Answers
Answer:
f(x) = 2e^(x^3/3) +1
Step-by-step explanation:
This is called a "separable" differential equation, because the variables can be separated:
[tex]\dfrac{dy}{y-1}=x^2\cdot dx[/tex]
Now, both sides can be integrated.
[tex]\displaystyle \int{\dfrac{dy}{y-1}}=\int{x^2}\,dx\\\\\ln(y-1)=\dfrac{x^3}{3}+c_1\\\\y-1=c_2\cdot e^{x^3/3}\qquad c_2\text{ is a free constant different from $c_1$}\\\\3=c_2e^0+1\qquad\text{apply initial condition to find $c_2=2$}\\\\\textsf{Add 1 to get y alone. Use the found value of $c_2$. Replace $y$ with $f(x)$.}\\\\\boxed{f(x)=2e^{x^3/3}+1}[/tex]
Related Questions
If the area of triangle is 360 cm2 and the height is 18cm, find its base
Answers
Formula for area of a triangle is 1/2 x base x height.
musing the information given you have:
360 = 1/2 x base x 18
First multiply both sides by 2:
720 = base x 18
Now divide both sides by 18:
Base = 720/18
Base = 40 cm
Solution:
Note that:
Area of triangle = 1/2 x Base x HeightArea of triangle = 360 cm²Height = 18 cmUsing the formula to find the area:
1/2 x Base x Height = Area of triangle=> 1/2 x Base x 18 = 360 cm²=> Base x 9 = 360 cm²=> (Base x 9)/9 = 360/9 cm²=> Base = 40 cmif you solve an equation and you end up with 0 = 6 that means the answer is 6?
Answers
Answer:
It means that the equation has no solution
Step-by-step explanation:
The formula E= MHz, where E = gravitational potential energy , mass, g = gravity, and h= Height, is used to calculate gravitational potential energy. Solve this formula for h.
Answers
Find the product. (-3x - 7)(5x + 8)
Answers
Step-by-step explanation:
= -15x²-24x-35x-56
= -15x²-59x-56
2. In the diagram below of parallelogram ROCK, m ZC is 70° and mZROS is 65°. What is mZKSO?
Answers
Check the picture below.
Pete's Pasteris sells cupcakes in packs of 4. A caterer needs between 42 and 50 cupcakes for dessert. Name two possible number between 42 and 50 that are multiple of 4. Explain
Answers
Answer:
44 48
Step-by-step explanation:
Determine the slope and y-intercept given the equation below, explain your answer.
x + y = -1
Answers
Answer:
slope is -1, y-intercept is -1
Step-by-step explanation:
x+y=-1
convert to slope-intercept form
y=-x-1
y=-1x-1
slope is -1, y-intercept is -1
Solution:
Let's convert the equation into slope-intercept form.
x + y = -1y = -x - 1In this equation, the slope is the coefficient of x.
The following points can be made:
Since there is a "-" in front of the x variable, the coefficient of x is -1.Since the coefficient is -1, the slope of the line is -1.The y-intercept of the equation will be a constant.
The following points can be made:
Since there is a constant on the RHS, that constant will be the y-intercept.Since the constant on the RHS is -1, the y-intercept of the line is -1.In conclusion...
Slope of line: -1y-intercept of line: -110(-0.4x + 3y) = ?x + ?y
10(? + ?) = ? + ?
?=?
Answers
Answer:
2x(57x74)94
Step-by-step explanation:
please answer my question correctly
Answers
Answer:
The First one is an Octagon, the second is a Pentagon
Step-by-step explanation:
An Octagon has 8 sides, Octo also means eight. A pentagon has 5 sides, Penta means Five.
HOME IMPROVEMENT Percy is building a deck behind his house. He measures the location for his deck and rounds to the nearest tenth of afoot. If lumber costs $11.99 per square foot, then what is the possible range for the cost of the lumber needed to build the deck?
