I'm guessing the equation should read something like
[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]
or possibly with minus signs in place of +.
Multiply both sides by [tex]\frac1{x^2}[/tex] to get
[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]
Now substitute
[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]
to transform the equation to
[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]
which simplifies to
[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]
The ODE is now separable.
[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]
Integrate both sides. On the left, substitute
[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]
[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]
[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]
[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex].
[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]
[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]
[tex]w^{5/24} = \dfrac Cx[/tex]
Put this back in terms of [tex]v[/tex].
[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]
Put this back in terms of [tex]y[/tex].
[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]
Solve for [tex]y[/tex].
[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]
[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]
[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]
[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]
Prove that x² - 2px + 2p² is non-negative for all real values of x.
[tex]x^2-2px+2p^2 \\ \\ =(x^2-2px+p^2)+p^2 \\ \\ =(x-p)^2+p^2[/tex]
Assuming [tex]p \in \mathbb{R}[/tex], [tex](x-p)^2 \geq 0[/tex] and [tex]p^2 \geq 0[/tex], meaning that [tex](x-p)^2+p^2 =x^2-2px+2p^2 \geq 0 \forall x \in \mathbb{R}[/tex]
A 50centimeter picece of wire is bent into a cricle. What is the area of this cricle?
The area of the circle is 1962.5cm²
What is area of a circle?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr², (Pi r-squared) where r is the radius of the circle.
The length of the wire will be the diameter of the circle. Therefore the radius of the circle = 50/2 = 25 cm
Area of a circle is given as = πr²
A = 3.14×25×25
A= 1962.5 cm²
Therefore the area of the circle when a length 50cm of wire is bent into circle is 1962.5cm²
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Gwen can a photo that i 4inche wide by 6 inche long into her computer. If he cale the length down to 3inche how wide hould the imilar photo be?
The width of a similar photo will be 2 inches.
As per the given problem,
Width of original photo = 4 inches
Height of original photo = 6 inches
After scaling the photo,
Height of new photo = 3 inches.
Let’s understand about scale factor.
An amount that multiplies (or "scales") a quantity is called a scale factor.
Scale factor = height of the sized image/size of the original image.
Scale factor = 3/6 = 1/2.
Therefore, the scaled image's width = scale factor *the size of the original image.
The width of the scaled photo = (½)*4 = 2.
Hence, the width of a comparable image measures 2 inches.
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Find the area of a circle with a radius of 21 inches. Use
area: about
in.
22/7
for π.
Answer:
[tex]1386 in^2[/tex]
Circle Formulasr: radius
Circumference: [tex]2\pi r[/tex]
Area: [tex]\pi r^2\\[/tex]
In this case, we are using 22/7 as an estimation for pi.
Q)Plug into the area formula.
22/7 * (21)^2
22/7 * 441
[tex]1386 in^2[/tex]
stressed bc test due tonight help plese ty
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:
y < 2x + 4.
ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.
iii) | x + 3 | = y, you can split this into two cases:
i. x + 3 = y
ii. -(x + 3) = y
iv) |2x – 6| + 2 = y, you can split this into two cases:
i. 2x - 6 + 2 = y
ii. -(2x - 6) + 2 = y
We can use these equations to plot the graph on a coordinate plane.
Hence, the solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
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The corresponding angles in these polygons are congruent.
struggling please help I'll mark brainliest
What is the solution to the inequality |2x + 3| < 7?
4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2
Answer:
its the second one: -5<x<2
Step-by-step explanation:
I did out the math
Which of the following equations have an -intercept of (-2, 0) and y-intercept of (0, 3)?
Select all that apply.
y=3/2x+3
y=3x-2
2y-3x=6
y=-2x+3
y-1=-2(x+3)
Answer:
The first and third choices
[tex]y = \dfrac{3}{2}x + 3[/tex]
and
[tex]2y-3x=6[/tex]
Step-by-step explanation:
(I cannot properly see the leading negative signs in choices 4 and 5, I copied/pasted your question choices from Brainly post and zoomed)
First understand what x and y intercepts are
The y-intercept is the value of y where the graph of the equation crosses the y-axis, It is the value of y when x = 0
The x-intercept is the value of x where the graph of the equation crosses the x-axis, It is the value of x when y = 0
We are given that the x-intercept is (-2, 0) and y = (0,3)
We can use a process of elimination to get rid of obviously incorrect choices and then work on the possible correct ones depending on whether we come up with the correct values of y first and eliminating those that do not match x =0, y =3 or (0,3) and then see if the x-intercept is (-2,0)
First choice let's find the y-intercept for the first choiceFind the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4
units up on the parent function f(x)=x²
a. f(x)=(x-5)² +4
8
6-
4
2+
864 -2
-2
L
19
do
+
Mark this and return
+
b. f(x) = (x+3)² + 2
2 4 6
C. f(x)=(x-3)² +4
N
864
d. f(x)=x²-4
2+
-2
4
Top
+
2 4 6
3+
Next
Submit
Answer:
C. f(x) = (x - 3)² + 4
Step-by-step explanation:
Given parent function:
[tex]f(x)=x^2[/tex]
When a graph is translated "a" units right, subtract "a" from the x-value of the function.
