Answer:
[tex]\large\text{$y=ke^{\frac{1}{3}x^3+x}$}[/tex]
Step-by-step explanation:
Given differential equation:
[tex]\large\text{$\dfrac{\text{d}y}{\text{d}x}=y(x^2+1)$}[/tex]
Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:
[tex]\large\text{$\implies \dfrac{1}{y}\;\text{d}y=(x^2+1)\;\text{d}x$}[/tex]
Integrate both sides, remembering to add the constant of integration (C):
[tex]\large\begin{aligned}\implies \displaystyle \int\dfrac{1}{y}\;\text{d}y & =\int(x^2+1)\;\text{d}x\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\end{aligned}[/tex]
Rewrite C as ln k:
[tex]\large\text{$\implies \ln y = \dfrac{1}{3}x^3+x+\ln k$}[/tex]
Solve for y, applying:
[tex]\textsf{Log rule}: \quad e^{\ln a}=a[/tex][tex]\textsf{Exponent rule}: \quad \:a^{b+c}=a^ba^c[/tex][tex]\large\text{$ \implies e^{\ln y} =e^{\frac{1}{3}x^3+x+\ln k}$}[/tex]
[tex]\large\text{$ \implies y=e^{\ln k} \cdot e^{\frac{1}{3}x^3+x}$}[/tex]
[tex]\large\text{$\implies y=ke^{\frac{1}{3}x^3+x}$}[/tex]
Integration rules
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.1 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\\\(where $n$ is any constant value) \end{minipage}}[/tex]
Answer:
[tex]{ \tt{ \frac{dy}{dx} = y( {x}^{2} + 1) }} \\ [/tex]
- Simplify by collecting each term according to its corresponding d
[tex]{ \tt{ \frac{dy}{y} = ( {x}^{2} + 1) \: dx}} \\ [/tex]
- Integrate both sides;
[tex]{ \tt{ \int \frac{1}{y} \: dy = \int ( {x}^{2} + 1) \: dx }} \\ \\ { \tt{ ln(y) = \frac{1}{3} {x}^{3} + x + c }}[/tex]
- To make y the subject, you must remove the natural log;
[tex]{ \tt{ log_{e}(y) = \frac{1}{3} {x}^{3} + x + c }} \\ \\ { \tt{y = {e}^{( \frac{1}{3} {x}^{3} + x + c) } }} \\ [/tex]
In which interval is the radical function f of x is equal to the square root of the quantity x squared 2 times x minus 24 end quantity increasing?
We get that the function f (x) = √ x² - 2 x - 24 is increasing at the interval [6, ∞).
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.
We are given the function as:
f (x) = √ x² - 2 x - 24
From the graph, the function f (x) = √ x² - 2 x - 24 is increasing over the interval [6, ∞).
Therefore, we get that the function f (x) = √ x² - 2 x - 24 is increasing at the interval [6, ∞).
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Sin^-1(x) when x=0.3
Solve by using limits (h—>0)
Answer:
please rate as brainliest
17[tex]\leq -10y-3\leq 97[/tex]
The solution for the given inequality is -10 < y ≤ -2.
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
The question gives:
17 ≤ -10y -3 ≤ 97
For solving this exercide, you should write the previous compound inequality as:
17 ≤ -10y -3 (1)
-10y -3 ≤ 97 (2)
For inequality 117 ≤ - 10y -3
10y ≤ -3 -17
10y ≤ -20
y ≤ -20/10
y ≤ -2
For inequality 2-10y -3 ≤ 97
-10y ≤ 97 +3
-10y ≤ 100 *(-1)
10y ≥ - 100
y ≥ - 100/10
y ≥ - 10
Combining the intervals, you have -10 < y ≤ -2.
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An angle measure of 134.26° is converted to DMS notation as what
Angle measurement of 134.26° becomes 134° 15' 36" in DMS notation.
What is DMS notation?The standard way to express fractional parts of a degree is in decimal form or in minutes and seconds. The units of a degree are a minute (') and a second (′′). For degrees, minutes, and seconds, this form is frequently referred to as the DMS Form. Use the decimal's whole number portion for the degrees.Divide the final decimal by 60 to get the number of minutes. Use the answer's whole number component as minutes.The new decimal that is left after multiplying by 60 is the seconds.So, an angle measure of 134.26° is converted to DMS notation as:
= 134° 15' 36"(Refer the image given below for calculation)
Therefore, the angle measurement of 134.26° becomes 134° 15' 36" in DMS notation.
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A recipe for one loaf of bread uses 2 cups of flour, 12
tablespoons of water, and 1 teaspoon of salt.
