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Find constants a , b, and c such that the function
y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
In 1980, the number of high school dropouts in a country was 5217 thousand. By 2008, this number had decreased to 3120 thousand. Find and interpret the average rate of change
per year in the number of high school dropouts.
Answer:
74893 students per year
Step-by-step explanation:
The Average rate of change is calculated as
= Difference in number of students / Difference in years
= 3120 thousand - 5217 thousands/ 2008 - 1980
= (3120000 - 5217000)/(2008 - 1980)
= -2097000/28
= -74892.857143 per year
Therefore, the average rate of change
per year in the number of high school dropouts is approximately 74893 students per year
At a sale this week, a suit is being sold for $306 . This is a 15% discount from the original price.
What is the original price?
Answer:
260.1
Step-by-step explanation:15% of 306=45.9
306-45.9=260.1
Answer:
351.9
Step-by-step explanation:
x/306=15/100. then I cross multiplied. And when I do I get 100x/100=4590/100.
I cross out the 100/100 and I leave with x, then I divide 4590 with 100 and get 45.9. So x=45.9.
Then I added the price it was sold..=306+45.9=351.9
PLZ HELP!!!!!
how can 28/8 be a decimal?
Answer:
What is 28/8 as a decimal you ask? Converting the fraction 28/8 into a decimal is very easy.
To get 28/8 converted to decimal, you simply divide 28 by 8. Don't worry. You don't need to get the calculator out, because we did this for you.
28/8 as a decimal is:
3.5
Kevin bought a used guitar at a garage sale for $150. He fixed it up and sold it for $200. What was the percent increase?
(Need explanation to show my work)
Answer:
33.3
Step-by-step explanation:
You need to divide 200 and 150 to get you 4/3. Then you will have to _____________________________
If Megan's tuition, fees, and expenditures for books this year total $19,000, what will they be during her senior year (three years from now),
assuming costs rise 7 percent annually? Round Future value of a Single
Amount in intermediate calculations to four decimal places.
Answer:
$23,275.817
Step-by-step explanation:
To get this answer, multiply 19,000 by 1.07.
$19,000 x 1.07 = 20,330 (one year later)
$20,330 x 1.07 = $21,753.10 (two years later)
$21,753.10 x 1.07= $23,275.817 (three years later)
The answer round to cents would be $23,275.82
Can someone help me solve this?
Answer:
2313
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
Find the measure of the missing angle
Answer:
M1=108° M2=72°
Step-by-step explanation:
M1 and the original 108° angle are equal, and to calculate M2, which is on the same straight line as the original 108°, we must remember that all angles on a straight line add up to 180°. So, 180-108=72, making M2 72°
In 1998, Susie Maroney set a record for the longest ocean swim without flippers. She swam 122 miles from Mexico to Cuba. Use a conversion factor to find the distance in feet. 1mile=5280 feet
Answer:
it's 644160 u need to times it if she swam 122 miles and each mile is 5280 and u answer is 644160
A cougar jumped a distance of 13 yards. How many inches did this cougar jump?
Answer:
468 in
Step-by-step explanation:
Step 1: Define conversions
3 feet = 1 yard
1 foot = 12 inches
Step 2: Use dimensional analysis
[tex]13 \hspace{3} yards(\frac{3 \hspace{3} feet}{1 \hspace{3} yard} )(\frac{12 \hspace{3} inches}{1 \hspace{3} feet} )[/tex] = 468 inches
is 3/4 less than,greater than,or equal to -1/2 ?
Answer: Greater than
3/4 greater than -1/2
3/4 > -1/2
Any positive number is always larger than any negative number
On a number line, stuff on the right side is always larger than stuff on the left side.
Answer:
it"s greater then
1.) 4x+2y-z=21
2.) -x-2y+2z=13
3.) 3x-2y+5z=70
Answer:
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): Dot was discarded near "2.-".
(2): "133.3" was replaced by "(1333/10)".
Too Many Equal Signs
Step-by-step explanation:
A bookshelf at a bookstore is 3 feet 9 inches wide. There are 18 copies of the same book on the shelf, which fit the shelf exactly. What is the width of 1 of the books?
Answer:
5 / 2 inches OR 2.5 in
Step-by-step explanation:
3 ft 9 in = 45 inches
45in/18 books
5 in / 2 book
What is the slope of a line that is perpendicular to the line y =-1/5
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 0 0 . All lines that are parallel to y=−15 y = - 1 5 have the same slope of 0 .
how to find the area figure of square inches
I NEED THIS ANSWER QUICK PLEASE!!!!!!!!!!
During the first hour of a snowstorm, 1 2/8 inches of snow fell. In the next hour, 4 3/8 inches fell. In the third hour, the snow stopped and 1 inch of snow melted. How much snow was on the ground at the end of the third hour?
Answer:
1 + 4 = 5
4/8 +3/8 = 7/8
5 7/8 - 7/8 = 5 inches left on the ground after 3 hours
Step-by-step explanation:
The length of a rectangle is (3x − 5) inches, and its width is 2x inches. Find the area of the rectangle.
Hint: Area of a rectangle = length × width.
Answer:
A = 6x² - 10x
General Formulas and Concepts:
Area of a Rectangle: Length × Width
To expand, use FOIL - First, Outside, Inside, Last
Step-by-step explanation:
Step 1: Define variables
l = 3x - 5
w = 2x
Step 2: Find area
Substitute: A = (3x - 5)(2x)Expand (FOIL): A = 6x² - 10xAnswer: A=6x^2-10x ✅
Step-by-step explanation:
Hii, do you need to find the area of the rectangle? Let me help you out! (:
Luckily, there's a formula to find this! (:
AreaTo find the area of a rectangle, multiply its length times its width. This is shown below.
