[tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)² using convolution property.
What is convolution property?Convolution is a mathematical operation on two functions (f and g) that results in a third function (f×g) that expresses how the shape of one is altered by the other. It is a mathematical operation on two functions (f and g) in mathematics, more specifically in functional analysis.
Convolution is a term that describes both the method of computing a function and its result. Its definition states that it is the integral of the product of the two functions after one of them has been shifted and reflected about the y-axis. The result of the integral remains unchanged regardless of which function is chosen to be reflected and shifted before it (see commutativity). The convolution function is created by evaluating the integral across all shift values.
[tex]\begin{aligned}& =\frac{1}{a} \int_0^t \cos a u \sin a(\mathrm{t}-\mathrm{u}) \mathrm{du} \\& =\frac{1}{a} \int_0^t[\cos a u \sin (a \mathrm{t}-a u)] \mathrm{du} \\& =\frac{1}{a} \int_0^t\left[\frac{\sin (a \mathrm{t}-a u+a u)+\sin (a \mathrm{t}-a u-a u)}{2}\right] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\& =\frac{1}{2 a} \int_0^t[\sin (a \mathrm{t})+\sin a(\mathrm{t}-2 u)] \mathrm{du} \\\end{aligned}[/tex]
[tex]\begin{aligned}\\& =\frac{1}{2 a}\left[(\sin \mathrm{at}) \mathrm{u}+\left(\frac{-\cos a(\mathrm{t}-2 \mathrm{u})}{-2 a}\right)\right]_0^t \\& =\frac{1}{2 a}\left[(\sin a t) \mathrm{u}+\frac{\cos a(\mathrm{t}-2 \mathrm{u})}{2 a}\right]_0^t \\& =\frac{1}{2 a}\left[t \sin \mathrm{at}+\left(\frac{\cos a t}{2 a}\right)-\left(0+\frac{\cos a t}{2 a}\right)\right] \\& \therefore L^{-1}\left[\frac{s}{\left(\mathrm{~s}^2+\mathrm{a}^2\right)^2}\right]=\frac{1}{2 a} t \sin \mathrm{at}\end{aligned}[/tex]
Thus, [tex]\dfrac{1}{2a}t \ \text{sin} \ \text{at}[/tex] is the solution of (18s)/(s²+36)² using convolution property.
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A given rectangle has a length expressed as 4x^3 + 2x^2 -6x + 3 and a width expressed as 2x^2 + 6x.
Therefore , the solution of the given problem of rectangle comes out to be area = 8x⁵ + 28x⁴ -30x² +18x.
Rectangle: What is it?In Euclidean plane geometry, a rectangle is a square with four right angles. You may also refer to it as a quadrilateral that seems to be equiangular, meaning that each of its angles is equal. Another possibility for the parallelogram is a straight angle. Four of the sides of a square are of identical length. Four 90 ° vertices and equal equal sides make up a rectangle-shaped quadrilateral.
Here,
Given :
Length of rectangle = 4x³ + 2x² -6x +3
and
Width = 2x² + 6x.
Thus ,
Area of rectangle = length * width
=> (4x³ + 2x² -6x +3) * (2x² + 6x)
=> 8x⁵ + 28x⁴ -30x² +18x
Therefore , the solution of the given problem of rectangle comes out to be area = 8x⁵ + 28x⁴ -30x² +18x.
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Solve this fraction and show your work
9/28 +29/70=?
Answer:
103/140
or
0.74
Step-by-step explanation:
9/28 +29/70
taking L.C.M of 29 and 70
= (9×5 + 29×2)/140
= (45 + 58)/140
= 103/140
= 0.74
6. Tara is solving an equation. Her first step is shown below
Solve: 4y - 8(y-2) = 6
Step 1: 4y - 8y + 16 = 6
Which property justifies Tara's first step?
O Associative Property of Multiplication
O Identity Property
s
O Distributive Property
Subtraction Property of Equality
re to show all your work to
Answer:
Distributive property
Step-by-step explanation:
8 x y = 8y, -8 x -2 = 16
2. Triangle XYZ is rotated 90° clockwise about the origin to form triangle
XYZ.
Y
N
у
6
L
3
N
1
-7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
N
12
3 4 5
X
67
X
Which state ment is true
Answer:
21 because 21x2 is 21 rrrr
Kyle draws a quadrilateral with a perimeter of 30 centimetres. What is the maximum possible area of Kyle's shape?
Answer:
225 square cm.
Step-by-step explanation:
The maximum possible area of Kyle's quadrilateral occurs when it is a square with side length equal to half the perimeter, which is 30/2 = 15 cm. The area of a square with side length 15 cm is 15 x 15 = 225 square cm.
Find the volume of a square based pyramid with a base length of 10 and a height of 14.
Volume of a square pyramid with base length (a) 10 and height(h) 14 is
466.67 cubic units.
