The solution of the differential equation t ln (t) dr/dt + r = 3te^t is r = (3/t) - 3e^(-t)/ln(t) + C/ln(t)
To solve the given differential equation:
t ln(t) dr/dt + r = 3te^t ...... (1)
Divide the equation (1) by t ln(t) then equation (1) chages to:
dr/dt + (1/t ln(t))r = 3e^t/t ln(t)
The given equation is a reducible linear differential equation to reduce in linear form we multiply by the integrating factor.
The integrating factor is given by:
μ(t) = e^∫(1/t ln(t))dt
= e^ln(ln(t))
= ln(t)
Thus,
ln(t) dr/dt + r ln(t) = 3te^t
d/dt (r ln(t)) = ln(t) dr/dt + r/t
Substituting this into the equation, we get:
d/dt (r ln(t)) = 3te^t/t
Integrate both sides;
r ln(t) = 3e^t ln(t) - 3e^t + C
r = (3/t) - 3e^(-t)/ln(t) + C/ln(t)
r = (3/t) - 3e^(-t)/ln(t) + C/ln(t)
hence, the solution of the differential equation is r = (3/t) - 3e^(-t)/ln(t) + C/ln(t), where C is a arbitrary constant.
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An expression is shown.
5(−4)
-2
Create an expression that is equivalent to the expression shown.
If we expand the bracket, -20 -2 = -22.
So the equivalent expression would be -22.
How can this expression be shown?The expression 5(-4) means to take the number -4 and multiply it by 5.
Since multiplication is distributive, this is the same as -4 * 5 which results in -20.
And -20 -2 is -22.
So the equivalent expression is -22.
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How many groups of ten make 120?
12
12 times ten is 120
Answer: 12 groups of ten makes it 120
Step-by-step explanation:
here one group consists of ten.
and to make 120 we will need 12 groups of ten.
Seven more than the product of a number and 3 is 8.
Answer:
x = 1/3
Step-by-step explanation:
Seven more than the product of a number and 3 is 8.
7 + 3x = 8
3x = 8 - 7
3x = 1
x = 1/3
-------------------
check7 + 3 x 1/3 = 8 (remember PEMDAS)
7 + 1 = 8
8 = 8
the answer is goodHow do you write coordinates in quadratic form?
To write coordinates in quadratic forms,
Obtain the equation y = ax2 + bx + c.Determine -b / 2A. The vertex's x-coordinate is given here.Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate. The vertex's y-coordinate is given here.What is coordinate quadratic function?When a quadratic equation is written in standard form, the vertex's coordinates are (-b/2a, f(-b/2a)), where x = -b/2a and y = f(-b/2a). This suggests that the formula x = -b/2a should be used to determine the x-value of the vertex in the equation y = -3x2 + x + 1. The equation for a straight line, y = mx + c, is one of the key coordinate geometry formulas. The angle that the line makes with the positive x-axis is represented by the symbol, where m is the slope and c is the y-intercept (tan = m).When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point.To learn more about quadratic form refer to:
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What are the 4 transformations of a function?
The four transformations of a function are translation, reflection, stretching/shrinking, and rotation.
What is function?Function is a group of related statements that perform a specific task. It is a block of organized, reusable code which can be used to perform a single, related action. Functions help make code more reusable and efficient. It also reduces the complexity of a program by breaking it down into smaller and simpler parts.
Translation involves shifting the graph of a function along a given axis; reflection involves flipping the graph of a function about a given axis; stretching/shrinking involves changing the scale of a graph along a given axis; and rotation involves rotating the graph of a function about a given point. All of these transformations can be used to modify the graph of a function, allowing for a variety of different outputs.
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NEED HELP ASAP!!!!!!!!
Answer:
A = 5, B= 4, C = 2, D = 1, E= 3
Step-by-step explanation:
x^5 times x^8 = x^13 following the x^n times x^m = x^n+m [rule]
The 1 and 3 for D and E satisfy this. Each number is used only once.
Hope this helps!
Solve for x.
5.3 > x + 2/5
Responses
x < 5 7/10
x > 5 7/10
x < 4 9/10
x > 4 9/10
Answer:
your answer is D
Step-by-step explanation:
I literally just finished the quiz on edge
Which of the following is a trinomial ?(а) -7z(b) z² – 4y²(c) x²y – xy² + y²(d) 12a – 9ab + 5b – 3.
As we know that Trinomial means a polynomial with three terms.
Therefore, option (c) x²y -xy² +y² is correct.
Given polynomials are:
(а) -7z
(b) z² – 4y²
(c) x²y – xy² + y²
(d) 12a – 9ab + 5b – 3.
To Find : Which one is Trinomial.
Monomial:
A monomial is defined as an expression with one non-zero term. It consists of various parts such as variables, coefficients and orders. A unary variable is the character it contains. A coefficient is a number that is multiplied by a monomial variable. The monomial degree is the sum of the exponents of all variables.