The cost would be at least _____, but less than _____
there is a photo under
Answers
The cost would be at least $755.1302 to build the deck.
The deck is in the shape of a rectangle. Therefore,
Area of rectanglearea = lwwhere
l = length
w = width
length = 9.4 ft
width = 6.7 ft
area = 9.4 × 6.7 = 62.98 ft²
Therefore,
1 ft² of lumber = $11.99
62.98 ft² of lumber = ?
cross multiply
cost = 62.98 × 11.99 = $755.1302
learn more on area here: https://brainly.com/question/2292989
Find the value of x that makes the quadrilateral a parallelogram.
Please help
Answers
Answer:
x = 2/3
Step-by-step explanation:
Since it's a parallelogram, the bisected parts of the diagonal must be equal
So 6x must equal 3x + 2:
6x = 3x + 23x = 2x = 2/3-Chetan K
Original price:
Discount:
30%
Sale price:
$206.50
Answers
C
Jane got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon
was 21 cents per yard. If after that purchase there was $16.39 left on the card, how many yards of ribbon did Jane buy?
yards
?
Answers
Step-by-step explanation:
so, she spent 25-16.39 = $8.61 on the ribbon.
1 yard of the ribbon costs $0.21.
how many yards did she buy with that amount of money ?
well, as many times as 0.21 fits into 8.61 :
8.61 / 0.21 = 41
so, she bought 41 yards of ribbon.
I'm happy to help you today!
Answer:
41 yards is correct
Step-by-step explanation:
Step 1. The information we have is:
Originally Jane had $25 on her debit card.
She made a purchase of bulk ribbon for 21 cents per yard.
And after that she ended up with $16.39 on the card.
Step 2. Make an equation to describe the situation.
The equation that describes this situation is:
[tex]\tt 25-0.21y=16.39[/tex]
Where 25 is the initial amount and to that, we subtract 0.21y, where y is the number of yards that she bought of ribbon. And all of this has to be equal to the final amount of 16.39.
Step 3. Solve the equation for y:
To solve for y, we subtract 25 to both sides of the equation:
⇒ [tex]\tt-0.21y=16.39-25[/tex]
⇒ [tex]\tt -0.21y=-8.61[/tex]
Then, divide both sides of the equation by -0.21:
[tex]\tt y=\frac{-8.61}{-0.21}[/tex]
The result is:
[tex]\tt y=41[/tex]
The answer is 41 yards of ribbon.
Hope this helps you!Have an awesome day! :)[tex]-Nature-[/tex]
Help please I don't know how to do this and it is due soon!!
Answers
Answer:
its an isosceles triangle not a right angle triangle.part A:
[tex]\sf AB^2 = (-2-1)^2 + (1+3)^2[/tex]
[tex]\sf AB^2 =25[/tex]
[tex]\sf AB =5[/tex]
[tex]\sf AC^2 = (2-1)^2 + (4+3)^2[/tex]
[tex]\sf AC^2 = 50[/tex]
[tex]\sf AC = \sqrt{50}[/tex]
[tex]\sf AC = 5\sqrt{2}[/tex]
[tex]\sf BC^2 = (2--2)^2 + (4-1)^2[/tex]
[tex]\sf BC^2 = 25[/tex]
[tex]\sf BC = 5[/tex]
use the formula:
short side² + short side² = long side²
( 5√2 )² + 5² = ( 5√2 )²
75 = 50
It's isosceles
A(-3,1)B(1,-2)C(4,2)[tex]\\ \rm\hookrightarrow AB=\sqrt{(-2-1)^2+(1+3)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
[tex]\\ \rm\hookrightarrow BC=\sqrt{(2+2)^2+(4-1)^2}=\sqrt{16+9}=5[/tex]
[tex]\\ \rm\hookrightarrow AC=\sqrt{(4+3)^2+(2-1)^2}=\sqrt{50}[/tex]
AB=BCIts isosceles
Please help!
A (-2,3)
B (3, -2)
C (-8, 12)
D (12, -8)
Answers
Answer
A(-2,3)
Step-by-step explanation:
-4 6 are the actual coords, and then we do 1/2 so divide it by 2 -4/2 6/2 and u get the answer A
Answer:
A. (-2,3)
Step-by-step explanation:
Rectangle ABCD is dilated by a scale factor of 1/2.
Scale factor of k with a center of dilation at the origin:
[tex](x,y)[/tex] → [tex](kx,ky)[/tex]
It is given that rectangle ABCD is dilated by a scale factor of 1/2 with a center of dilation at the origin, then:
[tex](\frac{1}{2}x,\frac{1}{2}y)[/tex]
The coordinates of B are (-4,6). So, the coordinates of B:
[tex]B(-4,6)[/tex] → [tex]B(\frac{1}{2}(-4),\frac{1}{2}(6)[/tex]
[tex]B(-4,6)[/tex] → [tex]B(-2,3)[/tex]
The coordinates of B → (-2/3)
Hence, -2/3 is the correct answer.
[RevyBreeze]
Help will give brainlest!
Answers
Answer:
1; 4; 3;
Step-by-step explanation:
i think this involves ratios>> if not, sorry-
Consider the equation -16 * 10^(6x) = -80
Solve the equation for x. Express the solution as a logarithm in base-10
x=
Approximate the value of x. Round your answer to the nearest thousandth
x=
Answers
The approximate the value of x in the equation -16 * 10⁶ˣ = -80 is 0.116.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
-16 * 10⁶ˣ = -80
Dividing both sides by -16:
10⁶ˣ = 5
Taking ln of both sides:
6xln(10) = ln(5)
Finding the value of x:
x = 0.116
The approximate the value of x in the equation -16 * 10⁶ˣ = -80 is 0.116.
Find out more on equation at: https://brainly.com/question/1214333
Please give question for the answer.
Answers
Answer:
[tex]f(x)=\sqrt[3]{x} \\a=5[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt[3]{x} \\a=5[/tex]
a = 5
f(x) 3 x
Which TWO systems of equations have exactly one solution ?
6x−3y=3
2x−y=4
y=−2x−8
y=x+1
6x−3y=12
2x−y=4
x−4y=8
3x+2y=10
y=2x+1
y=2x−2
Answers
Answer: 2nd and 4th set
Step-by-step explanation:
1st set has no solution because the left side of the second equation is that of the first equation divided by 3, but the right side is not.
2nd set has 1 solution because it is the set of 2 lines with different slopes and y-intercepts.
3rd set has infinitely many solutions because multiplying the top equation by 1/3 gives you the bottom equation.
4th set has only solution for the same reason as 2nd set.
5th set has no solution because the two lines are parallel, but have different y intercepts, meaning they never intersect.
Solve the system of equations.
y = -5x - 8
y = 4x + 1
a.
( 1, -3)
c.
( 3, 1)
b.
( -1, -3)
d.
No solution
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer: B
Step-by-step explanation:
Setting the equations equal to each other,
-5x-8 = 4x+1
-8 = 9x + 1
-9 = 9x
x = -1, meaning y=-5(-1)-8 = -3.
HELP ASAP PLSPLSPLS Question 8 (Fun-The-Blank Worth 6 points)
(05.03 LCJA polygon is shown
4 units
M
N
2 ore
3 urits
1.
R
7 units
square units input whole numbers only, such as 8.)
The area of polygon INOPOR S Area of a rectangle that is 12 square units Area of a rectange that is
Numerical Answers Expected!
Answer for Blank 1
Answers
Answer:
3
Step-by-step explanation:
(7 - 4) * (3 - 2) = 3
x=2y-1 solve this equation
3x+y=11
Answers
Step-by-step explanation:
substitute y into x
3(2y-1)+y=11
6y-3+y=11
add like terms
6y+y-3-11=0
7y-14=0
look for a common factor
7(y-2)=0
y-2=0
therefore y=0 or y=2
find x
if x=2y-1
x=2(0)-1
x=-1
if x=2y-1
x=2(2)-1
x=3
therefore (-1;0) and (3;2)
HELPPPP ASAP THIS IS DUE IN 5 MINUTES I WILL GIVE ALL MY POINTS!
A shipping container will be used to transport several 60-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24000 kilograms. Other shipments weighing 3300 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 60-kilogram crates that can be loaded into the shipping container.
Answers
Answer:
x </= (24000-3300)/60 or x </= 345
A room measure 9.68 metres long and 6.2 m wide Find its area Also find how many tiles will be needed to pave if the size of a tile 22cm × 10cm .
Answers
Answer:
Area is easy, just do 9.68*6.2 which = 60.02 (Rounded to the nearest hundreth)
Step-by-step explanation:
For how many tiles we need
60.02 m is the area of the room, each tile would be 22cmx10cm
There are 100 cm in 1 m
What we can do is find the area of the tiles
22x10 which is 220 CM
220CM is 2.2M
Now that we know the area of the tile is 2.2M we can do 60.02/2.2
Which would be 27.28 tiles (Rounding to the nearest hundreth)
Stephanie scored 18 points fewer than her friend Jenna.
If Stephanie scored 12 points, how many points did Jenna
score? HELP PLEASEEE
Answers
Answer:
30 points
Step-by-step explanation:
Points by Jenna = J
=> J - 18 = 12
=> J = 30 points
Explanation
. J-18=12
12+18=30
Jenna scored 30 points :)
A 141 inch pipe is cut into two pieces. One piece is two times the length of the other. Find the lengths of the two pieces
Answers
Your father is planning to cook for 35 people using a recipe that specifies two and a half cups of sugar for each six people,
For the larger group, your father will require
cups of sugar
Answers
Your father will require 14.6 cups of sugar for the larger group
Ratio and proportionsFrom the question, we have that 2.5 cups of sugar can be used to make recipes for 6 people that is;
6 people = 2.5 cups of sugar
In order to calculate for 35 people, we will have;
35 people = x
Taking the ratio of the expressions
6/35 = 2.5/x
6x = 87.5
x = 87.5/6
x = 14.6
Hence your father will require 14.6 cups of sugar for the larger group
Learn more on ratio and proportions here: https://brainly.com/question/19994681
Beatrice spent a total of $54 at
a restaurant. The bill is shown
in the table. The prices include
tax. What percent of the total
check did Beatrice leave as a
tip for her server? Choose the correct answer below
Answers
Answer
C. .20 or 20%
Explanation
The table is
2 drinks $4.50
Entree $13.50
Entree $16.00
2 desserts $11.00
Total $45.00
9/45=20%
Select the correct answer.
What is the solution of 5/2x-7=3/4x+14?
А.x=-6
В.x=6
C.x=8
D. r= 12
Answers
Answer:
D) x = 12
Step-by-step explanation:
we can change 5/2 to 10/4 and now have:
10/4x-7 = 3/4x + 14
we can subtract 3/4x from each side:
7/4x-7 = 14
add 7 to each side:
7/4x = 21
multiply each side by 4/7:
x = 84/7
x = 12
Verify the identity.
Answers
Answer:
first blank box:
cos^2(a)
second blank box:
sin^2(a)
see image.
Step-by-step explanation:
Usually, to "verify" you work on the equation using algebra and identities...BUT ONLY CHANGING ONE SIDE. Keep the other side the same and try to make them look the same.
The step to get what's in the first blank box is multiplying
(1-cos a)(1+cos a)
which will make a difference of two squares.
The second blank is using a pythagorean identity that
cos^2 + sin^2 = 1
so
1 - cos^2 = sin^2
see image.