Therefore, the translation of the parent function 3 units right is:
[tex]\implies f(x-3)=(x-3)^2[/tex]
When a graph is translated "a" units up, add "a" to the function.
Therefore, the translation of the function 4 units up is:
[tex]\implies f(x-3)+4=(x-3)^2+4[/tex]
i forgot how to it can i please get some help2x+1 + x+6=
Answer:
3x+7
Step-by-step explanation:
You need to combine like terms. Add 2x + x. It is 3x add the six and the one to make seven \
Hope this helps
Answer:
3x+7
Step-by-step explanation:
First, you want to group the variables, which in this case, is x. You take the 2x and x and make it 3x.
3x+1+6
Now that you have this done, you want to group the numbers, by making the 1+6 to 7.
3x+7
This is your answer, 3x+7.
the perimiter of a rectangle is 30 inches. if its length is three times its width, find the dimensions
The answer is l = 3.75 and l = 11.25.
Given the length l and width w of a rectangle, its perimeter is:
P=2(l+w)
This formula can be used to form an equation as we already know the value of P.
So, Let the width be w. The length will be 3w. As the perimeter is 30 inches, the width can be found as follows.
2(w+3w)=30
4w=15
w=3.75
Thus, the width is 3.75 inches. The length will be 3*3.75=11.25 inches.
Steps:
Step 1: Let the width of the rectangle be w. Step 2: Since the length is 3 times the width, the length of the rectangle is 3w. Step 3: The perimeter of the rectangle is 30 inches. Step 4: We can write the formula for the perimeter of the rectangle as 2w + 2(3w) = 30. Step 5: Solve for w, then we get w = 3.75Step 6: therefore l = 3w = 3.75 * 3 = 11.25.To know about the Parameters of Rectangle:
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3/1107
Long division please show work! Tysm
ninas garden is 4 1/5 meters long 3/10 meters wide . what is the area of ninas garden? please help asap
Based on the information provided, the area in Nina's garden is 0.26 square meters.
What is the area?The word area refers to the space occupied by a surface, in this case, the space of the garden. In a rectangle, this area can be calculated with the following formula, although for other shapes the formula might be different:
area = length x width
What is the area of the garden?To make this process easier, let's convert the fractions into regular numbers
4 1/5 = 4.2 (1/5 = 0.2)
3/10 = 0.3
4.2 x 0.3 = 1.26 square meters
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What is the formula of a triangular method?
The formula for a triangular method is: (x1 + x2 + x3) / 3
1. The triangular method is the average of three different values: x1, x2, and x3.
2. To calculate the average, add the three values together and divide by three.
3. The formula for a triangular method is therefore (x1 + x2 + x3) / 3.
The triangular method is a method used to calculate an average of three different values. This method is most useful when there is not enough information available to calculate a more accurate average. To calculate an average using the triangular method, the three values (x1, x2, and x3) are added together and then divided by three. The formula for a triangular method is (x1 + x2 + x3) / 3. This method is useful for finding an average when a more accurate average cannot be calculated due to a lack of data. It is also used when data points are not necessarily related, as the triangular method is less affected by outliers than other methods of calculating an average. The triangular method is a quick and easy way to find an average when more complex calculations are not possible.
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cosec⁴A-cosec ²A=cot ⁴A-cot ²A
from the internet it's different and i did in in this way :
cosec ²A)²-cosec ²A
1+cot ⁴A-2cot²A-1+cot ²A(1-1=0)(2cot ²A-cot ²A=cot ²A)
cot ⁴A-cot ²A
Therefore , the solution of given trigonometric equation has been proved.
The trigonometric equation is what?A trigonometric equation is one that contains one or more ratios of unknown trigonometric angles. The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it. A trigonometric equation is cos2 x + 5 sin x = 0, for instance.
Here,
Given :
Cosec A cosec²A cot A+ cot² A
LHS=(1+cot2A)2- (1 + cot2 A)
=1+2cot2A+cot A-1- cot2 A
= cot2A+ cot1A
= RHS
Hence, Cosec1A- cosec² A = cot ⁴A-cot ²A
Therefore , the solution of given trigonometric equation comes out to be it has been proved
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Is the absolute value of a complex number real?
The absolute value of a complex number is real.
