A line has the equation y = 3x + 16 what are the coordinates of the y intercept of the line?
Answers
Answer:
(0, 16)
Step-by-step explanation:
y = 3x + 16Plug x = 0-> y = 3*0 + 16-> y = 0 + 16-> y = 16-> y- intercept = (0, 16)Answer:
(0, 16)
Step-by-step explanation:
The intercepts of a graph are points at which the graph crosses the axis. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph cross the y-axis.
In a slope-intercept equation, the format goes like this:
y = mx + b / c
M = slope
B/c = y-intercept
So in the equation y = 3x + 16, 3 is the slope and 16 is the y-intercept.
Hence, the coordinates of the the y-intercept of the line are (0, 16).
Related Questions
Is {(-3,0,4),(0,-1,2),(1,1,3)} a linearly independent set for R?
Answers
No, the set {(-3,0,4),(0,-1,2),(1,1,3)} is not linearly independent for R.
To determine if the set is linearly independent, we need to check if there exist scalars c1, c2, and c3, not all zero, such that c1(-3,0,4) + c2(0,-1,2) + c3(1,1,3) = (0,0,0).
Let's write out the equation and solve for the coefficients:
c1(-3,0,4) + c2(0,-1,2) + c3(1,1,3) = (0,0,0)
Simplifying each component, we get:
(-3c1 + c3, -c2 + c3, 4c1 + 2c2 + 3c3) = (0,0,0)
From the first and second components, we have -3c1 + c3 = 0 and -c2 + c3 = 0.
Adding these two equations gives -3c1 - c2 + 2c3 = 0.
From the third component, we have 4c1 + 2c2 + 3c3 = 0.
We now have a system of three equations with three unknowns:
-3c1 - c2 + 2c3 = 0
4c1 + 2c2 + 3c3 = 0
-3c1 + c3 = 0
By solving this system of equations, we find that there are non-zero solutions for c1, c2, and c3, satisfying the equation c1(-3,0,4) + c2(0,-1,2) + c3(1,1,3) = (0,0,0). Therefore, the set {(-3,0,4),(0,-1,2),(1,1,3)} is linearly dependent for R.
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1. Ben joins a book club. He pays $12 for each book and $5 for shipping and handling
charges for each order.
a.Name the quantities that change in this problem situation and the quantities that
remain constant. Determine which quantity is independent and which quantity
is dependent.
B. Create a table of values to represent the total cost if Ben orders 1 or 2 books or
spends $41, $65, or $125.
Answers
Answer:
A. The quantities that change in this problem situation are the number of books Ben orders and the total cost. The quantities that remain constant are the cost per book ($12) and the shipping and handling charge per order ($5).
The independent variable is the number of books Ben orders, as this is the variable that Ben has control over and chooses to change. The dependent variable is the total cost, as it depends on the number of books Ben orders.
B.
(imagine this as a chart)
Number of books Total cost
1 $17
2 $29
3 $41
5 $65
10 $125
----------------------------------------------------------------------------------------------------------
To create this table, we used the formula:
Total cost = (Cost per book x Number of books) + Shipping and handling charge
For example, when Ben orders 3 books, the total cost is:
Total cost = ($12 x 3) + $5 = $41
Similarly, when Ben spends $65, the number of books he can order is:
Number of books = (Total cost - Shipping and handling charge) / Cost per book
Number of books = ($65 - $5) / $12 = 5
And so on for the other values in the table.
Answer:
See below
Step-by-step explanation:
Let x be he cost per book and y be the total cost including shipping and handling.
The relevant equation is
y = 12x + 5
A. Variables are number of books ordered(x) and total cost(y)
The constant is the shipping and handling cost
Since the total cost depends on the number of books ordered, the independent variable x = number of books
The total cost y is the dependent variable
--------------------------------------------------------------------------------------
B. Cost of 1 or 2 books can be found by plugging in x = 1 and x =2 into the equations and solving for y
Total Cost of 1 book = 12(1) + 5 = $17
Total cost of 2 books = 12(2) + 5 = 24 + 5 = $29
To compute the number of books that can be ordered for different total cost amounts is obtained by substituting for y and solving for x
For $41:
41 = 12x + 5
41 - 5 = 12x
36 = 12z
x = 36/12 = 3 books
For $65:
65 = 12x + 5
65 - 5 = 12x
60 = 12x
x = 60/12 = 5 books
For $125:
125 = 12x + 5
125 - 5 = 12x
120 = 12x
x = 120/12 = 10 books
Here is the table
Number Total Cost(y)
of books (x)
1 $17
2 $29
3 $41
5 $65
10 $125
4 x + 2 + x = blank x – 19
Answers
The result of the equation 4 x + 2 + x = x – 19 is - 5.25.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.