Binomial:
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each has a Boolean result of Success (probability p) or failure. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
Trinomial:
A ternary expression is an algebraic expression with three terms. An algebraic expression consists of variables and constants in one or more terms. These expressions use symbols or operations such as +, –, ×, and ÷ as separators. Trinomials fall into this algebraic expression, along with monomials, binomials, and polynomials.
In Short :
Monomial - A polynomial with single Term
Binomial - A polynomial with 2 terms
Trinomial - A polynomial with 3 terms
Based on the information:
(а) -7z only one term hence Monomial
(b) z² – 4y² Two terms Hence Binomial
(c) x²y – xy² + y² Three terms hence Trinomial
(d) 12a – 9ab + 5b – 3. Four terms hence quadrinomial.
So correct option is c) x²y – xy² + y²
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What is the exponential form of 8 * 8 * 8 * 8?
Answer:
8^4
Step-by-step explanation:
suppose you spend $180 on equipment to make a new board game. In addition, each game costs $2 to make. After doing market research, you determine that the games will sell or $20 each.
what is the y-intercept of the cost equation?
Answer:
The y-intercept of an equation is the point where the line crosses the y-axis, i.e when x = 0.
In this case, the cost equation is C = 2x + 180, where C is the total cost and x is the number of board games produced.
So when x = 0, C = 2(0) + 180 = 180
Therefore, the y-intercept of the cost equation is (0,180)
So the y-intercept of the cost equation is 180.
Answer:
90
Step-by-step explanation:
Judy need 2/3/4 yard of flannel to ew a kirt. She obtain 3/8 yard of flannel from the local market. How much more fabric doe he need to titch the kirt?
Judy needs 1 5/8 yards area more of flannel to stitch the kirt.
To find how much more fabric Judy needs, we need to subtract the amount she already has from the amount she needs.
Judy needs 2/3 yard of flannel
Judy has 3/8 yard of flannel
To subtract these fractions, we first need to convert them to the same denominator.
2/3 yard = 4/6 yard
3/8 yard = 6/8 yard
4/6 yard - 6/8 yard = (24 - 24)/48 = 0/48
To simplify, 0/48 = 0
Therefore, Judy needs 0 yards more of flannel.
However, Judy needs 2/3 yard of flannel to stitch the kirt. Since she has 3/8 yard, we can subtract the two to find how much more fabric she needs.
2/3 yard - 3/8 yard = (16 - 12)/24 = 4/24
To simplify, 4/24 = 1/6
Therefore, Judy needs 1 1/6 yards area more of flannel to stitch the kirt.
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What's a substitution property?
Substitution property is a property in algebra that helps in substituting the value of a quantity/variable into an algebraic expression to solve a given mathematical problem.
The substitution property is a notion in algebra that is used for substituting the value of a given variable or a quantity into an expression to find the value of the unknown.
In other words, we can express that the substitution property is utilised to replace the value of a quantity in an equation or an expression to solve a mathematical problem.
For example, Using the substitution property of equality, find the value of the algebraic expression g(x) = sin x + cos x if x = 45°.
We will replace x with 45° in the expression. So we have
g(45°) = sin 45° + cos 45°
= 1/√2 + 1/√2
= 2/√2
= √2
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Help With Both Please!
Answer:
1. (0,2)
2. (-2,-1)
Step-by-step explanation:
1.
y = 2x + 2
y = x + 2
2x + 2 = x + 2
2x = x
x = 0
Now we put 0 back in for x and solve for y
y = 2(0) + 2
y = 2
So, our answer for Q1 is (0,2)
2.
y = 3x + 5
y = -x - 3
3x + 5 = -x - 3
4x + 5 = -3
4x = -8
x = -2
Now we put -2 back in for x and solve for y
y = 3(-2) + 5
y = -6 + 5
y = -1
So, our answer for Q2 is (-2,-1)
How many solutions are there for 12x 1 3 4x 1 )- 2?
The equation have infinite solutions.
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
We can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.
12x + 1 = 3(4x + 1) - 2
12x + 1 = 12x + 3 - 2
12x + 1 = 12x + 1
The equation have infinite solutions.
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How many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2
Does 17 15 8 Make a right triangle?
It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 17 and 15.
17 + 15 > 8
32 > 8
Now we add 17 and 8
17 + 8 > 15
25 > 15
Now we add 15 and 8
15 + 8 > 17
23 > 17
It is possible to construct a triangle whose sides are 17 cm 15 cm and 8 cm because the sum of two sides are greater than third sides.
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I need help with this question
Answer:
the answer is C should be
Step-by-step explanation:
the answer is C should be, I'm in middle school btw
Yesterday a chef used 30 eggs to make 6 chocolate souffles and 6 lemon meringue pies. The day before, he made 4 chocolate souffles and 8 lemon meringue pies, which used 24 eggs. How many eggs does each dessert require?