The absolute value of a complex number is also known as its magnitude. It is a non-negative scalar quantity that represents the distance of the complex number from the origin in the complex plane.
The absolute value of a complex number is represented by the symbol "|z|" where z is the complex number.
The absolute value of a complex number is always a real number. For example, the absolute value of the complex number 4 + 3i is 5 (the distance of this point from the origin), which is a real number.
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Solve this problem using 45-45-90
The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners.
given
Let's say we don't know the triangle's hypotenuse and that angle A is approximately 33.56.
Cos and Cos-1 are available. Make sure it is set to degrees.
Cos(33.56)=6750/h
h=8100.25
The right angled triangle's side measures 19, its hypotenuse is approximately 8100.25.
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please help its for a test and I need these done so I can be free. its due tonight and I did this all day
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
An inequality is defined as an unfair comparison between two numbers or other mathematical expressions. When comparing the sizes of two numbers on a number line, it is most commonly used. The graph for each inequality or equation is included in the attachment.
What is graph?A graph is a visual representation of statistical data or a functional relationship between variables. Graphs are useful for forecasting because they can highlight broad trends in the quantitative behaviour of data. However, as mere approximations, they can be inaccurate and occasionally deceptive.
Most graphs have two axes: one for a set of independent variables and one for a set of dependent variables. The most common type of graph is a broken-line graph, with time serving as the independent variable.
16. 2y – 4x < 8
= 2y < 4x + 8
= y < 2x + 4
17. -4y > -x + 12
= y > x/4 + -3
18. | x + 3 |= y
y = | x + 3 |
19. |2x – 6| + 2 = y
y = |2x – 6| + 2
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Convert this equation into standard form
The standard form of the given linear equation is; -x + 3y = 15
How to write the Linear Equation in standard form?The standard form of a linear equation is expressed in the form;
Ax + By = C
Now, we are given the equation as;
y - 4 = ¹/₃(x + 3)
Multiply through by 3 using multiplication property of equality to get;
3y - 12 = x + 3
Add 12 to both sides to get;
3y = x + 15
Subtract x from both sides to get;
-x + 3y = 15
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What is substitution method formula?
Particularly there is no formula for substitution just insert the given values in the equations.
One of the methods to solve a system of linear equations in two data algebraically is the substitution method. In this method, we find the value of any one of the variables by discordant it on one side and taking every other term on the other side of the equation.
This method is a simple way to resolve a system of linear equations algebraically and find the answer to the variables.
As the name suggests, it involves finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or exchanging the value of the x-variable in the second equation.
The substitution method is one of the algebraic methods to solve coincident linear equations. It concludes by substituting the value of any one of the variables from one equation into the other equation.
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what is equivlent to 4/9x7
Answer:
Step-by-step explanation:
The expressions that are equivalent to 4/9 x 7 are 28/9, 3¹/₉ and 3.11
As no options are included, I will include the expression that is equivalent to 4/9 x 7 in both fractions and decimal.
In fractions:
= 4/9 x 7
= 28/9
or,
= 3¹/₉
In decimals:
= 4/9 x 7
= 28/9
= 28 ÷ 9
= 3.11
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A garden in the shape of a square measures 15 feet on each side. A triangular paved patio is in the center.
The area occupied by the garden is 185 square feet.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given:
Base = 10 feet, height = 8 feet
First, Area of Garden without patio
= 15 x 15
= 225 square feet.
Now, The patio is in the shape of a triangle which has a height of 8 feet and a base length of 10 feet.
So, Area of triangular patio
= 0.5 x 8 x 10
= 0.5 x 80
= 40 square feet.
Then, Actual Area of garden
= area of garden without patio - area of patio
= 225 square feet - 40 square feet
= 185 square feet.
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What is table of numbers?
A table of numbers is a collection of numbers arranged in a specific format, usually in rows and columns.
Write the uses of table of numbers.The numbers in the table can represent various types of data, such as measurements, counts, or statistical values. Tables of numbers can be used to organize, compare, and analyze data in a clear and easy-to-read format. They are often used in fields such as math, statistics, and data analysis. Tables can be created using spreadsheet software, or they can be created manually using a pen and paper. The table can be used to represent a function, a data set, a matrix or a multiplication table, etc
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Complete question is: What is table of numbers?
Which quadrant the point p(2,3) and q(-3,2) lie?
The given points lies in the following quadrant :
Point P ( 2,3 ) lies in first quadrant and point Q( -3,2 ) lies in the second quadrant.
As given in the question,
Given points are as follow:
Coordinates of point P are ( 2, 3)
Coordinates of point Q are ( -3, 2)
Sign of coordinates in each quadrant of the coordinate plane:
Let ( x, y) be the coordinates.