Given equation -
4 x + 2 + x = x – 19
Simplify the equation
5x + 2 = x - 19
5x - x = -19 - 2
4x = -21
x = -21 / 4
x = -5.25
Hence, -5.25 is the answer to the equation 4 x + 2 + x = x - 19.
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let f(x, y, z) = xy3z2 and let c be the curve r(t) = et cos(t2 1), ln(t2 1), 1 t2 1 with 0 ≤ t ≤ 1. compute the line integral of ∇f along c.
Answers
The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\) .
What is the line integral of a gradient vector field along a curve ?The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of ∇f along the curve C, is
\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)
if the curve C is defined on the interval [0,1].
in our question: \(f = xy^3z^2,\)
\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)
So the line integral along the curve C is
\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)
\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)
\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)
So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)
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As asked, the question is incomplete:
The complete question is:
let \(f = xy^3z^2,\) and
\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)
In this case compute the line integral of ∇f along c.
The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\) .
What is the line integral of a gradient vector field along a curve ?The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of ∇f along the curve C, is
\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)
if the curve C is defined on the interval [0,1].
in our question: \(f = xy^3z^2,\)
\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)
So the line integral along the curve C is
\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)
\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)
\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)
So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)
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As asked, the question is incomplete:
The complete question is:
let \(f = xy^3z^2,\) and
\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)
In this case compute the line integral of ∇f along c.
Amy picks 3 of 7 colors of the rainbow, but she doesn't pick red with green, she doesn't use blue at all. How many different combinations of 3 colors can Amy pick?
Answers
Answer:
red orange yellow, green purple orange,yellow green purple, red orange purple, green orange yellow, 4
Step-by-step explanation:
15. Which expression shows the sum of 72 and 96 as the product of the GCF
and a sum of two numbers with no common factor?
A 12(6 + 8)
B 24(3 + 4)
© 24(6 + 8)
D 48(3 + 4)
Answers
Here, we are required to determine which expression shows the sum of 72 and 96 as the product of the GCF and a sum of two numbers with no common factor?
The answer is Choice B: 24(3 + 4)
Factors of 72 are;
2 × 2 × 2 × 3 × 3
Factors of 96 are;
2 × 2 × 2 × 2 × 2 × 3
The factors in bold above are common to 72 and 96 and therefore gives a total of 24 which is the GCF of 72 and 96.
The remaining factor of 72 and 96 are 3 and 4 respectively.
And, since 3 and 4 have no common factor,
Therefore, the expression which shows the sum of 72 and 96 as the product of the GCF
and a sum of two numbers with no common factor is:
24(3 + 4)
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Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°,
150°, 175°.
Answers
Step-by-step explanation:
180(n-2)/n=90 ( this is the solution for the 90)
cross multiplying
180n-360=90n
180n-90n=360
90n=360
90n/90=360/90
n=4, the number of sides for the polygon with 90° is 4 sides
Solution for 100°
180(n-2)/n=100
180n-360=100n
180n-100n=360
80n=360
80n/80=360/80
n=4.5
Same applies to the rest 110°,125° ,150°,175°
A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Answers
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with a standard deviation of 0.5.a. What is the mean (±0.1)of the average number of moths x in 30 traps?b. What is the standard deviation? (±0.001)c. Use the central limit theorem to find the probability (±0.01) that the average number of moths in 30 traps is greater than 0.4.
Answers
The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.
The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:
mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018
So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.
The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:
standard deviation = standard error of the mean * sqrt(sample size)
standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5
So the standard deviation of the average number of moths in 30 traps is approximately 0.5.
Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.
To do this, we can standardize the sample mean using the formula:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257
Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.
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The Moon is 4,530,000,000 years in scientific notation
Answers
Answer:
4.53 * 10⁹
Step-by-step explanation:
4530000000 = 4.53 * 10⁹
Find the value of x.
Answers
x = 64
Desmond spends $800 per month on fixed expenses. Desmond earns $10,00 per hour,
How many hours does Desmond need to work each month to spend 50% of his/her income
on fixed expenses?
Answers
Answer: 160 hours
============================================================
Explanation:
He earns $10.00 an hour. Let x be the number of hours worked in a month. So 10x represents how much he earns after working x hours.
If he spends $800 per month on fixed expenses, and wants this to be 50% of his total earnings, then this must mean that the other 50% is for other things (eg: spending on a vacation or putting it to savings). So his goal is to earn 800+800 = 1600 dollars per month.
Set 10x equal to this and solve for x
10x = 1600
x = 1600/10
x = 160
He needs to work 160 hours a month.
-------------------------------
Extra info:
Divide 160 over 4 (the approximate number of weeks in a month) and we see that he'll need to work 160/4 = 40 hours a week
If he only works Monday through Friday, that's 5 days of the week. So he'll put in 40/5 = 8 hours per day.