Complete the table to show the quantities needed to
make multiple loaves of bread,
Loaves
J
#11
4
Flour (cups)
2
Water (tbsp)
12
48
Salt (isp.)
1
Answer:
Flour 4) 8
Water 2) 24
Salt 2 - 4) 2 and 4
[tex]\bold{Table}[/tex] [tex]\bold{Rule:}[/tex]
[tex]x \times y = z[/tex]
[tex]\mathrm{where~"z"~is~the~next~value}[/tex]
What type of Solution is the product of 2x+1=2x+2
Answer: no solution
Step-by-step explanation:
Evaluate each expression if x is 2/5, y is -4, and z is -0.2. Then match each expression with the correct answer.
A) 1x + y + z
B) 1 x + y + z
C) 2(y)(x)
D) 2 (y)(x)
E) 32x - z
F) 3 2x - z
G) 4x + y
The expressions evaluated for the given values of x, y, and z, and matched to the values are
1x + y + z → -3.8
2(y)(x) → -3.2
32x - z → 13
4x + y → -2.4
Evaluating an expressionFrom the question, we are to evaluate the given expressions for the given values of x, y and z
The given values of x, y, and z are
x = 2/5, y = -4, and z = -0.2
A. 1x + y + z
1(2/5) + (-4) + (-0.2)
2/5 - 4 - 0.2
0.4 - 4 - 0.2
= -3.8
C) 2(y)(x)
2(-4)(2/5)
-8(0.4)
= -3.2
E) 32x - z
32(2/5) - (-0.2)
32(0.4) + 0.2
12.8 + 0.2
= 13
G) 4x + y
4(2/5) + (-4)
4(0.4) - 4
1.6 - 4
= -2.4
Hence, the expressions evaluated for the given values of x, y, and z, and matched to the values are
1x + y + z → -3.8
2(y)(x) → -3.2
32x - z → 13
4x + y → -2.4
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Correct answer gets brainily!
The measure of ∠YZW is given as 180 degrees.
What is an angle on a straight line?
In the field of geometry, and in mathematics, the straight angle is one that is said to be equal to 180 degrees. That is, it is the angle that is called so based on the fact that it appears on a straight line. The sides of the angle are on separate positions compared to that of the vertex that appears also in a straight line.
Based on this explanation, we can see that ∠YZW appears on a straight line in the image that we have here.
Hence we would conclude by saying that The measure of ∠YZW is given as 180 degrees.
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The cost of 4 tables and 3 chairs is $695. If the table costs $25 more than the chair, find the cost of a
table.
Answer:
110 bucks
Step-by-step explanation:
4t+3c=695
c=t-25
4t+3(t-25)=695
7t=770
t=110
Use what you know about scientific notation to write the number -20,000 with a power of 10.
- 20,000
- 20,000=
(Type your answer in scientific notation using the appropriate symbol from the math palette for any multiplication.)
Help me solve this View an example Get more help.
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Question
The scientific notation to write the number -20,000 with a power of 10.
The scientific notation to write the number -20,000 with a power of 10 is -2 ×10⁴.
Given that
The number is -20,000To find
We have to find the scientific notation form of number -20,000So, according to the question
We have
The number = -20,000For finding the scientific notation form of given number, first we have to know about scientific notation with a power of 10.
Scientific notation with a power of 10
To write any number with the help of power of 10 in very easy way is telling Scientific notation with a power of 10 . Because in that universe there is a lots of smallest and largest number present, so we can't write every numbers in single page. To write that numbers in very easy way the scientists was create a way to write that numbers with the help of power of 10.
So, now we can convert that number in a form of Scientific notation.
n = -20,000
Now multiply [tex]\frac{10^4}{10^{4}}[/tex], we will get
n = -20,000 × [tex]\frac{10^4}{10^{4}}[/tex]
n = [tex]\frac{-20,000\times 10^4}{10000}[/tex]
n = - 2× 10⁴
The scientific notation with the power of 10 form of -20,000 is - 2× 10⁴.
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Use compatible numbers to estimate the whole number quotients 5320/61?
The whole number quotients of the expression; 5320/61 as required to be evaluated in the task content is; 88.
What is the best estimate of the whole number quotients of the expression; 5320/61 as given in the task content?It follows from the task content that the use of compatible numbers is to be used to estimate the whole number quotients 5320/61.
On this note, since the numbers can be written as follows;
= (53.2 × 100)/(0.61 × 100)
= 53.2/0.61
The estimate can therefore be determined by evaluating;
= 53/0.6
= 88 remainder 1.