What is a pyramid ?A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. It has a polygonal basis and is a conic solid. There are n + 1 vertices, n + 1 faces, and 2n edges in a pyramid with an n-sided base. Every pyramid is dual in itself.
A pyramid with a square base is known as a square pyramid. It is a right square pyramid with symmetry if the apex is perpendicular to and above the square's center. It is an equilateral square pyramid, the Johnson solid, if all edge lengths are equal.
A square pyramid has the following characteristics:
5 Faces.Triangles make up the 4 side faces.It has a square base.It has 8 Edges and 5 Vertices (corner points).Volume of a square pyramid with base length (a) 10 and height(h) 14 is
V = (1/3)*(a)²h = 10²*14/3 = 466.67 cubic units.
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Solve for r
9/p=8q-3/r
Answer:
r=8/3q-3/p
Step-by-step explanation:
9/p=8q-3r
9/p+3r=8q
3r=8q-9/p
3r/3=8q/3-(9/p)/3
r=8q/3-3/p
a person buys 5 cups of coffee at a kiosk in the mall. the bill is under $20.00. what is the cost of each cup?
Answer: So the cost of each cup is $4.00.
We know that the cost of 5 cups of coffee is under $20.00. To find out the cost of each cup we need to divide the total amount by the number of cups.
$20.00 / 5 = $4.00
So the cost of each cup is $4.00.
Step-by-step explanation:
hope this helps
well this could go two different ways.
all five cups could be one dollar each and it would simply just be $5.
you could also do all five cups could cost 2 dollars each that would equal 10 dollars in total
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which "8" is a solution are as follows:
x + 2 = 10 x minus 4 = 4 3 x = 24Step-by-step solution:
x + 6 = 2⇒x=2-6
⇒x= -4
x + 2 = 10⇒x=10-2
⇒x= 8
x minus 4 = 4⇒x-4=4
⇒x=4+4
⇒x=8
x minus 2 = 10x-2=10
x= 10+2
⇒x= 12
2 x = 4⇒2*x=4
⇒x=4/2
⇒x=2
3 x = 24⇒3*x=24
⇒x=24/3
⇒x=8
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Cindy jacobs borrowed 100 shares of stock from her broker, and then sold the stock for $45 a share ($4500). The commission was $65. A month later, the price of the stock was $42.50 a share, so she bought the 100 shares. The commission was $60. She returned the 100 shares to the broker
Cindy made a loss of $75 ($4,435 - $4,310) on this transaction.
Who are investors in Class C?A level load that comprises yearly fees for fund marketing, distribution, and servicing, set at a fixed percentage, is one feature of class C mutual fund shares. These charges are a commission paid to the company or person assisting the investor in selecting the fund they want to participate in.
Cindy made a profit or loss on this transaction as follows:
Cindy sold the 100 shares for $45 each, for a total of $4,500.
She paid a commission of $65 to the broker, so her net proceeds from the sale were $4,435 ($4,500 - $65).
A month later, the price of the stock was $42.50, so Cindy bought 100 shares for a total cost of $4,250 ($42.50 x 100).
She paid a commission of $60 to the broker, so her net cost of buying the shares was $4,310 ($4,250 + $60).
Therefore, Cindy made a loss of $75 ($4,435 - $4,310) on this transaction.
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If AB = 25 what is AC?
Answer:In the first paragraph, we establish that AC has to equal 50 since B is the midpoint and AB = 25. That means segment BC is also equal to 25. Thus AB + BC = 50. Since x is 6, (8x + 2) (the formula for the line AC) is 50, as expecte
Step-by-step explanation:
What is the k value to this problem
The k value of the given problem is 8. The solution is obtained using the concept of algebra.
What is algebra?A branch of mathematics known as algebra deals with symbols and the fine operations performed on them. Variables are the name given to these symbols because they warrant set values.
Algebra aids in the result of fine problems and enables the derivate of unknown figures, similar as interest rates, rates, and probabilities. In order to remake the equations, we can express the associated unknown amounts using variables from algebra.
We are given equation: y=8x.
General form of an equation is y=kx where k is the constant of variation.
Also, y varies directly with both i.e. k and x.
So, from the above explanation, we find that k=8.
Hence, the k value of the given problem is 8.
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Solve the inequality
Show clear algebraic working.
m² + 3> 21
—————
4
Therefore , the solution of the given problem of inequality comes out to be m > 4.24.
What is inequality, exactly?In mathematics, an inequality is a relationship of linear solution or integers without the equal sign. Inequity inevitably leads to imbalance. When two numbers are not equal, there is an inequality between them. Between equality and inequality, there are differences. In instances when the variables aren't similar or equal, I've used the most common symbol (). There are many inequalities that may be utilised to compare values regardless of how small or huge they are.