So his goal of working 160 hours per month is reasonable. Keep in mind that this doesn't include factors like him missing time from work due to being sick (unless he has paid sick leave).
Solve for x:
3х + 2 = 11
Answers
Answer:
Move all terms that don't contain x to the right side and solve.
x = 3
Step-by-step explanation:
Answer:
x = 3
Step-by-step explanation:
3x + 2 = 11
Subtract by 2 on both sides
3x = 9
Divide by 3 on both sides
x=3
what is the unit rate of the number of miles driven per number of hours of driving
Answers
Answer:
35 miles per hour
Step-by-step explanation:
Answer:
35 miles
Step-by-step explanation:
c took the test on edg
Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
Answers
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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hello My name es Liliana y arigato bye
Answers
Answer:
?????.... hii erica herrrr
Answer:
Hi Liliana i love your name! it's very pretty:) my name is Melody
Step-by-step explanation:
Write 51/7 in radical form
Answers
QUICK QUESTION: did I do this right?
Answers
Answer:
Yup looks correct
Step-by-step explanation:
Lol I verified using the calculator :)
Ella is going to invest $18,000 and leave it in an account for 8 years. Assuming til
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Ella to end up with $22,000?
Answers
Answer:
90
Step-by-step explanation:
Answer:2.51
Step-by-step explanation:
PLEASE ANSWER FAST
Taking 0 on the number line.If the day before yesterday is 17 January, what is the date 3 days after tomorrow
Answers
Answer:
And 6th day after day before yesterday, that is, 17 January. So, we just need to add 6 to 17 to get the desired date. Thus, the date 3 days after tomorrow is 23rd January.
Step-by-step explanation:
hope it hlp
Answer:
ajahdhsbabsjssjjasjjsjs
A coordinate plane. Quadrant 1 is the top right quadrant, quadrant 2 is the top left, quadrant 3 is the bottom left, and quadrant 4 is the bottom right.
A point with a positive x-coordinate and a negative y-coordinate will lie in which quadrant?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answers
Answer:
D. im answering for the purpose of the first person getting brainliest
Step-by-step explanation:
What is the least 2-digit number?.
Answers
10 is the least 2-digit number having 0 on one's place and 1 on ten's place.
There are just two place values in 2-digit numbers: the units place and the tens place. Every number with more than one digit has various digits, each of which is described by its place value. 2-digit numbers range in value from 10 to 99. In other words, the smallest and largest 2-digit numbers are 10 and 99, respectively. When a number has two digits, it is called a 2-digit number. 2-digit numbers have two digits and range from 10 to 99.
Any number between 1 and 9 can be used as the digit in the tens place. The placement of each digit in a number is known as place value. There is just one place value that matters when discussing 1-digit numbers, and that is the ones place.
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Please help me due soon
Answers
Answer:
The pictures are too small :(
Step-by-step explanation:
Point K is located at (1.5) on the coordinate plane. Point K is reflected over the Z-
acis to create point K'. What ordered pair describes the location of K"?
Answers
Answer:
hold on i'm abt to answer it
Step-by-step explanation:
Heather Johnson bought a new set of tires for $436.00 and a car seat for $22.85. The state tax rate is 6%, the county tax rate is 1.5%, and the city tax rate is 0.5%. What is the total purchase price?
Answers
Answer:
$495.56
Step-by-step explanation:
Tax increases the price paid for a good or service. So, the total price paid for the goods would increase by the total amount of tax
Sum of the three taxes = 6% + 1.5% + 0.5% = 8%
Total cost of items purchased = $436 + $22.85 = $485.85
Total purchase price = Total cost of items purchased x (1 + total tax)
$485.85 x (1.08) = $495.56
A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 7 in by (2)3/4 in by (2)1/4 in. If the brick cost $0.05 per cubic inch, find the cost of 750 bricks
Answers
Answer:1624.22
Step-by-step explanation:
Width
=
Width=
2
3
4
in
=
2.75
in
2
4
3
in=2.75 in
Convert fraction to decimal
Height
=
Height=
2
1
4
in
=
2.25
in
2
4
1
in=2.25 in
Convert fraction to decimal
Volume
=
Volume=
�
�
ℎ
lwh
Volume of rectangular prism
=
=
7
⋅
2.75
⋅
2.25
7⋅2.75⋅2.25
Substitute
=
=
43.3125
in
3
43.3125 in
3
Cost per brick
=
Cost per brick=
43.3125
in
3
1
⋅
$
0.05
1
in
3
1
43.3125in
3
⋅
1in
3
$0.05
=
=
43.3125
in
3
1
⋅
$
0.05
1
in
3
1
43.3125
in
3
⋅
1
in
3
$
0.05
=
=
$
(
43.3125
⋅
0.05
)
$(43.3125⋅0.05)
=
=
$
2.165625
$2.165625
Careful not to round too soon
Total cost
=
Total cost=
750
⋅
$
2.165625
750⋅$2.165625
=
=
$
1624.21875
$1624.21875
≈
≈
$
1624.22
$1624.22
Round to the nearest cent
Given the linear ODE: exy' - 2y = x. The standard form of it is: y' - 2e xy = xe-x None of the mentioned y' + 2e xy = xe-x y' – 2e*y = xex
Answers
For any positive integers a₁, a₂, ..., aₙ, there exist integers x₁, x₂, ..., xₙ such that a₁x₁ + a₂x₂ + ⋯ + aₙxₙ = gcd(a₁, a₂, ..., aₙ).