First quadrant : ( x , y) both are positive
Second quadrant : ( -x , y)
Third quadrant : ( -x , -y )
Fourth quadrant : ( x , -y )
Point P( 2,3) represent both are positive:
Point P lies in the first quadrant.
Point Q(-3,2) represent (-x ,y).
Point Q lies in the second quadrant.
Therefore, point P (2,3) lies in the first quadrant and point Q(-3,2) lies in the second quadrant.
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What are the factors of 10m?
Answer:
1, 2, 5 and 10
Step-by-step explanation:
Step-by-step explanation:
1x10
2x5
4x5
.................
Josh collected 2 pounds of plastic during the park clean up. Sherri collected 1 ¾ times as much as Josh.
How many pounds of plastic did they collect together?
Therefore , the solution of the given problem of unitary method comes out to be 3.5.
A unitary method is exactly what?One can utilize the unit strategy to solve a problem by first multiplying the value of one unit by the quantity of units required. The unit function, to put it simply, is used to separate a single entity amount from just a given many. 400 pence, or the equivalent of one pen, would buy 40 needles. There might be a common approach to determining this. only one country. Anything has a distinguishing feature. Matrix logic, algebra, and its interpellation & inverse are all comparable terms.
Here,
Given : Josh gathered 2 pounds of plastic while cleaning up the park.
Josh received 1 ¾ times as much money from Sherri.
thus ,
To find the total plastic collected by both of them:
=> 1 ¾ * 2 + 2
=> 7/4 * 2
=> 14/4
=> 7/2
=>3.5
Therefore , the solution of the given problem of unitary method comes out to be 3.5.
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Is y² 5y 10 a quadratic equation justify?
Yes, y² = 5y - 10 is a quadratic equation.
In algebra, a quadratic equation is that which can be rearranged in standard form as
ax² + bx + c = 0,
where x is an unknown value, and a, b, and c are known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear). Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
We have the equation
y² = 5y - 10
y² - 5y + 10 = 0
The highest degree of this equation is 2, therefore it is a quadratic equation.
-- The given question is incorrect, the correct form of equation is
"Is y² = 5y - 10 a quadratic equation justify?" --
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HELPPPP PLEAAAASE I HAVE NO IDEA WHAT IM SUPPOSED TO DOOOOO
Answer:
[tex]\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]
Step-by-step explanation:
This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.
I presume your school has provided you the resources for both.
Anyways, here goes a brief explanation
To find the roots(zeros) of a polynomial, [tex]f(x)[/tex] , set [tex]f(x) = 0[/tex] and solve for values of [tex]x[/tex]
In general, if [tex]a[/tex] is a zero of [tex]f(x)[/tex], then [tex]f(x) \div(x-a)[/tex] will leave no remainder. In other words, it is a factor of the polynomial. It also means [tex]x - a = 0[/tex]
The given polynomial is [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
We are given that [tex]- 2[/tex] is a zero of [tex]f(x)[/tex]. This simply means that [tex]f(-2) = 0[/tex]
Plugging [tex]-2[/tex] into the function gives
[tex]f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30[/tex]
Which indeed is 0
Here [tex]a = -2[/tex] , so [tex]x - (-2)[/tex] which is [tex]x + 2[/tex] is a factor of[tex]f(x)[/tex]. It also means that
[tex]x-(-2) = 0 \;or\; x + 2 = 0[/tex]
Steps to factor the polynomial [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] :
Divide [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex] by [tex]x+2[/tex]Multiplying both sides of the above by [tex]4[/tex] gives [tex]4x -3 = 0.[/tex] So [tex]4x-3[/tex] is the third factor, replacing [tex]x - \dfrac{3}{4}[/tex]
The factors of [tex]4 x^{3} - 15 x^{2} - 31 x + 30[/tex]
are:
[tex]x+2, x-5 \;and \;4x-3[/tex]
Answer:
[tex]\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}[/tex]
Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)
Two angles are complementary the difference between four times the measure of the smaller angle and the measure of the larger angle is 10 what is the measure of the larger angle
The measure of the larger angle is obtained as follows:
70º
What are complementary angles?Two angles are defined as complementary is the sum of their measures is of 90º.
The variables that represent each angle in this problem are given as follows:
x and y.
They are complementary angles, hence:
x + y = 90.
The difference between four times the measure of the smaller angle and the measure of the larger angle is 10, hence:
4y - x = 10.
x = 4y - 10.
Hence the value of y is obtained as follows:
4y - 10 + y = 90
5y = 100
y = 100/5
y = 20º.
Hence the measure of the larger angle is given as follows:
x + 20 = 90
x = 70º.
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Which of the following are factors of 56? A.4 B.6 C.7 D.9 E.10
Answer:
Step-by-step explanation:
A and C will both work. 4 goes into 56 evenly and so does 7.