Using the Laplace transform, the value of y' + y = (t − 1), y(0) = 5 is y(t) = 5e ^ -t + u (t - 1)e^(1-t)
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' + y = (t − 1)
y (0) = 5
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (5+ e^-s)/s + 1
⇒y(t) = L^-1{5/s+1} + {e ^-s/s + 1}
⇒y(t) = 5 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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Evaluate the following fractions giving your awnser in its simplist form. 50 POINTS!
a) 2/5 divided by 6
b) 3 and 1/3 times 5 and 2/5
c) 1/4 + 1/3 -1/2
a. 1/ 15
b. 76/ 15
c. 1/12
How to determine the valuea. 2/5 divided by 6
= 2/ 5 ÷ 6
= 2/ 5 ÷ 6/ 1
Take the inverse of the dividing fraction, we have
= 2/ 5 × 1/ 6
Multiply through
= 2/30
= 1/ 15
b. 3 and 1/3 times 5 and 2/5
= 3 + 1/ 3 × 5 + 2/ 5
From the knowledge of BODMAS, we multiply first
= 3 + 5/3 + 2/ 5
Find the LCM
= 45 + 25 + 6/ 15
= 76/15
c. 1/4 + 1/3 -1/2
Let's find the LCM
= 3 + 4 - 6 / 12
Add first
= 7 - 6/ 12
= 1/ 12
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Pythagorean Theorem
In a right triangle, the square of the _____ equals the sun of the squares of the ______.
Answer: In a right triangle, the square of the Hypotenuse equals the sun of the squares of the other two sides.
Step-by-step explanation: a^2+b^2=c^2
Answer: the Pythagoras theorem states that in a right angled triangle, the square of THE HYPOTENUSE is equal to the sum of the squares of the OTHER TWO SIDES.
Step-by-step explanation: :)
Find the total surface area of the cone in the figure. (Use π = 3.14.)
radius - 5cm, height - 12cm
PLS HELP LOTs OF POINTS!!!!What is the difference of….
[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference.
What is an expression?
⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
Calculation :
⇒ [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]
⇒ [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]
⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]
⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]
⇒1/(x-2) [ (-2x²+25x)/(x-5)]
⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]
at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.
⇒ [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference
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(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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If the graph of f(x)=x2, how will the graph be affected if it is changed to f(x)=3x2?
There will be a vertical stretch with a factor of 3.
Please answer quickly! It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
Answer:
[tex]\textsf{19.} \quad S_{20}=1490[/tex]
33. None of these are correct.
Step-by-step explanation:
Question 19General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven values:
[tex]a_n[/tex] = 27n = 20d = -5Substitute the given values into the formula and solve for a:
[tex]\implies 27=a+(20-1)(-5)[/tex]
[tex]\implies 27=a+(19)(-5)[/tex]
[tex]\implies 27=a-95[/tex]
[tex]\implies a=27+95[/tex]
[tex]\implies a=122[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]
where:
a is the first term.d is the common difference.Given values:
a = 122n = 20d = -5Substitute the given values into the formula and solve:
[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]
[tex]\implies S_{20}=10[244-95][/tex]
[tex]\implies S_{20}=10[149][/tex]
[tex]\implies S_{20}=1490[/tex]
Question 33Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
where:
a is the first termr is the common ratioGiven values:
a₁ = 1458r = ¹/₃Substitute the given values into the formula and solve:
[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]
[tex]\implies S_6=2184[/tex]
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You randomly choose a block from each
set in the diagram. What is the probability
that you will choose a block labeled with a
Tor a block labeled with a 6?
Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:
There are 8 outcomes with a T and a block from the second square.Removing the 2 outcomes below with a 6 and a T, as they are already counted, there are 7 outcomes with a six.Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:
p = 15/64 = 0.2344.
0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
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b)Find z
: (√z+√22)(√z-√22) = 35
Answer: [tex]\Large\boxed{z=57}[/tex]
Concept:
Here, we need to know how to expand expressions like (a - b)(a + b).