Here,
Given :
=> m² + 3> 21
=> m² > 21-3
=> m² > 18
=> m > √18
=> m > 4.24
Therefore , the solution of the given problem of inequality comes out to be m > 4.24.
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(Look at picture) and ty btw <3
The system of inequalities to represent this real-world scenario is
[tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]
Explain the system of inequalities?A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilised.Polynomial inequality, rational inequality, and absolute value inequality are the many forms of inequalities that can exist in mathematics.A system of inequalities can be solved by graphing each individual inequality and then determining where the multiple solutions overlap.Multiply all terms by the fractions' least common denominator to get rid of any fractions.Simplify the inequality by merging like words on either side.To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts.Given data :
Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
[tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]
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Jamal sliced an orange into four equal pieces he ate one slice what fraction of the orange did Jamal eat?
it would be 3/4 with is three over four
The number 1500 can be said correctly as "one-thousand five hundred" or as "fifteen hundred."
Write out at least four different ways to say 743.
The four words are Seven hundred forty-three, Seven-four-three, Seven four three, Seven hundred and forty-three.
What is number?Number is a mathematical object used to count, label, and measure. It is a fundamental concept in mathematics and is used in many different ways. Numbers can be used to represent anything from quantities of objects to ideas and concepts. Additionally, numbers are used to describe relationships between different objects or concepts. Numbers are also used to represent positions in space, as well as represent data in a graph or table.
1. Seven hundred and forty-three
2. Seven four three
3. Seven fourty-three
4. Seven hundred forty-three.
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Simplify this fraction 12/16 to lowest terms and find an equivalent fraction that has a denominator of 32.
A. 3/4, 12/32
B. 2/6, 24/32
C. 3/4, 24/32
D. 6/8, 28/32
Show your work on how you got your answer
Answer: C
Step-by-step explanation:
12/4=3
16/4=4
3*8=24
4*8=32
To simplify 12/16 to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 4:
12/16 = 3/4
Now we need to find an equivalent fraction with a denominator of 32. To do this, we can multiply both the numerator and denominator of 3/4 by 8:
3/4 = (38)/(48) = 24/32
So the answer is C. 3/4, 24/32.
What is the value of Y in this equation? X+Y=5 and 2X-Y=7
Step-by-step explanation:
88888 ists kakakskwkakq
Answer:y=3/2
Step-by-step explanation:
which of the following is an odd function?
f(x) = 3x2 + x
f(x) = 4x3 + 7
f(x) = 5x2 + 9
f(x) = 6x3 + 2x
Answer:
(d) f(x) = 6x³ + 2x
Step-by-step explanation:
You want to identify the odd function from a list of functions:
f(x) = 3x² + xf(x) = 4x³ + 7f(x) = 5x² + 9f(x) = 6x³ + 2xOdd functionAn odd polynomial function will have terms with only odd powers of x. Functions containing constant terms or squared terms cannot be odd functions.
f(x) = 3x² + x — has a squared termf(x) = 4x³ + 7 — has an added constantf(x) = 5x² + 9 — has a squared termf(x) = 6x³ + 2x — this is an odd function__
Additional comment
An odd function can be identified by the fact that it satisfies ...
f(-x) = -f(x)
Its graph is symmetrical about the origin.
Answer:
D
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
(x - 4)2 + y2 = 36 and (x + 6)2 + y2 = 144 are the equations represent circles that have a diameter of 12 units and a center that lies on the y-axis
What is a diameter?In geometry, the diameter of a circle is the straight line passing through the center of the circle and connecting two points on the circumference.
Also, a diameter is a straight line that passes through the center of a circle or other curved object and has its endpoints on the circumference. It is the longest line that can be drawn in a circle and is equal to twice the radius.
Consequently, the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are (x - 4)2 + y2 = 36 and (x + 6)2 + y2 = 144
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Height Consider the fountain shown. The initial velocity of the stream of the water is 48 feet per second. The velocity v of the water at any time t (in seconds) is given by v = 48 − 32t. Find the time for a drop of water to travel from the base to the maximum height of the fountain. (Hint: The maximum height is reached when v = 0.)
A drop of water will reach the maximum height after 1.5s.
How long takes a drop of water to reach the maximum height?The velocity of the water is modeled by the linear equation:
v(t) = 48 - 32t
And the water reaches the maximum height when the velocity is zero.
Then we just need to solve the equation below:
48 - 32t = 0
48 = 32t
48/32 = t
1.5 = t
So it takes 1.5 seconds for a drop of water to reach its maximum height.
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Here is a list of numbers:
−
3
,
12
,
−
18
,
2
,
−
18
,
−
9
,
−
12
,
−
16
,
−
4
,
−
5
State the median.
The median of the list of numbers is -7.
What is Median?Median is the middle element when the data set is arranged in an increasing or decreasing order.