Therefore, the closest estimate of the whole number quotients 5320/61 as given in the task content is; 88.
Ultimately, the whole number quotients of the expression; 5320/61 as required to be evaluated in the task content is; 88.
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Solve these absolute value equations.
18. |3р + 7| = 6p
The absolute value of the given statement is a -3/7 and 3/7.
According to the statement
We have to find that the value of the absolute equations.
So, For this purpose, we know that the
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
From the given information:
|3р + 7| = 6p
And we know that the
If we want to solve equations with absolute values we must know we have to find the solution for both positive and negative values. This is because positive and negative values have a positive absolute value.
Then
|3р + 7| = 6p
6p - 3p = 7
3p = 7
Then
p = 3/7.
According to the absolute value the answer become -3/7 and 3/7.
So, The absolute value of the given statement is a -3/7 and 3/7.
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can someone give me an answer ??
Answer:
150, 175, 4
Step-by-step explanation:
Multiply the amount of ammonia by 50 to get the amount of distilled water.
Conversely, divide the amount of distilled water by 50 to get the amount of ammonia.
The cost of purple dye has been increasing over the last few months, and Robyn uses this dye as part of her tie dye scarf business. She’s worried that it will continue to rise to the point where she no longer makes a profit on her scarf sales. She currently has a 20% profit margin ([price - unit costs]/price) and dye is currently 60% of unit costs. What is the lowest percentage increase in the cost of dye that would make Robyn’s scarves unprofitable?
The lowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%
How to calculate the percentage?(Price- Unit Cost)/Price= 20% or 0.2
Price- Unit Cost= 0.2 Price
0.8 Price = Unit Cost
Let Unit Cost be x
Price = x/0.8= 1.25x
Dye is 60% of unit costs= 0.6x
Cost of remaining material= 1 - 0.6x = 0.4x
Unit Cost= Cost of Dye+ Cost of remaining material
So, in order to become unprofitable, Unit Cost must be 1.25x
Therefore
1.25x= Maximum cost of dye+ 0.4x
Maximum Cost of Dye = (1.25-0.4)x = 0.85x
Percentage change in cost of dye= {(0.85x-0.6x)/0.6x}*100= 41.66 or 42%
Therefore, theowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%.
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stephanie added 20 more apps to get tablet, making the total more than 61. How many apps were originally on the tablet
In a case whereby stephanie added 20 more apps to get tablet, making the total more than 61 the number of apps that were originally on the tablet is [tex]a +20 > 61[/tex].
What is inequality?Inequality can be described as the statement that do follow some orderly relationship, it should be noted that this usually consist of greater than as well as greater than or equal to.
As regards the question, we will have a>61-20 then a>41
Therefore, In a case whereby stephanie added 20 more apps to get tablet, making the total more than 61 the number of apps that were originally on the tablet is [tex]a +20 > 61[/tex].
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NOTE; This is a complete question , no given option , even on internet.
<
Use the Venn diagram shown to list the set (An Bn C)' in roster form.
U
3
6
20
2
10
11
7
13
19
14
8
9
Answer:
A=(2,3,6,10,11)
B=(8,9,14)
C=(19)
(AnBnC) = {7,13}
Step-by-step explanation:
So, basically (n) means intersection which says that the elements of A, B, C being common come under
Please please please please please please please please please help me I don’t know this question asking questions like this like I’m in high school
Answer:
Multiplication -- > 6 × 3 - 8
Division --> (4 + 3)/2
Subtraction --> 4 - 5 + 7
Addition --> 15 + 8 ÷ 4 - 6
The height of a triangle is 4 ft less than the base x. The area is 126ft^2 find the dimensions of the triangle
The dimension of the triangle are base = 18 ft , height = 14 ft .
The area of a triangle is defined as the total area bounded by the three sides of a given triangle. It's basically equal to half the base multiplied by the height which is given by [tex]A=\frac{1}{2} \times b \times h[/tex] ..(1)It is given that height of a triangle is 4 ft less than the base x which can be represented as height = x - 4 ....(2) and base = x
Putting above values in equation (1) , we get
[tex]126=\frac{1}{2} \times(x-4)\times x\\252=x(x-4)\\252=x^2-4x\\x^2-4x-252=0[/tex]
On factorizing , we get
[tex]x^2-(18x-14x)-252=0\\(x^2-18x)+(14x-252)=0\\x(x-18)+14(x-18)=0\\(x+14)(x-18)=0[/tex]
On equating it with zero , we get
[tex]x+14=0\\x=-14[/tex]
as length cannot be in negative so , we will not consider this solution.
