura del sistema:
m ∝ 1 / ΔT
En consecuencia, a mayor masa, menor cambio en la temperatura.
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Solve pls brainliest
Answer:
In given right angled triangle,
h=30 cm,p=18 cm,b=?
By Pythagoras theorem,
h²=p²+b²
or,b²=h²-p²
or,b²=(30)²-(18)²
or,b²=900-324
or,b=√576
or,b=24 cm
hence, the length of missing side is 24 cm
How many terms are there in the expression 5xy 9yz 3zx 5x 4y?
The number of terms that the expression 5xy 9yz 3zx 5x 4y has is 5 terms.
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
How to determine terms?To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.
5xy 9yz 3zx 5x 4y has 4 spaces
4 + 1 = 5 terms.
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I’LL MARK BRAINLIEST IF CORRECT!!
The display shows how much water is used in a household in a given day.
Which of the following describes this data set?
A) Categorical and bivariate
B) Categorical and univariate
C) Numerical and bivariate
D) Numerical and univariate
The coordinate 3 has a weight of 2,
and the coordinate 9 has a weight of 1.
Find the weighted average.
PLEASEEE HELPPP
Answer:
1.5
Step-by-step explanation:
avj=total/n n=no of thingsavj=1+2/2avj=3/2 or 1.5Answer: Answer is
Step-by-step explanation:
I don't know how to explain it but I went over it with my teacher and it is
How do you use transformations to determine if figures are congruent or similar?
Geometric shapes that are identical in size and shape are known as congruent figures. Congruent figures are those in which you may use a series of translations, rotations, and/or reflections to turn one figure into another.
What is rigid transformations?The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape.
There are isometric rotations, reflections, and translations. Accordingly, the size of the figure is unaffected by these adjustments. The figures are consistent if neither the size nor the form of the figure is altered.
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What is a correct first step in solving the inequality 4 3 5x ≥ 6x 9 brainly?
The first step in solving the inequality is -12 + 20x ≥ -6x + 9
An inequality can be defined as a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Given the inequality
–4(3 – 5x)≥ –6x + 9
Solving the inequality
⇒-12 + 20x ≥ -6x + 9
Keeping all x on one side it can be written ,
⇒20x + 6x ≥ 12 + 9
Adding both sides,
⇒26 x ≥ 21
divide both sides by 26,
⇒x ≥ 0.80
So, the first step in solving the inequality is -12 + 20x ≥ -6x + 9
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The correct question is :
What is the correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
How do you tell if a function grows faster than another?
f(x) g(x) = L = 0, where L is some finite number. This definition implies that if f grows faster than g, then f will eventually be much larger than g. Similarly, if f grows slower than g, then f will eventually be much smaller than g.
Now, According to the question:
f(x) g(x) = L = 0, where L is some finite number. This definition implies that if f grows faster than g, then f will eventually be much larger than g. Similarly, if f grows slower than g, then f will eventually be much smaller than g.
Steps on How to Compare the Rates of Change of Two Functions Using Limits
Step 1: Given the functions f(x) and g(x), compute the limit limx→∞f(x)/g(x).
Step 2: If the limit in Step 1 is a finite constant a≠0, then the growth rate of f(x) is a times the growth rate of g(x) at sufficiently large x. If the limit in Step 1 is ∞, then the growth rate of f(x) is greater than the growth rate of g(x). If the limit in Step 1 is 0, then the growth rate of g(x) is greater than the growth rate of f(x).
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Denzel must practice the piano for 210 min each week. He practices for 30 min each day. Write a linear equation represent the number of minutes denzel still has to practice after x days?.
Answer:
y = 30x - 210
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Polygon ccc has an area of 777 square units. Jennie drew a scaled version of polygon ccc and labeled it polygon ddd. Polygon ddd has an area of 282828 square units. What scale factor did jennie use to go from polygon ccc to polygon ddd?.
19.25 scale factor did jennie use to go from polygon ccc to polygon ddd if Polygon ccc has an area of 777 square units.
What is polygon and examples?
A polygon is a closed shape with straight sides. Rectangles, triangles, hexagons, and octagons are all examples of polygons. The word polygon comes from the Greeks, like most terms in geometry, which they invented. It simply means many (poly) angles (gon).