Answer:
Let the chocolate souffles be x and lemon meringue pies be y.
For yesterday, it will be 6x+6y=30
For the day before, 4x+8y=24
By solving the two equations, the answers will be obtained.
4 eggs is required for chocolate souffles and an egg for lemon pie.
How do I find the solution to a system?
If the system consists of 2 variables we can use the method of elimination or substitution to get the answer easily.
In the method of elimination from the two given sets of equations, we make one of the coefficients of a variable the same so that when in the next step when we will subtract them they will get canceled out and we will get the value of one of the variables which after substituting in one of the equation we'll get the value of another variable.
If we have more than 2 variables the method of row reduction using a matrix is the best way to solve the system. In the system we make an augmented matrix of the coefficients of the variables and row reduce them in such a way that when we multiply the matrix with the row matrix we get the values of the variables easily.
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DECIDING WHETHER A FUNCTION IS INCREASING, DECREASING, OR CONSTANT
Some recent studies suggest that a teenager sends an average of 60 texts per day.[2] For each of the following scenarios, find the linear function that describes the relationship between the input value and the output value. Then, determine whether the graph of the function is increasing, decreasing, or constant.
The total number of texts a teen sends is considered a function of time in days. The input is the number of days, and output is the total number of texts sent.
A teen has a limit of 500 texts per month in his or her data plan. The input is the number of days, and output is the total number of texts remaining for the month.
A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month. The input is the number of days, and output is the total cost of texting each month.
According to given data, we can prove that Statement 1 is increasing function, Statement 2 is Decreasing Function, and Statement 3 is Constant Function.
1. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts sent) is y = 60x, where y is the total number of texts sent and x is the number of days. The graph of this function is increasing because as the number of days increases, the total number of texts sent also increases at a constant rate of 60 texts per day.
2. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts remaining for the month) is y = 500 - 60x, where y is the total number of texts remaining for the month and x is the number of days. The graph of this function is decreasing because as the number of days increases, the total number of texts remaining for the month decreases at a constant rate of 60 texts per day.
3. The linear function that describes the relationship between the input value (number of days) and the output value (total cost of texting each month) is y = 50, where y is the total cost of texting each month and x is the number of days. The graph of this function is constant because the cost of texting is the same regardless of the number of days.
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Factor the following expression
x²- 15 x 56 =
Multiply the numbers X²-15x56
x²-840
What is factor expression?A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and yWrite each term as the. prime factorization. of the coefficient or constant, listing any variables separately. For example, write. x. y. as. x. y. , and write. x. as. x. x. .Identify the factors that all of the terms have in common.Multiply those common factors.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).To learn more about factor expression refers to:
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What is the value of the missing angle?
Answer: Missing angle= 42°
Step-by-step explanation:
Since the whole angle is a right-angled triangle the angle will obviously be 90 degrees therefore subtract the given value in order to find the missing angle.
Missing angle= 90°- 48°
= 42°
Lisa worked 26 hours last month and earn seven dollars per hour she spent $17 on her earring since then how much money does she have left?
After spending $17 the amount of money left with Lisa is $165.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Lisa worked 26 hours last month.
For each hour she earns $7.
Total earnings of Lisa in last month is equated as -
Earning = 26 × 7
Earning = $182
She spent $17 dollars on earring.
The amount of money left with her is equated as -
Total Earning - Money spent
Money Left = 182 -17
Money Left = $165
Therefore, the money left with Lisa is $165.
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I need helppppppppppp
Answer:
$4.45
Step-by-step explanation:
First, we try to find the slope of the table. We can do this by doing the following- [tex]\frac{Change \ in \ y }{Change \ in \ x}[/tex]
When we do this, we find that the slope (or the change in y / change in x) is equal to 5.27
Now we subtract this from the slope of the price of steak at Store B which is 9.72
[tex]9.72-5.27 = 4.45[/tex]
You get 4.45 which is $4.45 or 4 dollars and 45 cents.
Suppose that l is a tangent line to this circle which is parallel to the line y=5x+7 and has a negative y intercept. Then the point of tangency of l with this circle is.