[tex]x-18=0\\x=18[/tex]
Using equation (2)
Height will be = 18 - 4 = 14 ft.
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Is -71/80 rational???????
It is rational because it is a fraction of two integers
-71 and 80 are those two integers
Answer:
Yes, it's rational because it's a fraction that terminates in decimal form.
Describe the continuity of the graphed function.
A. The function is continuous.
B. The function has a removable discontinuity at x=0.
C. The function has a jump discontinuity at x=0.
D. The function has an infinite discontinuity at x=0.
The correct option regarding the continuity of the function at x = 0 is given by:
A. The function is continuous.
What is the missing information?
The graph is missing, and is given at the end of this problem.
A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
From the graph of the function, at x = 0, we have that:
[tex]\lim_{x \rightarrow 0^-} f(x) = \lim_{x \rightarrow 0^+} f(x) = f(0) = 0[/tex]
Which means that the function is continuous at x = 0, hence option A is correct.
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Solve.
13. A rectangular picture frame has the dimensions shown in
the figure. Write a polynomial that represents the perimeter
of the frame.
5x-2
3x+1
Answer:
(5x-2)^2+(3x+1)^2
Step-by-step explanation:
find the value of y
Answer:
y = 11°
Step-by-step explanation:
Since it is a right angle, subtract 28 from 90 which equals 62.
Then, use the equation to find that 11 × 6 = 66, subtract 4, and it equals 62 too.
Which expression is equivalent to -51-(-60)?
A -51 + 60
B -60+51
C -51 -60
D -60 + (-51)
Solve: 3⁴ × 3² × 3³
...............................
Answer:
19,683
Step-by-step explanation:
3⁴ × 3² × 3³
Solve the exponents
81 x 9 x 27
Multiply each number and you get
19,683
4 is a rational number because it can be written as the fraction 4/1. True of false?
Answer:
true
Step-by-step explanation:
Graph the image of the figure using the transformation given.
Captionless Image
last 3 pics are the options
The reflection of triangle WXY across the x axis gives the points W'(0, 1), X'(3, -3) and Y'(2, 1).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
The reflection of a point across the x axis is given by the rule (x, y) ⇒ (x, -y). Triangle WXY have endpoints at X(3, 3), Y(2, -1) and W(0, -1).
The reflection of triangle WXY across the x axis gives the points W'(0, 1), X'(3, -3) and Y'(2, 1).
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Use the associative property of addition to rewrite (9+12)+20
Answer:
41
Step-by-step explanation:
Use the associative property of addition to rewrite 9+12+20 .
20+(11+5
Is a way to rewrite the associative property of 9+12(+20)
9x{[14÷2+(4‐1)]-8 can someone show step by step?
Answer:
82
Step-by-step explanation:
9 x {[14÷2+(4‐1)] - 8
9 x {[7 + (3)] - 8
9 x [7 + 3] - 8
9 x [10] - 8
90 - 8
82
I hope this helps!
A quadratic function is shown on the graph.
a downward opening parabola beginning with open circle at negative 3 comma negative 7 increasing to a vertex at 0 comma 2 and then decreasing to a closed circle at 2 comma negative 2
What is the range of the function?
{y | −7 < y ≤ 2}
{y | −7 ≤ y ≤ 2}
{x | −3 ≤ x ≤ 2}
{x | −3 < x ≤ 2}
The range of the quadratic function is shown on the graph.is {x | −3 ≤ x ≤ 2}
What is a quadratic function ?
A quadratic function is a type of function that has polynomials, if the polynomial in a quadratic function is of degree two then the polynomial is said to be quadratic. we can therefore say that quadratic functions are a special type of polynomials with a power of 2
The graph of a quadratic function is represented by a curve opening upward or downward, it may also open sideways depending on ow the values are chosen.
The range are the input values, they are on the x axis. Form the description of the graph the range is fount to be {x | −3 ≤ x ≤ 2}
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6 of 10
Factorise
x² - 12x - 220
After factorization, the factors are (x - 22) (x + 10).
What is factorization?In mathematics, factorization is the process of dividing a large number into smaller numbers that, when multiplied together, yield the original number. Factorization occurs when you divide a number into its factors or divisors. For example, the factorization of the number 12 could be 3 times 4. The Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes are the four main types of factoring.So, x² - 12x - 220:
x² - 12x - 220x² - x( 22 - 10 ) - 220x² - 22x + 10x - 220x(x - 22) + 10(x - 22)Factors: (x - 22) (x + 10)Therefore, the factors are (x - 22) (x + 10).
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