For expressions like (a - b)(a + b), the expanded form must be:
a² - b²
For checking whether it is true:
(a - b)(a + b)
= a² - ab + ba - b²
= a² - b²
Solve:
Given equation
[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]
Expand the parenthesis by the concept
[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]
Simplify the exponents
[tex]z-22=35[/tex]
Add 22 on both sides
[tex]z-22+22=35+22[/tex]
[tex]\Large\boxed{z=57}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The volume of a cone is 1,782 cubic centimeters. a cylinder has the same radius and height as the cone. what is the volume of the cylinder?
The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³
What are the 3-D figure?Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.
What is the Volume of a Cylinder?Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.
According to the given figure:
Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,
therefore,
Volume of the cylinder = 3 x (1,782)
Volume of the cylinder = 5,346 cubic centimeters
Hence, the volume of the cylinder is 5,346 cubic centimeter.
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Lines b and c are parallel.
Which is the measure of 6
Answer:
m∠6 = 54°
Step-by-step explanation:
Given the diagram, we know that line b is a straight line and angles 1 (the angle measuring 13x + 9°) and 2 are supplementary angles and thus add up to 180.
We also know angles 2 and 7 (the angles measuring 5x + 9°) are alternate exterior angles and are therefore congruent.
So since angle 2 = 5x + 9, we can do:
13x + 9 + 5x + 9 = 180
18x + 18 = 180
18x = 162
x = 9
Angles 7 and 6 are also congruent plugging x into angle 7 also gives us the measure of angle 6:
5(9) + 9 = 45 + 9 = 54°
From the figure below, identify all pairs of alternate interior and alternate exterior angles
A.
alternate exterior
exterior means outside
like a front entrance to a home
1. o & t
2. n & u
B.
alternate interior
interior means inside
like as if its inside a house
1. p & s
2. q & r
( p & s ) AND ( q & r ) both look like the letter Z
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16. The average age of a group of 8 people is 22. After the oldest person leaves the room the average age decreases to 20. How old was the person who left the room? (A) 15 (B) 16 (C) 24 (D) 36
The age of the oldest person that leaves the room is 36 years
How to calculate the average of a data?The average of a data is defined as the ratio of the sum of the data to the sample size. Mathematically;
Average = sum/sample size
If the average age of a group of 8 people is 22. then;
22 = Xn/8
Xn = 22 * 8
Xn = 176
If after the oldest person leaves the room the average age decreases to 20, hence;
20 = H/7
H = 140
Xn = H + x
176 = 140 + x
x = 176 - 140
x = 36
Hence the age of the oldest person that leaves the room is 36 years
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Verify whether the given differential equation is exact or not. if exact, solve. cosx y/x dx dy
The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
For given question,
we have been given a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]
We have to determine given differential equation is exact or not.
Compare it with M dx + N dy = 0
⇒ M = cos(x) and N = y/x
Find the derivative of M with respect to y.
[tex]\Rightarrow M_y=-sin(x)[/tex]
Now, find the derivative of N with respect to x.
[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]
Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.
Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
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Choose the equation that satisfies the data in the table.
-1 0 1
0
3
6
X
Y
OA. y = 3x +3
B.y = -x +9
Oc.y=x+9
OD. y=-3x +3
Answer: A: y= 3x + 3
Step-by-step explanation:
The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.
3. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: Less than 33.2
Answer:
93.32 %
Step-by-step explanation:
33.2 is 1.2 away from 32 this is 1.2 / .8 = 1.5 standard deviations ABOVE the mean z -score = + 1.5
from z-score table this corresponds to .9332 this is 93.32 %
The probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.
What is P- value?The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
Let the random variable X represent the miles-per-gallon rating of passenger cars. Compute the probability that a randomly selected passenger car gets more than 33.2 mpg as follows:
The probability will be calculated as below;-
[tex]P(x > 33.2) = p(\dfrac{x-\mu}{\sigma} > \dfrac{33.2 - 32}{0.8})[/tex]
P( x > 33.2) = 1 - P ( z < 1 )
P( x > 33.2) = 1 - 0.86
P( x > 33.2) = 0.14
Thus, the probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.
