Answer:
k=4/3
Step-by-step explanation:
9(k-2)=-6
-expand the bracket
9k-18=-6
-keep "k" on one side
9k=12
-divide both sides by 9 to get k
k=4/3
8.5 Exercises
In Exercises 1-20 use the Laplace transform to solve the initial value problem. Where indicated by C/G, graph the solution.
#17.
y" + 3y' + 2y = {
e⁻ᵗ, 0 ≤ t < 1
0, t ≥ 1
y(0) = 1
y'(0) = - 1
We can express the forcing function (the piecewise expression on the right side) in terms of the step function as [tex]e^{-t}(u(t) - u(t-1))[/tex] where
[tex]u(t) = \begin{cases}1&\text{for }t\ge0\\0&\text{otherwise}\end{cases}[/tex]
Let F(s) be the Laplace transform of a function f(t). Now recall the transform pair
[tex]f(t-c) u(t-c) \mapsto e^{-cs} F(s)[/tex]
This means
[tex]e^{-t} u(t) \mapsto \dfrac1{s+1}[/tex]
[tex]e^{-t} u(t-1) = \dfrac1e \times e^{-(t-1)} u(t-1) \mapsto \dfrac{e^{-(s+1)}}{s+1}[/tex]
I assume you're familiar with the transform rule for derivatives of y(t). Now we're ready to take the transform of both sides of the ODE:
[tex]y'' + 3y' + 2y = e^{-t}(u(t) - u(t-1))[/tex]
[tex]\implies \left(s^2 Y(s) - s y(0) - y'(0)\right) + 3 \left(s Y(s) - y(0)\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]
Plug in the initial values and solve for Y(s) :
[tex]\left(s^2 Y(s) - s + 1\right) + 3 \left(s Y(s) + 1\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]
[tex](s^2 + 3s + 2) Y(s) - s + 4 = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]
[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)(s^2 + 3s + 2)}[/tex]
[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)^2 (s+2)}[/tex]
Consider the partial fraction expansion
[tex]\dfrac1{(s+1)^2(s+2)} = \dfrac a{s+1} + \dfrac b{(s+1)^2} + \dfrac c{s+2}[/tex]
Solve for the coefficients:
[tex]1 = a(s+1)(s+2) + b(s+2) + c(s+1)^2[/tex]
[tex]s = -1 \implies b = 1[/tex]
[tex]s = -2 \implies c = 1[/tex]
[tex]1 = (a+c)s^2 + \cdots \implies a+c = 0 \implies a = -1[/tex]
Hence we can expand Y(s) as
[tex]Y(s) = \dfrac1{(s+1)^2} + \dfrac1{s+2} + \dfrac{e^{-(s+1)}}{s+1} - \dfrac{e^{-(s+1)}}{(s+1)^2} - \dfrac{e \times e^{-(s+2)}}{s+2}[/tex]
The last transform pair we need is
[tex]e^{ct} f(t) \mapsto F(s - c)[/tex]
Now, taking inverse transforms of everything yields
[tex]\dfrac1{(s+1)^2} \mapsto te^{-t}[/tex]
[tex]\dfrac1{s+2} \mapsto e^{-2t}[/tex]
[tex]\dfrac{e^{-(s+1)}}{s+1} \mapsto e^{-t} u(t-1)[/tex]
[tex]\dfrac{e^{-(s+1)}}{(s+1)^2} \mapsto e^{-t} (t-1) u(t-1)[/tex]
[tex]\dfrac{e \times e^{-(s+2)}}{s+2} \mapsto e^{-(2t-1)} u(t-1)[/tex]
and putting everything together gives the same solution as the one provided.
Q. What are the solutions to this equation? (x-3)(x+2)=0
answer choices
Сх
Cx=3,2
A x=3,-2
B x=2,3
x
D x=3,2
X=
Answer:
x=3,-2
Step-by-step explanation:
take the first part ;(x+2)=0. x=-2 x_3=0 so x=3
What is the answer to3/8 + 3/4=?
Mike invests $1,778 in a retirement
account with a fixed annual interest rate of
3% compounded 2 times
per year.