[tex]\LARGE\boldsymbol{A=L W}[/tex]
Here, "A" denotes the area
"L" denotes the length
"W" denotes the width
NB : "L" and "W" are interchangeable
Next, it's just a matter of sticking in the known values...
[tex]\twoheadrightarrow\sf A=2x(3x-5)[/tex]
===> it's perfectly legal to stick in the values the other way around, because they are interchangeable
Alright, the next step is to multiply the values...
[tex]\twoheadrightarrow\sf A=(2x\cdot3x)-(2x\cdot(-5)[/tex]
Then we need to simplify...
[tex]\twoheadrightarrow\sf A=6x^2-10x[/tex]
Voila! There's the area of this rectangle! (:
Cheers! (:_______________Hope I helped! Best wishes.
⚜ Reach far. Aim high. Dream big. ⚜
_______________if angle 4 equals 50 degrees find the measure of angle 5 will mark brainiest
Answer:
∠5 = 50°Step-by-step explanation:
its alternate internal angles:
∠4 ≅ ∠5 (angle 4 is congruent or equal to alternate internal angle)
therefore,
∠5 = 50°
The measure of angle 5 should be considered as the 50 degrees when angle 4 should be equivalent to 50 degrees.
What is alternate internal angles?Alternate interior angles should be created via intersecting the 2 parallel lines in a transversal way. It should be located that lies between the two parallel lines.
Since the given diagram shows the alternate internal angles
Since angle 4 is 50
So angle 4 should be congruent or equivalent to alternate internal angle)
So angle 5 should be 50 degrees.
learn more about an angle here: https://brainly.com/question/21103473
HELPPPPPPPPPPPPPPPPPPP
Answer:
15
Step-by-step explanation:
Mike has at least 250 in his savings account.Which inequality represents this situation
The lines y = 3x + 4 and y = 3x - 17 are perpendicular
Answer: No
Step-by-step explanation: Here's something that I learned. Same slope different y-intercept (no solution). Same slope and same y-intercept (Infinitely many solutions). Different slope and same y-intercept (one solution). Different slope and different y-intercept (one solution).
Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50 monthly maintenance fee. Jill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. What is the mean number of checks Jill wrote per month during the last four months? Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. Estimate the total monthly fees Jill will pay each month for the new checking account.
Step-by-step explanation:
Kindly find attached a summary of the checks she has written from May to August.
A. What is the mean number of checks Jill wrote per month during the last four months
mean= (14+19+23+24)/4
mean= 80/4
mean= 20 checks
B. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account.
the expression for the total is given as
y=12.50+0.2x
y=12.50+0.2(20)
y=12.50+4
y=16.5
=$16.5
C. Estimate the total monthly fees Jill will pay each month for the new checking account.
May= 12.50+0.2(14)
May=12.5+2.8= 15.3
June= 12.50+0.2(19)
June=12.5+3.8= 16.3
July= 12.50+0.2(23)
July=12.5+4.6= 17.1
August= 12.50+0.2(24)
August=12.5+4.8= 17.3
total will be = 15.3+16.3+17.1+17.3= $66
A:20
B:$4.00
C:$16.50
A: 14+19+23+24/4 = 20
B: 20/.2 = 4
C: 12.50+4= 16.50
Why do we use coordinate planes to do
transformations and dilations?
Answer: a coordinate plane is used in order to track the location of the object.
Translations are congruence transformations that move an object, without changing its size or shape
Dilations are transformations that generate an enlargement
Step-by-step explanation:
A recipe calls for 18 ounces of cream cheese with 15 ounces of sugar." How many ounces of cream cheese are there per ounce of sugar?
PLEASE HELP
Answer:
1.2
Step-by-step explanation:
Just divide
Answer:
1.2
Step-by-step explanation:
Divide 18 by 15 and get the answer.
What polyhedron can be assembled from this net? Explain how you know.
Find the surface area of this polyhedron. Show your reasoning.
Answer:
It would be a triangular prism.
Step-by-step explanation:
We know this because of the two triangles at the top and bottom of this net and the rectangle connecting them. Then, if you imagine folding the second rectangle up, it would be one of the triangle's sides. Lastly for the third rectangle, it would be folded over the two triangles to finish the shape.
I hope this helps!!
Answer:
It would be a triangular prism
Step-by-step explanation:
If they ask how you got that say since the triangles at the top and bottom are both parell and to be a prim you need to have parell sides
The sum 51 + (-37) is equal to what? -14 88 88 14
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
the answer is 14 and it's postive
pls help <3 thank you sm ;)
Which two numbers both round to 1,500 when rounded to the nearest hundred?
Answer:
C
Step-by-step explanation:
Just take it lol
The two numbers where both round to 1,500 when rounded to the nearest hundred is option c. 1457 and 1547.
What is Rounded number?
The rounded number should be that where the number should be rounded to the nearest tenth, hundred or thousand
Since the number is 1500
So for hundred the number should be likely 1457 and 1547.
hence, the option c is correct.
learn more about number here: https://brainly.com/question/21474983
Which of the expressions below will have a 8 in the thousandths place of the quotient? Select all that apply.
A) 765.812 ÷ 100
B) 98.14 ÷ 1,000
C) 18.723 ÷ 100
D) 22.38 ÷ 10
Answer:
A
Step-by-step explanation: