Find the general solution to the following differential equation x^3•y’- y = 0
Answer:
y(x) = c_1 e^(-1/(2 x^2))
Step-by-step explanation:
Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:
Solve for (dy(x))/(dx):
(dy(x))/(dx) = y(x)/x^3
Divide both sides by y(x):
((dy(x))/(dx))/y(x) = 1/x^3
Integrate both sides with respect to x:
integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx
Evaluate the integrals:
log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.
Solve for y(x):
y(x) = e^(-1/(2 x^2) + c_1)
Simplify the arbitrary constants:
Answer: y(x) = c_1 e^(-1/(2 x^2))
The width of a rectangle is six meters less than the length. The perimeter is 56 meters. Find the length and width (in meters).
Answer:
length: 18
width: 12
Step-by-step explanation:
Good Luck
Does the Equation open up or open down ?
Answer:
Opens up.
Step-by-step explanation:
See the 2 in front of the x? If that's positive, it opens up. If it's negative, it opens down.
What does period mean in math
Answer:
It means multiple•
Step-by-step explanation:
Answer:
multiplication
Step-by-step explanation:
if this isnt what you mean, please comment down below so i can help you out !!
What is the greatest common divisor of 120 and 5040
1 The vertices of 3 squares are joined to form a right triangle. What is the area of the largest square?
A 6.5 cm?
B 7 cm?
C 33 cm?
D 43 cm?
The area of a triangle is 142cm2. Two sides of the triangle measure 24cm and 38cm. What is the measure of the included angle between the side, approximated to 1 decimal place?
Answer:
C = 18.1°
Step-by-step explanation:
A = 142 m²
a = 24 cm, b = 38 cm
Use the formula A = a*b*sinC/2
142 = 24 * 38 * sinC/2 = 456*sinC
sinC = 0.3114
C = 18.1°
Vivian has spent $2,500 shopping during the weekend. If she went into 10 stores, on average, how much money did she spend in each store? *
Answer:
$250.00 on average at each store
Step-by-step explanation:
2500 ÷ 10=250
Write the word sentence as an equation.
5 more than a number x is -4.
An equation is
Solve the equation.
X =
The unknown number is x .
An equation to find the value of x :-
[tex]x + 5 = - 4[/tex]
Let us solve this equation :-
[tex]x + 5 = - 4[/tex]
[tex]x = - 4 - 5[/tex]
[tex]x = - 9[/tex]
The value of x is -9 . Let us place -9 in the place of x , to check whether or not we have found out the correct value of x .
So :-
[tex] - 9 + 5 = - 4[/tex]
[tex] - 4 = - 4[/tex]
[tex]LHS = RHS [/tex]
As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct value of x .
Therefore , -9 + 5 = -4 and ( x = -9 ) .
5+x=-4 is equation of sentence 5 more than a number x is -4 and -9 is the solution of equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given sentence is 5 more than a number x is -4.
Whenever there is a more than in a sentence means added with some number.
Let us consider the number be x.
5 more than a number x is -4 means 5 is added to number x which gives -4.
5+x=-4
This is the equation for the sentence.
Now let us solve the equation.
5+x=-4
Subtract 5 from both sides
x=-4-5
x=-9
Hence, 5+x=-4 is equation of sentence 5 more than a number x is -4 and -9 is the solution of equation.
To learn more on Equation:
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There are 16 marbles in total . Maria has 2 more than Felipe. How many marbles does each person have
Answer:
maria has 9 and felipe has 7
Step-by-step explanation:
if felipe has 7 then 9+7=16
Suppose f(x)=x^3 find the graph of f(x)+2
so when we add to the function outside of the parentheses of (x)^3, we are moving the graph in the up down direction so it would look like x^3 but shifted up 2 units. the way to easily know which one it is, plug in zero for x in the original and 0^3 is zero so we know the original fuction will go through the origin so the function who's center is is only shifted up (because it's positive 2) two units so graph 1
note: the reason i know that what looks like a center point is actually at the origin is because f(x)= x^3 is a very famous graph that you should know the shape of :)
Answer:
See attached image
Step-by-step explanation:
Attached
I need help quick!!! Will give brainliest to first person
Answer:
3 and 4 x=25, y=29
Step-by-step explanation:
I hope this helps. If you need any extra information, I will edit this later.
Help me please thanks :)
Answer:
c.
Step-by-step explanation:
if it has repeating y-values, then it's not a function.
The sum of two numbers is 30
and their quotient is 2
What are the two numbers?
Answer:
The numbers are 20 and 10.
Step-by-step explanation:
Let's say these teo numbers are x and y.
The sum of two numbers is 30
x + y = 30
Isolate y
y = 30 - x
Their quotient is 2
plug the newfound y value in the second equation.
x / y = 2
[tex]\frac{x}{30-x} = 2[/tex]
multiply both sides by (30 - x) to get rid of the fraction.
x = 2(30 - x)
x = 60 - 2x
x + 2x = 60 + 2x
3x = 60
dividie both sides by 3
x = 20
find y
y = 30 - x
y = 30 - 20 = 10
y = 10
The numbers are 20 and 10.
Answer:
10 and 20.
Step-by-step explanation:
x + y = 30
x/y = 2
x = 2y so substituting in the first equation:
2y + y = 30
y = 10
and x + y =30
so x + 10 = 30 giving x = 20.
I NEED THIS ASAP PLEASE HELP MEEEEE
Prove the Pythagorean Theorem using similar triangles.
Find a solution to the linear equation y=2x+18 by filling in the boxes with a valid value of x and y. PLEASE REPLY SOON. I am doing a test. Thank YOu
Answer: (20)=2(1)+18 or (54)=2(18)+18
Mindy had 1/2 of a can of soda left. If she shared it equally with her sister, how much of the can of soda did they each have? Choose the model that represents the answer.
A. 1/6
B. 1/2
C. 1
D. 1/4
Find the equation of the line shown
Answer:
y=2x
Step-by-step explanation:
Select all numbers that are solutions to the inequality w < 3.
1
-1.5
0
-7
5
Answer:
all of them except 5 because
[tex]5 > 3[/tex]
–5.4(–0.7 + u) =
What is the answer?
Answer:
3.78 + -5.4u
Step-by-step explanation:
Help please I’m so confused
Answer:
m<ACD = 124 degrees
Step-by-step explanation:
(2x+8) + (x-2) = 180 degrees
This is because both angles are on the same line (so they are a linear pair) and a straight line is 180 degrees. This means that they are supplementary
So:
(2x+8) + (x-2) = 180
Combine like terms:
2x + x + 8 - 2 = 180
3x + 6 = 180
-6 -6
3x = 174
Divide both sides by 3
x = 58
Now that you know x, you can put it into the equation for m<ACD:
2x+8
(2 multiplied by 58) + 8
(116) + 8
124
m<ACD = 124 degrees
Feel free to ask any follow-up questions if u don't understand
whats 3+2 I NEED TO KNOW MY SON IS IN PRE K
Answer:
i think its 6
Step-by-step explanation:
3 then add one more 3 so then you add 3+3 and you'll get 6..!!
Answer: 5
Step-by-step explanation: add 3 ( \ \ \) to two ( \ \) and that would leave you with Five. (\\\\\)
a^2 x a^3
plz answer
Answer:
a⁵
Step-by-step explanation:
During these events, when the base is same( in this case, 'a'), the powers gets added
thus
[tex]a^{2} * a^{3} \\a^{2+3}\\a^{5}[/tex]
Ernest has $900 in a savings account that earns 14% annually. The interest is not compounded. How much will he have in total in 2 years?
Help
Answer:
1152$
Step-by-step explanation:
Intrest is 252
5 1/3 divided by 4
make into improper fraction
Answer:
5 1/3 ÷ 4 = 16/3
Step-by-step explanation:
basically what I did was 5 × 3 = 15 + 1 = 16/3
Answer:
[tex]1\frac{1}{3}[/tex]
Step-by-step explanation:
Given the following question:
[tex]5\frac{1}{3} \div4[/tex]
To find the answer convert the mixed numbers into improper fractions and then divide using KCF. (Keep, Change Flip)
[tex]5\frac{1}{3} \div4[/tex]
[tex]5\frac{1}{3} =3\times5=15+1=16=\frac{16}{3}[/tex]
[tex]\frac{16}{3} \div4[/tex]
[tex]4=\frac{4}{1}[/tex]
[tex]\frac{16}{3} \div\frac{4}{1}[/tex]
Apply KCF:
[tex]\frac{16}{3} \div\frac{4}{1}[/tex]
[tex]\frac{16}{3} \times\frac{1}{4}[/tex]
[tex]16\times1=16[/tex]
[tex]3\times4=12[/tex]
[tex]=\frac{16}{12}[/tex]
Simplify by reducing:
[tex]\frac{16}{12}[/tex]
[tex]16\div4=4[/tex]
[tex]12\div4=3[/tex]
[tex]=\frac{4}{3}[/tex]
Convert into mixed number:
[tex]\frac{4}{3}[/tex]
[tex]\frac{4}{3} =4\div3=1\frac{1}{3}[/tex]
[tex]=1\frac{1}{3}[/tex]
Which means your answer is "4/3 or 1 1/3."
Hope this helps.
Solve for X.
A.
B.
C.
D.
Answer:
A. 3
Step-by-step explanation:
3x+137+2x+28 = 180
5x + 165 = 180
5x = 15
x = 3
Consider the expression below. 1.3 + 1.25
Sarah thinks that this sum will be an irrational number. Is Sarah's classification correct? Why or why not?
A Sarah is not correct, because 1.3 + 1.25 can be rewritten as + which results in the rational sum of 2
B. Sarah is not correct, because 1.3 + 1.25 results in a decimal number and all decimals are rational.
C. Sarah is correct, because 1.25 cannot be rewritten as a fraction which means the sum is irrational.
D.
Sarah is correct, because 1.3 cannot be rewritten as a fraction or terminating decimal which means the sum is
irrational
Answer:
First, let's find out the sum;
1.30 + 1.25 = 2.55, is rational, so A
Step-by-step explanation:
The reason being this is because, 2.55 is a terminating decimal meaning that the decimal place does not go on forever.
Sara's classification is not correct because the sum is a rational number.
What is an irrational number?Irrational numbers are real numbers that cannot be expressed in fractions.
First, we can find the sum
i.e 1.3+1.25 = 2.55
Here, 2.55 is a rational number.
51/20 = 2.55
Since the sum is a rational number Sarah is not correct.
To learn more about irrational number, use the given link below:
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which shape is a rectangle?
question 7 on -ready
Answer:
I’m not sure about I-ready, everyone has different ones but I’ll give you some options.
A rectangle is a quadrilateral
A rectangle is a parallelogram
Unless I-ready is asking bout which SHAPE can be a rectangle then it’s a lot of different options.
A square can be a rectangle
Or a parallelogram with the givens being able to fit in to all the things that defines as a rectangle.
These are the options I can think of but pretty sure theres more. But it’s I-ready so it’s not complicated.
Which of the binomials below is a factor if this trinomial?
x^2 - 3x - 4
A. x + 4
B. x + 8
C. x^2 + 4
D. x - 4
Answer:
D. x - 4
Step-by-step explanation:
x² - 3x - 4 = ( x - 4 )( x + 1 )
main formula: x² + ( a + b )x + ab = ( x + a )( x + b )
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answer:
50 the answer is 50
Step-by-step explanation:
50% that's it ok?
Hi, I believe your answer is ---150%--- because if each square is one whole, that makes them 200% combined. Since one square is only halfway shaded, it is only 50%. I hope this helps you! Good luck and have a great day. :)