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Use the elimination method to slice the system of equations Choose the correct ordered pair 6x+2y=8 12x+y=22
Answer:
x=2 and y=-2
Step-by-step explanation:
Solution Given:
6x+2y=8....................................................[1]
12x+y=22....................................................[2]
Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get
equation 1 becomes 12x+4y=16
and subtracting by equation 2 we get
12x+4y=16
-12x-y=-22[Note: while subtracting we must change sigh)
__________________
0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]
3y=-6
dividing both side by 3, we get
3y/3=-6/3
we get y=-2
Again similarly
Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get
equation 2 becomes 24x+2y=44
and subtracting by equation 1 we get
24x+2y=44
-6x-2y=-8
_____________________
18x-0y=36
18x=36
dividing both side by 18, we get
18x/18=36/18
x=2
Troy travels 100 miles in 2 hours. Find the unit rate of speed by filling in the missing number.
100 miles/ 2hours = ? miles/ 1 hour = ? miles/hour
Answer:
50 miles/1 hour = 50 miles/hour
Step-by-step explanation:
The fraction is reduced by dividing numerator and denominator by their common factor of 2.
100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour
Simplify 7 + (−3)
A: -10
B: -4
C: 4
D: 10
Answer: 4
Step-by-step explanation:
[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]
PLEASE HELP IM STUCK
Answer:
y = -3x + 1
Step-by-step explanation:
First, we can find the slope of the line.
The slope is (change in y)/(change in x).
We can use the points that are marked in orange: (0,1) and (1,-2)
The change in y is 1 to -2, which is -3.
The change in x is 0 to 2, which is 1.
The slope will be -3/1, which is also: -3.
We have y = -3x + b currently.
The b is the y-intercept, meaning (the point that touches the y axis, the vertical line).
The point (0,1) touches the y-intercept, so b will be 1.
We can finish our equation as: y = -3x + 1
Two marbles are to be pulled from a bag that contains 2 yellow marbles, 4 green marbles, and 6 orange marbles. After the first marble is drawn, it is not replaced. What is the probability that two red marbles are chosen from the vase?
Using it's concept, the probability that two red marbles are chosen from the vase is of 0%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that there are no red marbles, hence the number of desired outcomes is of 0, and there is a 0% probability that two red marbles are chosen from the vase.
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Annel sells a phone which costs $180 and earns $9 commission. If he sells $640
worth of phones the following day, how much will he earn on commission?
Answer:
he will earn 32$ worth of commision
Step-by-step explanation:
so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$ which is 32$
Fiona wrote the linear equation y = 2/5x -5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s?
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
This question is incomplete, the missing answer choices are;
A. x- 5/4y =25/4
B. x-5/2y=25/4
C. x-5/4y =25/4
D. x- 5/2y=25/2
Which equation could be Henry’s?Given the linear equation written by Fiona; y = 2/5x - 5.
From the answer choices provided, they are in the form of x - (m)y = b.
We will transform Fiona's equation into that form.
y = 2/5x - 5
Divide each term by the coefficient of x.
y(5/2) = (5/2)2/5x - (5/2)5
5/2y = x - 25/2
25/2 = x - 5/2y
x - 5/2y = 25/2
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
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help me please 20 points
Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:
3.4 pounds 3.4 pounds 3.6 pounds3.8 poundsThe range of the sample means is 0.4 pounds.
The true statements on the mean weights to be used by the scientists are:
A single sample mean will tend to be a worse estimate than the mean of the sample means. The closer the range of the sample mean is to 0, the more confident they can be in their estimate. What does the means show?First, find the sample means of each sample.