What
will the account balance be after 15 years?
Answer:
A = $2,779.16
Step-by-step explanation:
A = $2,779.16
A = P + I where
P (principal) = $1,778.00
I (interest) = $1,001.16
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 1,778.00(1 + 0.03/2)^(2)(15)
A = 1,778.00(1 + 0.015)^(30)
A = $2,779.16
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $1,778.00 at a rate of 3% per year compounded 2 times per year over 15 years is $2,779.16.
Find the volume of the prism.
A triangular prism. The base triangle has a base of 7 feet and height 3 feet. The height of the prism is 5 feet.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's calculate its volume :} [/tex]
[tex] \textsf{V = Area of Triangle × Height } [/tex][tex] \sf{V = \dfrac{1}{2}\cdot 3 \cdot 7\cdot 5} [/tex][tex] \sf{V= \dfrac{105}{2}} [/tex][tex] \textsf{V = 52.5 ft³} [/tex][tex] \textbf{Volume if the prism is 52.5 ft³} [/tex]
Bo and Erica are yoga instructors. Between the two of them, they teach 48 yoga classes each week. If Erica teaches 12 fewer than twice as many as Bo, how many classes does each instructor teach per week?
Evaluate the function.
f(x) = 4x^2 + 6x - 2
=
Find f(-5)
Answer:
The answer is 68
Step-by-step explanation:
Plug -5 into each x value then solve.
The volume of a cylinder is 480pie cm3. The height of the cylinder is 30 cm. What is the radius of the
cylinder?
The radius of the cylinder is
cm. (Simplify your answer.)
Answer:
R = 4cm
Step-by-step explanation:
V = π(R)²h = 480π
Divide by π
(R)²h = 480
Substitute h with 30
30*(R)² = 480
Divide by 30
(R)² = 16
Square root
R = 4cm
We do not accept R= -4 because it's a length, so it must be positive.
Use the function rule f(x)= x• |-1|^x. Find the output f/(2).
Maya purchased a boat for $18,340. It's value depreciated by 15% in the first year she owned it. What was her boat worth at the end of this first year?
The worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Deprecated price = Initial price- amount of deprication
We have:
Initial price = $18,340
And the amount of deprication = 15% of $18,340
= [tex]\dfrac{18340}{100} \times 15 = 2751 \: \rm dollars[/tex]
(as deprication on first year was by 15% of the original price, and we want to know the deprication for the first year only)
Thus, we get:
Depricated price of Maya's boat = $18,340 - $2,751 = $15,589
Thus, the worth of the boat of Maya which goes for 15% deprication this year at the end of the first year of purchase, with the considered purchase price, is $15,589
Learn more about percent here:
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Which inequality is equivalent to |X-4| <9
a) -9>x-4<9
b) -9
c) x-4<-9 or -4<9
d) x-4>-9 or x-4<9
Answer:
D. x-4>-9 or x-4<9Step-by-step explanation:
To solve this inequality, you have to isolate the term of x from one side of the equation.
|x-4|<9-9<x-4<9
x-4>-9First, add by 4 from both sides.
x-4+4>-9+4
Solve.
-9+4=-5
x>-5x-4<9Add by 4 from both sides.
x-4+4<9+4
Solve.
Add the numbers from left to right.
9+4=13
x<13
Therefore, the correct answer is D. "x-4>-9 or x-4<9".I hope this helps. Let me know if you have any questions.
PLEASE HELP WILL MARK BRAINLIEST
Answer:
d
Step-by-step explanation:
hahaha
A circle has a diameter of 10 ft. What is its circumference? Use 3.14 for pie and do not round your answer. Be sure to include the correct unit in your answer.
Answer: 31.4
Step-by-step explanation:
Circumference = πd or 2πr
π = 3.14
Since the diameter is given we will use Circumference = πd
So
3.14 * 10 = 31.4
Answer:
C ≈ 31.4
Step-by-step explanation:
The circumference of a circle can be calculated using either of the following formulas: C=d or C=2r.
The circumference of a circle is the distance around the outside of the circle. It is like the perimeter of other shapes like squares. You can think of it as the line that defines the shape. For shapes made of straight edges this line is called the perimeter but for circles this defining line is called the circumference.
