The Laplace transformation is:
[tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]
Rewriting the f in terms of the unit step function:
[tex]\left \{ {{y=5} for 0\leq t\leq 7 \atop {x=-3}for t\geq 7} \right.[/tex]
⇒ f(t) = 5[u(t) - u (t-7)] - 3u(t -7 )
= 5u(t) - 8u (t-7)
Unit Step Function:
The unit step function, also known as the Heaviside function, is known in engineering applications as a function that can describe the switching process mathematically. We often encounter functions whose values change rapidly over a certain time unit t.
where,
u(t) = [tex]\left \{ {{y=1 for t\geq 0} \atop {x=0 for t < 0}} \right.[/tex]
Recall the time-shifting property of the Laplace transform:
L{u(t - c) f( t - c)}
= [tex]e^{-es} L{f(t)}[/tex]
Laplace Transformation:
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that transforms a function of real variables (usually t in the time domain) into a function is. Complex variable (complex frequency domain, also called s-domain or s-plane). As transformations are tools for solving differential equations, they have many applications in science and engineering. In particular, it converts ordinary differential equations to algebraic equations and converts convolutions to multiplications.
and the Laplace transform of a constant function,
L[k] = k/s
So we have
L[f(t)] = L[5u(t) - 8u (t-7)]
= [tex]5[L_{1} ] - 8e^{-7s} L[1][/tex]
Therefore,
[tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]
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When z1 and z2 are added together, the result moves z1 6 units and 3 units. The real part of z1 + z2 is. The imaginary part of z1 + z2 is i.
The real part of Z₁+Z₂ is 8 and imaginary part of Z₁+Z₂ is -2, when Z₁ and Z₂ are added together and the result moves Z₁ 6 units right and 3 units down
A complex number is of the structure a + bi, a, b are real numbers, and I = √(- 1). Deciding the upsides of square underlying foundations of negative numbers is utilized. It is addressed in the direction plane with the real part on the x-hub and imaginary part b on the y-pivot, the arranged pair being (a, b).
In the inquiry, we are given two complex numbers,
Z₁ = 2 + i
Z₂ = 6 - 3i
These focuses are addressed on the direction plane as a circle and a triangle separately. We ascertain their total, z3.
To add Complex Numbers, the real parts are added to the genuine parts and the nonexistent to the imaginary.
∴ Z₃ =Z₁+Z₂ = (2 + i) + (6 - 3i) = (2+6) + (1-3)i = 8 - 2i.
This point is addressed as a square on the Direction plane.
Hence, we can say that real part is 8, and its imaginary part is - 2.
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Gabe goes to the mall. If k is the number of items he bought, the expression 12.33k+24 gives the amount he spent in dollars at one store. Then he spent 30 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 4 items.
Answer:
Step-by-step explanation:
12.33(4)+24= 73.32
then add the extra 30$ that was spent
73.32+30= $103.32
Multiply −12y(9y − 7). I need this ASAP!
Answer: -108y^2 + 84y
Step-by-step explanation:
y^2 is y squared
give me brainiest! :D
The required simplified solution of the given expression is -108y² + 84y.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= −12y(9y − 7).
Simplify,
Applying distributive property,
= -12y×9y - 12y(-7)
= -108y² + 84y
Thus, the required simplified solution of the given expression is -108y² + 84y.
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what do americans think about preferential hiring of women? has there been a change in the past decade? in 2000(group 1) and 2010(group 2), the general social survey asked participants if they would favor or oppose preferential hiring of women. in 2000, out of 849 respondents, 271 said yes. in 2010, out of 696 respondents, 225 said yes. the 95% confidence interval is (-0.0509, 0.04273). for the alternative hypothesis, ha: p1-p2 does not equal zero, what can we say about the p-value?
Greater than 0.05 is the p-value, which indicates that it is greater than the significance level.
what is test of hypothesis?When determining whether the available data are sufficient to support a given hypothesis, one method of statistical inference is known as a statistical hypothesis test. Making probabilistic claims about a population parameter is possible through hypothesis testing.
given
a 95% confidence interval with bounds for the inference's outcome (-0.0509,0.04273).
As the value p1-p2=0 is included in the interval and is one of the possible values of the genuine difference between the proportions, this confidence interval indicates that the difference (p1-p2) is not substantially positive at the level of significance utilized in the study.
The null hypothesis would then not be rejected by a test of hypothesis performed with the same data and level of significance because the proportional difference is not significant.
In this example, the P-value is more than 0.05, which indicates that it is greater than the significance level.
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what’s the biggest number 7.06 or 7.9
Answer:
7.9
Step-by-step explanation:
7.06<7.9
What is area of plane figures?
The area of a plane figure is the region enclosed by the figure's boundary . Here the area is measured in square units of length such as a square meter or square centimeter
The area of plane figures is a mathematical concept that is used to measure the size of two-dimensional shapes. It is the amount of space inside the figure and can be calculated by multiplying the length and width of the figure. The measurement of the area is usually measured in square units, such as inches, centimeters, or meters. The area is a fundamental concept in geometry and is used in many areas of mathematics, such as calculus and trigonometry.
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How do you calculate the slope ratio of a ramp?
In order to calculate the slope ratio of a ramp, divide the difference between the elevations of two points by the distance between them, then multiply the quotient by 100, the resultant figure is the slope ratio.
What is the slope of a line?
The slope or gradient of a line in mathematics is a number that defines both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.
The difference between the elevations is also called as the rise. And the distance between the points is known as the run.
Thus, we can also say that,
Slope ratio= rise / run x 100.
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jake can mow a lawn in 3 hours. kellie can mow a lawn in 4 hours. if they work together, how long will it take them to mow one lawn?
if they work together it takes 12/7 hours to mow one lawn
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
jake can mow a lawn in 3 hours.
kellie can mow a lawn in 4 hours.
1/3 lawns can be cut per hour by Jake.
kellie has a 1/4 hour cutting rate for lawns.
They can cut 7/12 lawns per hour by working together at a rate of 1/3 + 1/4.
One lawn can be mowed in 12/7 hours at a rate of 7/12 lawns per hour.
Hence if they work together it takes 12/7 hours to mow one lawn.
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What does the scale factor from one figure to the other tell you about the figures?
The scale factor tells at what ratio a figure has been changed from other figures
Shapes in various dimensions can be scaled using the Scale Factor.
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:
y ∝ x
K can therefore be regarded as a proportionality constant in this context.
The scale factor tells a particular percentage increment or to calculate the percentage of an amount.
Also , To compare 2 Similar geometric figures: When we compare two similar geometric figures by the scale factor, it gives the ratio of the lengths of the corresponding sides.
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make a scatterplot of weight versus desired weight. describe the relationship between these two variables.
The relationship between the variable is the direction, strength, and linearity .
Scatterplots can be used when one continuous variable is under the control of the experimenter and the other is dependent on it, or when both continuous variables are independent. When one parameter is systematically increased and/or decreased by the other, it is called the control parameter or independent variable and is usually plotted along the horizontal axis. Measured or dependent variables are usually plotted along the vertical axis. In the absence of a dependent variable, any type of variable can be plotted on any axis and the scatter plot he only shows the degree of correlation (not causality) between the two variables.
Scatterplots can suggest different types of correlations between variables with specific confidence intervals. If the dot pattern slopes downwards from the lower left to the upper right, this indicates a positive correlation between the investigated variables. If the dot pattern slopes from top left to bottom right, it indicates a negative correlation. You can draw a line of best fit (also called a "trend line") to explore the relationship between variables. The formula for correlation between variables can be determined by established best-fit methods. For linear correlation, the optimal procedure is called linear regression, which guarantees a correct solution in finite time. There is no one-size-fits-all procedure that guarantees the correct resolution in any relationship. Scatterplots are also very useful for seeing how two comparable data sets match up to show non-linear relationships between variables.
Desired Weight:
A standardized table of desirable (or ideal) weight for adult height is based on life expectancy. Both malnutrition and obesity are associated with an increased risk of early death. A desirable weight corresponds to a body mass index (ratio of weight in kg/height in m2) between 20 and 25. Ideal weight charts based on actuarial data were first published in 1942 by the Metropolitan Life Assurance Company of New York and were replaced in 1959 by charts of average and desirable weights.
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I've been having problems with this and I was wondering if someone could give me the answers 1 - 5
The measures of x are obtained with the Pythagorean Theorem, as follows:
1. x = 10.2.
2. x = 7.2.
3. x = 13.7.
4. x = 36.2.
5. x = 10.7.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the lengths of the sides squared.
Hence, for item 1, we have that:
x² + 16² = 19²
x = square root(19² - 16²)
x = 10.2.
For item 2, we have that:
x² + 12² = 14²
x = square root(14² - 12²)
x = 7.2.
For item 3, we have that:
x² + 9.2² = 16.5²
x = square root(16.5² - 9.2²)
x = 13.7.
For item 4, we have that:
The bottom side is bisected into two equal sides of dimension 15.Then x is the hypotenuse of a right triangle of sides 15 and 33, thus:x² = 15² + 33²
x = square root(15² + 33²)
x = 36.2.
For item 5, first we find the side of the top right triangle, hence:
h² + 16² = 25²
h = square root(25² - 16²)
h = 19.2.
Then the value of x is obtained as follows:
x² + 19.2² = 22²
x = square root(22² - 19.2²)
x = 10.7.
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There is a spider in an infinite two-dimensional grid. You have absolutely no idea where she is. The only thing you know is that in each second she moves in the same direction. Unfortunately, you do not know the direction: it can be left, right, up or down. In each second, you can put your finger on one point in the grid. Devise a strategy to catch the spider after finitely many steps
The strategy to catch the spider is elaborated out here.
The best strategy for catching the spider after infinitely many steps is to start at one point in the grid and then move in a clockwise spiral, expanding your search area every time you move. As you move, you can use a combination of visual and physical cues, such as vibrations and sound, to detect the spider's presence. This method will ensure that the spider will eventually be caught in a finite amount of time. Additionally, if the spider changes directions, your search will be able to adjust to that change, as you will be able to detect it in the spiral pattern.
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Sam decides to build a square garden. If the area of the garden is 4x2 + 28x + 49 square feet, what is the length of one side of the garden?.
The length of one side of square garden that Sam built in Area 4x² + 28x + 49 is (2x+7) feet.
Area Of Any Shape :Area is the region enclosed by the shape of an object. The space covered by a figure or any two-dimensional geometric shape in the plane is called the area of the shape. Area is measured in square units (m², cm², inch², etc.)
Example: The area of a rectangular floor is equal to its length times its width
We have given that,
The shape of garden is Square.
The area of garden , A = 4x² + 28x + 49
We know that , Area of square= Side × Side --(*)
where side is dimension of square. We have to find out the side of the square garden.
A = 4² + 28x + 49
Factorize the middle term such that sum of factors is 28x and multiply of factors is 196x².
A = 4x² + 14 x + 14x + 49
=> A = 2x( 2x + 7 ) + 7(2x + 7)
=> A = (2x+7)(2x+7)
comparing this Area with equation(*) we get,
Side = 2x+7
Hence, the required side is (2x+7) feet.
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a passenger train leaves charleston, wv heading east at the same time a loaded coal train leaves charelston, wv heading west. the passeger train travels23mi/hr faster than the coal train, and in 4 hours the two trains are 412 miles apart. what is the speed of each train
The speed of the each train = 63
What is Speed?Speed is defined as : The rate of change of position of an object in any direction.
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Types of SpeedThere are four types of speed and they are:
1. Uniform speed
2. Variable speed
3. Average speed
4. Instantaneous speed
Given that
The passenger train travels23mphr faster than the coal train
In 4 hours the two trains are 412 miles apart
Let the speed of train = x
4*x+4*(x+23)=412
4x + 4x + 92 = 412
8x = 320
x = 40
the speed of the each train = x + 23 = 40 + 23 = 63
Given that
The passenger train travels 23mphr faster than the coal train
In 4 hours the two trains are 412 miles apart
let the speed of train = x
4*x+4*(x+23)=412
4x + 4x + 92 = 412
8x = 320
x = 40
the speed of the each train = x + 23 = 40 + 23 = 63
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help please
Rewrite 16x4y3 − 32x3y4 using a common factor.
2x4y4(8 − 16x)
2x3y3(8y − 16x)
8x4y3(2 − 4y)
8x3y3(2x − 4y)
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
a construction firm has bid on two different contracts. let e1 be the event that the bid on the first contract is successful, and define e2 analogously for the second contract. suppose that p(e1) 5 .4 and p(e2) 5 .3 and that e1 and e2 are independent. a. find the probability that both bids are successful. b. find the probability that neither bid is successful. c. find the probability that at least one of the bids is successful.
The required probabilities of the given parts are a) 56%, b) 6% , c) 94%.
What is Probability?The probability is the proportion of the probability of an occasion to occur. It estimates the conviction of the occasion. The recipe for probability is given by; P(E) = Number of Good Results/Number of absolute results.
According to question:a) These two occasions are autonomous, consequently, the probability of both is the increase of the probabilities of every, accordingly:
0.56 = 56% probability that the two offers are fruitful.
b) E1 has a 1 - 0.7 = 0.3 probability of being ineffective, while E2 has a 0.2
likelihood, thus:
0.06 = 6% probability that neither one of the bids is effective.
c) 1 - 0.06 = 0.94
0.94 = 94% probability that the firm is effective in no less than one of the two bids.
Thus, required probabilities are a) 56%, b) 6% , c) 94% .
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There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
Answer: 1.06 cm
Step-by-step explanation:
Take 2.7 divided by 2.54 = 1.062cm
Rounded the nearest hundredth, so it will be 1.06 cm
If the simple interest on $6,000 for 9 years is $4,320, then what is the interest rate?
Answer:
6.48%
Step-by-step explanation:
Solve the equation for v.
0.5v + 0.04 < 1.14
v > 2.2
v < 2.2
v > 2.4
v < 2.4
Answer:
v < 2.2
Step-by-step explanation:
0.5v < 1.14 – 0.04
0.5v < 1.1
v < 1.1/0.5
v < 2.2
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How do you calculate raw score in grades?
Raw score can be computed by using arithmetical operations such as addition, subtraction, multiplication, and division.
This can be done by hand or by using a calculator or a computer program. Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to compute raw data. Raw data can also be influenced in many ways.
For example, data can be organized, filtered, and sorted into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends feasible to understand. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.
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write and solve a system of equations for the situation. 2x+2y=6 4x+4y=4
SOLVING WORD PROBLEMS INVOLVING QUADRATIC INEQUALITIES:
As an architect, your job is to fulfill the requirements of the client. You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones. The desired length of the lot is 15 meters longer than its width. The area of the rectangular plot should not be more than 126 m^2.
Solution:
-15/2+√31.(3/2)i is the width of the garden.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
As an architect, your job is to fulfill the requirements of the client.
You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones.
Let width be x
The desired length of the lot is 15 meters longer than its width.
Length =x+15
The area of the rectangular plot should not be more than 126 m²
Area=Length×width
126=x(x+15)
126=x²+15x
x²+15x-126=0
Apply it in Quadratic formula.
x=-b±√b²-4ac/2a
a=1, b=15 and c=-126.
x=-15±√15²-4(1)(-126)/2(1)
x=-15/2+√31.(3/2)i.
Hence, the width of the garden is -15/2+√31.(3/2)i.
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X=
2 Michael bakes a soft pretzel and a loaf of bread. Use the system of equations to
find c, the amount of flour, in cups, needed for the soft pretzel, and b, the amount
of flour, in cups, needed for the loaf of bread. Show your work.
b = 24c
5
16+ 4c = 2/
SOLUTION
The value of b is 3.
The value of c is 1/8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 5 = 9 is an equation.
We have,
Two equations given are:
b = 24c ____(1)
(1/4)b + 4c = 5/4 _____(2)
Putting (1) in (2) we get,
(1/4)24c + 4c = 5/4
6c + 4c = 5/4
10c = 5/4
c = 5/40
c = 1/8
Putting c = 1/8 in (1) we get,
b = 24/8
b = 3
Thus,
b = 3.
c = 1/8.
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Which line represents “a number is one-half the difference of a number x and 4?”
Answer:
Line C
Step-by-step explanation:
Given:
"a number y is one-half the difference of a number x and 4”.Create the equation for the line using the given information:
[tex]\implies y=\dfrac{1}{2}(x-4)[/tex]
Distribute:
[tex]\implies y=\dfrac{1}{2}x-2[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Compare the found equation with the slope-intercept formula:
Slope = ¹/₂y-intercept = -2The y-intercept is the y-value of the point at which the line crosses the y-axis. Therefore, the line crosses the y-axis at y = -2.
The slope tells us how much y increases as x increases. Given the slope is ¹/₂, the line increases by one y-value for every two x-values.
Therefore, the line that represents the given information is line C.
The equation C = 5(F - 32) converts temperature in degrees Fahrenheit to
degrees Celsius. For each one-degree increase in Fahrenheit temperature, what is the change in the temperature in degrees Celsius?
Hence, a temperature increase of
9
5
degree Fahrenheit is equivalent to a temperature increase of
81
25
degree Celsius.
a portable cd player was originally priced at $79.95 and cost $39 is ultimately sold for $64.95. what was the reduction percentage on the portable cd player?
By using percentage, it can be calculated that
Percentage reduction on the portable cd player [tex]= 18.76 \%[/tex]
What is Percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 9% means [tex]\frac{9}{100}[/tex]. Here, 9 is expressed as a fraction of 100.
Original price of the CD player = $79.95
Selling price = $64.95
Reduction in price = $(79.95 - 64.95) = $15
Percentage reduction on the portable cd player = [tex]\frac{15}{79.95} \times 100 = 18.76 \%[/tex]
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What is the slope of the line − 3 3?
The slope of the line passing through points (3, -3) and (0, -3) is equal to zero.
If we look at the general meaning of slope then we find out that Slope is nothing but the elevation or the steepness of any curve plotted on a graph paper. Now, the formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as
m = (y₂ - y₁)/(x₂ - x₁)
where m is the slope between the points, (y₂ - y₁) is difference between the y coordinates and (x₂ - x₁) is the difference between the x coordinates.
We have the values as (x₁, y₁) = (3, -3) and (x₂, y₂) = (0, -3)
So, the slope will be expressed as
m = (-3 + 3)/(0 - 3)
m = 0/-3
m = 0 which is the required slope.
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Complete Question:
What is the slope of the line that passes through (3, -3) and (0, -3).
What is the greatest common factor of 45, 50, 84?
Answer:
1
Step-by-step explanation:
there's no common factor between them
help me pleaseeee ill give brainliest
Answer: A. 16.7%
The probability of the letter C being chosen is 16.7% because there are 6 options and the probability will always be out of 100%. If you divide 100 by those 6 choices you will get 16.66 and rounded it is 16.7
Answer:
the answer is option B. 20%
If 75% of a number is 225 and 20% of the same number is 60, find 95% of that number.
95% of the given number is 285 if 75% of that number is 225 and 20% of the same number is 60.
In mathematics, a percentage is defined as a number or ratio that can be expressed as a fraction of 100.
Let assume the number is x
So, according to first statement, we are given that 75 percentage of x=225,it means
=>(75/100) × x=225
=>(3/4) × x=225
=>x=(225 × 4) /3
=>x = (75 × 4)
=>x = 300
Now, check for same number whether 20% is 60 or not
=>20% of x=60
=>(20/100) × x=60
=>(1/5) × x =60
=>x= 60 × 5
=>x = 300
So, our assumption is correct.
Now,95% of the same number is 95% of x
=(95/100) ×300
=95 × 3
=285
Hence,95% of 300 is 285.
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