Sample 1:
= (3 + 2 + 6 + 4 + 2) / 5
= 3.4 pounds
Sample 2:
= (2 + 2 + 3 + 7 + 3) / 5
= 3.4 pounds
Sample 3:
= (6 + 4 + 2 + 2 + 4) / 5
= 3.6 pounds
Sample 4:
= (5 + 3 + 2 + 5 + 4) / 5
= 3.8 pounds
The range is;
= 3.8 - 3.4
= 0.4
The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.
Using all the sample means as an average captures the data better than if a single sample mean is used.
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Select the correct answer. the diameter of a sphere measures 10.4 inches. what is the surface area of the sphere? a. b. c. d.
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
Answer:
Step-by-step explanation:
The surface area of the sphere is 108.16π in². So, option b is correct.
What is the surface area of a sphere?
The surface area of the sphere is calculated by the formula,
A = 4πr²
In terms of diameter - d;
A = 4π × (d/2)²
= 4π × d²/4
= πd² sq. inches
Calculation:
The given sphere has a diameter d = 10.4 inches
So, the surface area of the sphere is calculated by
A = πd²
= π × (10.4)²
= 108.16 π sq. inches
So, option b is correct.
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Disclaimer: The given question on the portal is incomplete. Here is the complete question.
Question: Select the correct answer. the diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
a. 432.64π in²
b. 108.16π in²
c. 54.08π in²
d. 216.32π in²
The function f(x) = x2 is graphed above. which of the graphs below represents the function g(x) = (x 1)2?
The graph (C) Y represents the function g(x) = (x 1`)2.
What is a graph of a function?The graph of a function f is the set of ordered pairings where display style f(x) = y in mathematics. When x and f(x) are both real values, these pairings represent Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane.To find which of the graphs below represents the function g(x) = (x 1)2:
Parabola: It's a conic section formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements.
The equation of parabola: [tex]y =x^{2}[/tex]The graph of [tex]y=x^{2}[/tex] is given.To draw the graph of [tex]y=(x+1)^{2}[/tex], shift the graph of [tex]y=x^{2}[/tex] one unit left.The graph of [tex]y=(x+1)^{2}[/tex] is attached below.Therefore, the graph (C) Y represents the function g(x) = (x 1)2.
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Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
**The equation y = 15x + 100 can be used to model the amount of money, y, that has
been saved by Jared for his bike based on the number of months that have passed. What
does the coordinate (0, 100) mean in the context of the problem?
If the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
Given an equation y=15x+100 that shows the amount of money saved by Jared for his bike based on the number of months that have passed.
We are required to find what the coordinate (0,100) mean in the context of the equation.
Equation is like relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation, cubic equation or many more dependng on the power of variable present in that equation.
When we put x=0 in the equation we get the following:
y=15*0+100
y=100
It means that he had $100 in the beginning when he just started doing his savings.
Hence if the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
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If a diameter intersects a chord of a circle at a perpendicular, what conclusion can be made?
If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.
What is the relation between the chord and diameter of a circle?The segments of a circle whose endpoints are on its perimeter are called chords.A circle's diameter is the chord that passes across its center.The circle's longest chord equals its diameter.Any line that is perpendicular to a chord on the circle cuts it in half and goes through the center.The solution to the problem:
A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.
Therefore, the chord is bisected.
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What is the classification of AABC with vertices A(0, 0), B(4, 3), and C(4, -3) by
its sides?
(A) equilateral
(B) isosceles
(C) scalene
(D) right
Check the picture below.
well, let's take a peek at the distances of each side.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{[ 4- 0]^2 + [ 3- 0]^2} \\\\\\ ~\hfill AB=\sqrt{25}\implies \boxed{AB=5} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-3}) ~\hfill BC=\sqrt{[ 4- 4]^2 + [ -3- 3]^2} \\\\\\ ~\hfill BC=\sqrt{36}\implies \boxed{BC=6}[/tex]
[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0}) ~\hfill CA=\sqrt{[ 0- 4]^2 + [ 0- (-3)]^2} \\\\\\ ~\hfill CA=\sqrt{25}\implies \boxed{CA=5} \\\\\\ \textit{so it's an \underline{isosceles triangle}}[/tex]