The radius (r) and the diameter (d) are two more crucial distances on a circle (d). Every circle has three distinguishing features: a radius, a diameter, and a circumference. The circumference may be calculated using the radius or diameter and pi. The diameter of a circle is the distance between one side and the other at its widest points. The circumference of a circle will always pass through its center. This distance is divided in half by the radius. The radius may alternatively be thought of as the distance between the circle's center and its edge.
You can calculate the circumference of a circle if you know its diameter or radius. To begin, keep in mind that pi is an irrational number represented by the symbol. 3.14 is a close approximation.
The formula for calculating a circle's circumference is:
The circumference of a circle is equal to its diameter multiplied by its circumference.
C = d is a common notation for this. This indicates that the circle's circumference is three "and a half" times its diameter.
SOLUTION:Given radius (R) = 5
⇒ Diameter = 2R = 10
⇒ Circumference = 2πR
= 10π
= 31.415926535898
≈ 31. 4
Using the 68-95-99.7 rule
PROBLEM: The random variable
* = the stopping distance of a randomly
selected emergency stop for a pickup
truck on dry pavement from a speed of
62 mph can be modeled by a normal
distribution with u = 155 ft and
o= 3 ft. Use the 68-95-99.7 rule
to approximate:
(a) P(x > 158)
(b) The probability that a randomly
selected emergency stop is between 149 ft
and 152 ft.
Using the Empirical Rule, it is found that the desired probabilities are given as follows.
a) P(x > 158) = 0.16.
b) P(149 < x < 152) = 0.135.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Additionally, considering the symmetry of the normal distribution, 50% of the measures are below the mean and 50% are above.
Item a:
158 is one standard deviation above the mean, hence the probability is given by, considering that 32% of the measures are more than 1 standard deviation from the mean:
P(x > 158) = 0.5 x 0.32 = 0.16.
Item b:
Between one and two standard deviations below the mean, hence:
P(149 < x < 152) = 0.5 x (0.95 - 0.68) = 0.5 x 0.27 = 0.135.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
OLZ HELP ILL MARK AS BRAINLEST
Find the slope of the line that goes through the following points
Answer:
B. 1 :)
Step-by-step explanation:
Every time the x value gets bigger, the y laue does too. Positive numbers are larger than negative ones so every time we get closer to 0, our values get bigger :)
Have an amazing day!!
Please rate and mark as brainliest!!
Please help me answer this! Thank you! No links!
Answer:
139
Step-by-step explanation:
5. Solve for x.
a.
96
b. 87
C.
42
d. 68
Answer:
68
Step-by-step explanation:
62+50=112
180-112=68
Solve the inequality.
2(4+2x)≥5x+
What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x² - 2?
O a = 5, b=4, c = 2
a = 5, b = -4, c = -2
O
a=-4, b = 5, c = -2
O a=4, b = -5, c = -2
Answer:
a = -4, b = 5, c = -2
(the third option)
The values are a = -4, b = 5 and c = -2 in the quadratic equation.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to determine the values of a, b and c in the following quadratic equation :
0 = 5x - 4x² - 2
We know that a general quadratic equation is of the following form :
ax² + bx + c = 0
where a is the coefficient of x², b is the coefficient of x and c is the constant term.
Comparing the general equation with equation (i), we have that;
coefficient of x², a = -4,
coefficient of x, b = 5
and the constant term, c = -2.
Thus, the values are; a = -4, b = 5 and c = -2.
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The U.S. flag has 7 red stripes and 6 white stripes. Check if each ratio of red stripes to total stripes is correct. select all that apply.
A. 7:6
B. 7/13
C. 13 to 7
D. 7 to 6
E. 7:13
F. 7/6
7:13
hope it helps...!!
1. Find the volume of the figure.
4 cm
2 cm
10 cm
10 cm
1 cm
3 cm
1 cm 1 cm
HELP DUE ON FRIDAY
Some sewing supplies are stored in a container that is 5 inches tall, 7 inches wide, and 12 inches long a. Label the picture of the box with its dimensions b. What is the volume of the box?
