Depends upon what's the quadrilateral is
Solving according to square
Perimeter=4a
4a=88a=88/4=22So
Area:-
22²=484units²
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.
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
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]
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#3
e
100% Q
Twelve people are participating in a community walking fund raiser. Each person has to contribute equally to walking a total distance of
28.375 miles.
What will be the distance walked by each person to the nearest thousandth of a mile?
A 2.355 miles
OB 2.365 miles
OC 2.455 miles
OD 2.465 miles
Previous
Answer:
B. 2.365
Step-by-step explanation:
Divide total distance by total people in order to get distance each person traveled.
28.375 miles / 12 = 2.36458333.......
If you round taht to nearest thousandth of a mile, the answer is: 2.365
9) Find the domain of the inverse
Answer:
Domain is all real numbers
Range is (3, ∞) or y > 3
Step-by-step explanation:
Workers took a 10% pay cut to help their company stay open during economic hard
times. What is the reduced annual salary of a worker who originally earned $35,000?
Answer:
$31,500
Step-by-step explanation:
10% = 0.1
100% = 1
1 - 0.1 = 0.9
35,000 x 0.9 = 31,500
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
50 points + brainlest if you answer correctly
Answer:
5 is the value which makes the equation true .Step-by-step explanation:
In this question we have provided an equation that is 9 ( 3x - 16 ) + 15 = 6x - 24 . And we are asked to write the steps to solve the equation with explanation and to find the value of X .
Solution : -
[tex] \longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24[/tex]
Step 1 : Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :
[tex] \longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24[/tex]
Step 2 : Solving like terms on left side that are -144 and 15 :
[tex] \longmapsto \quad \:27x -129 = 6x - 24[/tex]
Step 3 : Adding 129 on both sides :
[tex] \longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}[/tex]
Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :
[tex] \longmapsto \quad \:27x = 6x + 105[/tex]
Step 4 : Subtracting with 6x on both sides :
[tex] \longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}[/tex]
On calculating further, We get :
[tex] \longmapsto \quad \:21x = 105[/tex]
Step 5 : Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :
[tex] \longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21} [/tex]
Now , by cancelling 21 with 21 on left side , We get :
[tex] \longmapsto \quad \:x = \cancel{\dfrac{105}{21}} [/tex]
Step 6 : Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :
[tex] \longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}[/tex]
Henceforth , value of x is 5Verifying : -
Now we are verifying our answer by substituting value of x in the given equation . So ,
9 ( 3x - 16 ) + 15 = 6x - 249 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 249 ( 15 - 16 ) + 15 = 30 - 249 ( -1 ) + 15 = 6-9 + 15 = 66 = 6L.H.S = R.H.SHence , Verified .Therefore, our value for x is correct that means it'll makes the equation true .
#Keep LearningUse the function rule f(x)= x• |-1|^x. Find the output f/(2).
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.
Learn more about quadratic equations;
https://brainly.com/question/17177510
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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.
Solve for x and explain your steps in detail using the R-E-S-T Method
8x - 4 = 92
Answer:
12
Step-by-step explanation:
you add 92 with the 4 and get 96 then you divide the 8x with the 96 and get 12
Hope it helps <333
x = 12
Calculations ↓Our goal is to find the value of x .
To find the value of x we need to get x by itself .
The first step is to move all numbers to the right . Luckily , there's only one number here : 4.
So we add 4 on both sides :
8x=96
Now divide by 8 on both sides :
x = 12
So the value of x is 12.[tex]\footnotesize\text{hope\:helpful~}[/tex]
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.
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.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!!
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
[tex]5x^{2}+|x+1|\ \textgreater \ 0[/tex]
Can someone explain me how this is done? My book says that the answer is R (all numbers), but i get [-1; infinity) and two other roots.
Simplify
5x²-x+ 9 =
X=3
Answer:
51
Step-by-step explanation:
you plug in 3 for x.
5(3)^2 - 3 + 9
5(9) - 3 + 9
45-3+9
51
Answer: 5x^2+6
Step-by-step explanation: sorry if wrong
Given that f(x) = 2x - 4 and g(x) = 2x + 8, determine gf(3)
[tex]\text{Given that,} ~f(x) = 2x-4~~ \text{and}~~ g(x) = 2x+8\\\\ g(f(3))\\\\=g(2\cdot 3 -4)\\\\=g(2)\\\\=2(2)+8\\\\=4+8\\\\=12[/tex]
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?
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?
5. Solve for x.
a.
96
b. 87
C.
42
d. 68
Answer:
68
Step-by-step explanation:
62+50=112
180-112=68
(06.01 MC)
Classify the expression: -2x
Quadratic expression
Linear expression
Cubic expression
Exponential expression
Answer:
Linear expression
Step-by-step explanation:
The greateest exponent on a variable is 1 on x, so it is a linear expression,
Answer: Linear expression
Graph the line Y minus 5X equals -2
Answer:
Step 1. Rewrite in the form of y=mx+b
Step 2. Find and plot 2 points (x and y-intercepts)
Step 3. Connect dots
y=mx+b
y - 5x = -2
y = 5x - 2
Find 2 points
y-intecept = (0, -2)
x-intercept = ?
0 = 5x - 2
2 = 5x
x = 2/5
x-intercept = (2/5, 0)
BRAINLIEST please if this helped!A Spanish test has 30 questions. A student answers 80% correctly.
How many questions does the student answer correctly?
Enter your answer in the box.
questions
Answer:
24
Step-by-step explanation:
Lets start by working out 80% of 30
80% x 30=24
so the student answered 24 questions correctly
PLEASE HELP WILL MARK BRAINLIEST
Answer:
d
Step-by-step explanation:
hahaha
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...!!
What is the absolute deviation of 4 in this data set?
{6, 22, 14, 9, 11,4}
A. 2
B. 3
C. 7
D. 11
Answer:
7
Step-by-step explanation:
I took the k12 quiz
Answer:
7
Step-by-step explanation:
I took the quiz on K-12 the quiz name is 6.04 Quiz: Mean Absolute Deviation (MAD)
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.
What are all the solutions to the equation sin 2x = 2sin x in the interval [0, 2π)?
{π}
{0, π}
{pi over 2}
{pi over 2, 3 times pi over 2}
[tex]sin(2x) = 2sin(x) \\ 2sin(x)cos(x) = 2sin(x) \\ sin(x)cos(x) = sin(x) \\ sin(x)cos(x) - sin(x) = 0 \\ \sin(x) (cosx - 1) = 0 \\ \sin(x) = 0 \\ x = \pi \: or \: x = 0 \\ cos(x) = 1 \\ x = 0 \: or \: x = \pi \\ \\ s[/tex]
[tex]s = > {0 < = > \pi}[/tex]