The area of polygon D is given by:
Ad = k ^ 2 * Ac
Where,
k: scale factor
Ac: area of polygon C
Substituting the values we have:
Ad = (1/2) ^ 2 * (77)
Ad = (1/4) * (77)
Ad = 19.25 square unit
the area of Polygon D is: 28
Ad = 19.25 square units
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Solve the system of equations
The required values are x = 12 and y = -3 solution to the given system of equations.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of equations is given as:
2x + 7y = 3 ....(i)
x = -4y ....(ii)
Substitute the value of x = -4y in the equation (i), and solve for y
2( -4y) + 7y = 3
-8y + 7y = 3-y = 3
y = -3
Substitute the value of y = -3 in equation (ii), and solve for x
x = -4(-3)
x = 12
Thus, the solutions are x = 12 and y = -3.
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Are all equilateral triangles congruent Why?
For a triangle to be equilateral all its angle should be same which is 60° but for them to be congruent their sides should also be same in measure.
Therefore two equilateral triangles are not always congruent with one another as because there can be difference in the measure of their sides.
The sum of angles of a triangle is 180 degree which is the sum of angles of the triangle's three angles.
There are three types of triangles based on different aspects .
Based on the lengths of their sides, triangles can be classified as
ScaleneIsoscelesEquilateralAs in an equilateral triangle all of the sides are of the same length. and all the angle measure will be 60 degrees. An equilateral triangle is also known as an equiangular triangle since its angles are all the same.
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What kind of sequence is 4/8 16?
It is an Arithmetic sequence
What is Arithmetic sequence?
Arithmetic sequences are collections of integers where the distance between succeeding items is consistently the same.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same. In this case, the difference between the two terms is 16 - 4/8 = 12.
So the sequence could be written as 4/8, 4/8 + 12, 4/8 + 2*12, ... and so on. Each term in the sequence is obtained by adding 12 to the previous term.
Hence, It is an Arithmetic sequence.
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What are the 3 types of dynamic semantics?
In linguistics, dynamic semantics is a theory of meaning that is based on the idea that the meaning of a sentence is determined by the way it is used in context, rather than by its compositionality. Within dynamic semantics, there are a few different approaches that have been developed. Three types of dynamic semantics are Discourse representation theory, situation semantics and event semantics.
Discourse representation theory: This theory proposes that the meaning of a sentence is determined by its role in the context of a discourse (i.e., a conversation or written text). The meaning of a sentence is represented as a set of constraints on the possible interpretations of the discourse, and the interpretation of the discourse is determined by the way these constraints are resolved.
Situation semantics: This theory proposes that the meaning of a sentence is determined by the way it refers to a particular situation or state of affairs. The meaning of a sentence is represented as a set of conditions that must be satisfied for the sentence to be true in a particular situation.
Event semantics: This theory proposes that the meaning of a sentence is determined by the events or actions it describes. The meaning of a sentence is represented as a set of conditions that must be satisfied for the events or actions described in the sentence to occur.
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What is the nature of roots of the quadratic equation 2x² √ 5x 1 0?
The roots of the quadratic equation 2x² √5x + 1 = 0 are two complex numbers.
To solve for the roots of the quadratic equation 2x² √5x + 1 = 0, we must first use the Quadratic Formula to solve for x. The Quadratic Formula is x = (-b ± √b²-4ac)/2a. In this equation, a = 2, b = √5, and c = 1. We then simplify the equation to be x = (-√5 ± √(5²-4(2)(1))/2(2). This simplifies to x = (-√5 ± √9i)/4. The two solutions to this equation are x = (-√5 + 3i)/4 and x = (-√5 - 3i)/4. Since both solutions involve complex numbers, the roots of 2x² √5x + 1 = 0 are two complex numbers.
x = (-√5 ± √(5²-4(2)(1))/2(2)
x = (-√5 ± √9i)/4
Root 1: x = (-√5 + 3i)/4
Root 2: x = (-√5 - 3i)/4
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Can a 5 year old count to 100?
Yes, a 5 year old can typically count to 100.
What is counting?Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.
Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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