Find the perimeter of an
equilateral triangle with
height of 42cm.
Answer:
The perimeter of an equilateral traingle with height 42cm is 126cm.
Step-by-step explanation:
Given that the height or edge of an equilateral traingle is 42cm. With this information, we are asked to find the perimeter of an equilateral traingle.
The perimeter of equilateral traingle is defined as the three times of the length of edge. Mathematically;
→ Perimeter = 3a
By substituting the given values in the formula, we get the following results:
→ Perimeter = 3(42)
→ Perimeter = 126
Hence, the perimeter of an equilateral traingle with height 42cm is 126cm.
Additional information:
A triangle has three sides or edges.A triangle has three angles.A triangle has three vertices or corners.The sum of all internal angles of a triangle is always equal to 180 degrees. This is known as the angle sum property of a triangle.The sum of the length of any two sides of a triangle is greater than the length of the third side.There are three types of triangle, Scalene Triangle, Isosceles Triangle, Equilateral Triangle.Area of triangle = 1/2 * b * h.Perimeter of triangle = sum of all sides.A new LED TV currently cost 1,300 when paid in full. There is also a payment plan available where the customer must pay a monthly payment of $72 for 2 years. How much more will a customer who pays in monthly installments end up paying for the LED TV than a customer who pays the 1,300 in full?
Answer:
$428
Step-by-step explanation:
you can do 72*24= the 2 year period and then you get 1728
you then do 1728-1300 and you will get $428 more
⦁ Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities.
⦁ What was the least amount of snowfall in any of the cities?
⦁ In which quarter is the data most concentrated? Explain how you know.
⦁ In which quarter is the data most spread out? Explain how you know.
Using the box plot, it is found that:
The least amount of snowfall in any of the cities was of 5 inches.The data was most concentraded in the third quarter, betwen 35 and 40.The data was most spread out in the second quarter, betwen 13 and 35.What is a box plot?It is a plot that focuses the interquartile range of the population, that is, it gives:
The smallest value.The first quartile.The median.The third quartile.The highest value.In this problem, the box plot starts at 5, hence the least amount of snowfall in any of the cities was of 5 inches.
The data was most concentraded in the third quarter, betwen 35 and 40, as it is the smallest quarter in the graph.
The data was most spread out in the second quarter, betwen 13 and 35, as it is the greater quarter in the graph.
More can be learned about box plots at https://brainly.com/question/27353162
Answer:
a) 5
b) 35 - 40 this is the smallest part in the purple bar
c) 13 - 35, this is the biggest part of the purple bar
Step-by-step explanation:
(this is off my test!)
By looking at the plot, you can see where everything is, and since it asks how you know, there you go.
Can someone pls help me I’m stuck on this problem and this is due tomorrow!
Answer:
I'm not sure if you are allowed to use improper fractions but that would be the only way to have an answer be greater than both of its factors if one of the factors has to be a fraction.
I would do something simple like:
[tex]\frac{2}{1} * 2 = 4[/tex]
Step-by-step explanation:
Since both factors are greater than 1 the product will be greater than both the factors.
Answer:
Equation is below. See model attached.
6/4 x 3 = 18/4
Circle A passes through B and circle B passes through A. Given that AB = 3, find the area of the
shaded region common to both circles
Answer:
The answer is six I think
where can I get study guide help for algebra 2 thank you
Answer:
Stay after school more often with your math teacher or come early to school to practice math or to see what your stuggling at.
Pls help me worth 50 points + brainliest
(i only can give brainliest if 2 PEOPLE answer)
box one
box three
box four
box two is incorrect because 0.80/100 x 400 is 3.2
and we are looking for the common denominator of 320 :)
how do i know the common denominator is 320? it's is 80% of 400!
i hope this helps
Answer:
first box, second box and third box.
Step-by-step explanation:
This is because they shared the same answer which is 320.
hope it helps =)
The Jurassic Zoo charges $7 for each adult admission and $5 for each child. The total bill for the 200 people from a school trip was $1124. How many adults and how many children went to the zoo?
Answer:
There were 29 adult admissions; and 72 child's.