How to prove that for any positive integers a₁, a₂, ..., aₙ, there exist integers x₁, x₂, ..., xₙTo prove that for any positive integers a₁, a₂, ..., aₙ, there exist integers x₁, x₂, ..., xₙ such that a₁x₁ + a₂x₂ + ⋯ + aₙxₙ = gcd(a₁, a₂, ..., aₙ), we will use the Euclidean algorithm and Bézout's identity.
Base case
For n = 2, the statement is equivalent to Bézout's identity, which states that for any positive integers a and b, there exist integers x and y such that ax + by = gcd(a, b). Therefore, the base case is true.
Inductive step
Assume that the statement holds for n = k, i.e., for any positive integers a₁, a₂, ..., aₖ, there exist integers x₁, x₂, ..., xₖ such that a₁x₁ + a₂x₂ + ⋯ + aₖxₖ = gcd(a₁, a₂, ..., aₖ).
Now, we will prove that the statement holds for n = k + 1.
Consider positive integers a₁, a₂, ..., aₖ₊₁. Let d = gcd(a₁, a₂, ..., aₖ) be the greatest common divisor of the first k numbers. By the assumption, there exist integers x₁, x₂, ..., xₖ such that a₁x₁ + a₂x₂ + ⋯ + aₖxₖ = d.
Using the Euclidean algorithm, we can write:
aₖ₊₁ = qd + r, where q is an integer and 0 ≤ r < d.
Now, let's rewrite the equation from the assumption by multiplying each term by q:
qa₁x₁ + qa₂x₂ + ⋯ + qaₖxₖ = qd.
Adding aₖ₊₁xₖ₊₁ to both sides of the equation, we get:
qa₁x₁ + qa₂x₂ + ⋯ + qaₖxₖ + aₖ₊₁xₖ₊₁ = qd + aₖ₊₁xₖ₊₁.
Substituting qd + aₖ₊₁xₖ₊₁ with aₖ₊₁, we have:
qa₁x₁ + qa₂x₂ + ⋯ + qaₖxₖ + aₖ₊₁xₖ₊₁ = aₖ₊₁.
Therefore, we have found integers x₁, x₂, ..., xₖ, xₖ₊₁ (where xₖ₊₁ = q) such that:
a₁x₁ + a₂x₂ + ⋯ + aₖxₖ + aₖ₊₁xₖ₊₁ = aₖ₊₁.
This shows that the statement holds for n = k + 1.
By the principle of mathematical induction, the statement holds for all positive integers n.
Hence, for any positive integers a₁, a₂, ..., aₙ, there exist integers x₁, x₂, ..., xₙ such that a₁x₁ + a₂x₂ + ⋯ + aₙxₙ = gcd(a₁, a₂, ..., aₙ).
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The standard form of the given linear ODE, exy' - 2y = x, is y' - 2e^xy = xe^(-x).
To obtain the standard form, we divide the entire equation by ex to isolate the coefficient of y' and rewrite the exponential term.
This manipulation allows us to express the equation in a more common form for linear ODEs.
The standard form equation highlights the dependent variable's derivative, the coefficient of y, and the right-hand side of the equation.
By transforming the original equation into the standard form, y' - 2e^xy = xe^(-x), we can readily identify the coefficient of y' as 1, the coefficient of y as -2e^xy, and the right-hand side as xe^(-x).
This representation enables a clearer understanding of the structure and characteristics of the linear ODE, aiding in further analysis and solution methods.
Therefore, the standard form of the given linear ODE, exy' - 2y = x, is y' - 2e^xy = xe^(-x).
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Find an equivalent ratio in simplest terms: 70:40
Answers
Answer:
7:4
Step-by-step explanation:
70 / 2 : 40 / 2
35:20
35 / 5 : 20 / 5
7:4
solve for x and y pls
Answers
X= 45
Since x is 45 the other angle on the other side is 45
Every triangle equals 180 so you take 45+45 to get 90 and subtract that from 180 and get 90
Y= 90
hope this helped ask questions
16.9 divided by 4? please show your work, thank you!
Answers
Answer:
4.225
Step-by-step explanation:
16.9/4 = 4.225
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