Given numbers are :
-3, 12, -18, 2, -18, -9, -12, -16, -4, -5
Write the numbers in the ascending order.
-18, -18, -16, -12, -9, -5, -4, -3, 2, 12
There are 10 numbers in the list which is even.
So the median is the average of the middle two elements.
Middle elements are -9 and -5.
Median = (-9 + -5) / 2 = -7
Hence the median of the set is -7.
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Find the value of b x 9 when b = 4
Answer: 36
Step-by-step explanation:b=4 4x9=36
What is the perimeter of this figure?
There are 2 semi circles.
One that is on left side ( say S1)and the other one at the bottom(say S2) of the figure. Both these semi circles have diameter 30.
perimeter of S1 = (2*pi*15)/2
perimeter of S2 = (2*pi*15)/2
There is another figure which is of a semicricle(say S3). The radius is 30.
Perimeter of S3 = (2*pi*30)/4
Required perimeter
= S2+ S3-S1
= [(15*pi)/2] + [(15*pi)]- [(15*pi)/2]
= (15*pi)
= (15*3.14)
= 47.1
Please help me with this math question! Thank you!
The expression that illustrate the diagram below is f(x) = 47-2x
What are linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
In the diagram, the total no of box is 45 and 2 boxes are missing on the second box. Therefore the constant in the the expression is 45+2 = 47. Let x be the variable.
Therefore f(x) = 47-2x
when it is pattern 1
x= 1
f(1) = 47-2 = 45
when it's pattern 2
f(x) = 47-2×2 = 43
when it's pattern 3
f(x) = 47- 2×3 = 41
therefore the expression that can illustrate the diagrams is f(x) = 47-2x
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You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
You:
Friend:
Your tutor for ___ hours.
1)
You tutor for 9 hours.
2)
You tutor for 4 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
From the tap diagram,
1)
You have three parts.
A friend has one part.
This means,
4 parts = 12 hours
1 part = 3 hours
Now,
You = 3 parts = 3 x 3 = 9 hours.
2)
You have two parts.
A friend has four parts.
This means,
6 parts = 12 hours
1 part = 2 hours
Now,
You = 2 parts = 2 x 2 = 4 hours.
Thus,
You tutor for 9 hours.
You tutor for 4 hours.
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Find the 2 two-digit numbers that divide 179 with a remainder of 4.
The two digit number that will make a remainder of 4 when it divides 179 is 35
How to find the two digit numberThe number 179 is a prime number hence it's only factors are 1 and 179.
For the number to have a remainder of 4, it means that subtraction 4 from 179 will give a number that will divide it without remainder
The subtracted 4 will serve as the remainder
179 - 4 = 175
factors of 175: 1, 5, 7, 25, 35 and 175.
175 / 35 = 5
because of this we can say that (175 + 4) / 35 will give a remainder of 4.
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which expression is equal to 1/64?
Answer: There are many but these are some of them
2/128
4/256
6/384
8/512
Step-by-step explanation:
1+6x+1+ 8= 1+ 7x + 2x
Answer:
x = 3
Step-by-step explanation:
Solve for x:
6 x + 1 + 1 + 8 = 7 x + 2 x + 1
Grouping like terms, 6 x + 1 + 1 + 8 = 6 x + (1 + 1 + 8):
(6 x + (1 + 1 + 8)) = 7 x + 2 x + 1
1 + 1 + 8 = 10:
6 x + 10 = 7 x + 2 x + 1
Grouping like terms, 7 x + 2 x + 1 = (7 x + 2 x) + 1:
6 x + 10 = ((7 x + 2 x) + 1)
7 x + 2 x = 9 x:
6 x + 10 = 9 x + 1
Subtract 9 x from both sides:
(6 x - 9 x) + 10 = (9 x - 9 x) + 1
6 x - 9 x = -3 x:
-3 x + 10 = (9 x - 9 x) + 1
9 x - 9 x = 0:
-3 x + 10 = 1
Subtract 10 from both sides:
(10 - 10) - 3 x = 1 - 10
10 - 10 = 0:
-3 x = 1 - 10
1 - 10 = -9:
-3 x = -9
Divide both sides of -3 x = -9 by -3:
(-3 x)/(-3) = (-9)/(-3)
(-3)/(-3) = 1:
x = (-9)/(-3)
The gcd of -9 and -3 is -3, so (-9)/(-3) = (-3×3)/(-3×1) = (-3)/(-3)×3 = 3:
Answer: x = 3
Answer:
X = 1
Step-by-step explanation:
start by simplifying both sides
6x + 10 = 1 + 9x
Next, subtract 6x from both sides
10 = 1 + 9x
Next subtract 1 from both sides
9 = 9x
Divide by 9 from both sides
X = 1
Help me please i dont not know the answer
Answer:
i believe the answer would be both c and f