A. The equation of a tangent line to the circle through the point (- 6 , 8) is y = 0.75x + 12.50
B. The point of tangency of L with the circle is (9.81 , - 1.96).
The full question is in the attachment. The equation of a tangent line to the circle with radius r centered at the origin through the point (p , q)
r = 10 p = - 6 q = 8px + qy = r²
- 6x + 8y = 10²
8y = 6x + 100
y = 6/8x + 100/8
y = 3/4x + 25/2
y = 0.75x + 12.50
The equation line y = mx + c has the slope or the gradient m. If two lines are parallel, the two lines have the same slope.
y = 5x + 7
m = 5m of L = 5 because parallelThe tangent line L to the circle with the gradient m and radius r
[tex]y \:=\: mx \pm r \: \sqrt{1 \:+\: m^2}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 5^2}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 25}[/tex]
[tex]y \:=\: 5x \pm 10 \: \sqrt{26}[/tex]
Because L has a negative y-intercept, it means when x = 0, y is negative. So the equation L
[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]
The point x of tangency of L with the circle
x² + y² = r²
x² + (5x - 10 √26)² = 10²
x² + 25x² - 100√26 x + 2,600 = 100
26x² - 100√26 x + 2,500 = 0
a = 26b = - 100√26c = 2,500[tex]x_{1.2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}[/tex]
[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{(- 100 \sqrt{26})^2 \:-\: (4 \times 26 \times 2,500)}}{2 \times 26}[/tex]
[tex]x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{260,000 \:-\: 260,000}}{52}[/tex]
[tex]x \:=\: \frac{100 \sqrt{26}}{52}[/tex]
[tex]x \:=\: \frac{50 \sqrt{26}}{26}[/tex]
x = 50/26 × √26
x = 9.81
The point y of tangency of L with the circle
[tex]y \:=\: 5x \:+\: 10 \: \sqrt{26}[/tex]
[tex]y \:=\: 5 \times \frac{50 \sqrt{26}}{26} \:+\: 10 \: \sqrt{26}[/tex]
[tex]y \:=\: \frac{250 \sqrt{26}}{26} \:+\: \frac{260 \sqrt{26}}{26}[/tex]
[tex]y \:=\: \frac{- 10 \sqrt{26}}{26}}[/tex]
y = - 10/26 × √26
y = - 1.96
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What is the process for converting 2D data to 3D data?
The process for converting 2D data to 3D data involves a few steps. First, a 3D model needs to be created, which is typically done using a 3D modeling software such as Blender or 3DS Max.
What is data?Data in math is information that can be used to draw conclusions or make decisions. It is typically collected, analyzed, and presented in the form of numbers, graphs, or tables. Data can be used to compare and contrast different scenarios, identify trends and patterns, or make predictions about the future. Data can also be used to help researchers develop hypotheses and develop models to explain phenomena.
Once the model is created, the data needs to be imported into the software in a format that can be used by the software, such as an .obj or .3ds file. The data can then be manipulated within the software to create the 3D model. Finally, the 3D model can be exported in a variety of file formats, such as .stl, .fbx, or .dae, that can be used for 3D printing, virtual reality, and other applications.
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What is the exponential form of 2 * 2 * 2 * 2 * 2?
Abebi,bella and chuku hare $112. Abebi receive $x. Bella receive $12 le than Abebi. Chuku receive twice a much a bella
From an equation in x and olve it to find how much abebi receive
By solving the linear equation in x Abebi receives $37.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.
On identifying the information given in the problem we have:
Abebi, Bella, and Chuku share $112. Abebi receives $x. Bella receives $12 less than Abebi. Chuku receives twice as much as Bella.
On setting up an equation using the information given:
We know that the total amount shared is $112 and we want to find out how much Abebi receives, represented by x.
We know that:
Bella receives $12 less than Abebi =(x - 12)
Chuku receives twice as much as Bella =(2 * (x - 12))
So we can set up the equation as:
x + (x - 12) + (2 * (x - 12)) = 112
On simplifying the equation:
x + x - 12 + 2x - 24 = 112
Combining like terms:
4x - 36 = 112
On solving for x we get:
Add 36 to both sides:
4x = 148
Divide both sides by 4:
x = 37
On interpreting the solution we get:
By solving the linear equation in x Abebi receives $37.
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what is a definition of a circle
Answer:
A round-shaped figure with no corners or edges.
Step-by-step explanation:
Answer: A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Step-by-step explanation:
How do you change to base 5?
Change to base 5 can be done by dividing the decimal number by 5 and then taking the remainder of the division in reverse order.
The number base is the number that forms the basis for the formation of other numbers in a number system.
The number base that we use a lot every day is the decimal system, which consists of 10 numbers, from 0 to 9. This decimal system is usually called the base 10 number system. Apart from base 10, there are also other base systems, for example, base 2 (biner system), 8 (octal system), and 16 (hexadecimal system) which are usually used in computer / digital systems.
Change of base 10 numbers to other base numbers is done by:
dividing the decimal number by the intended base number, writing the remainder down, repeating the division until the remainder is zero, taking a look at the remainder in reverse order.For example, we want to change 214₁₀ to a base 5 number:
214 : 5 = 42 remainder 4
42 : 5 = 8 remainder 2
8 : 5 = 1 remainder 3
1 : 5 = 0 remainder 1
Thus 214₁₀ = 1324₅
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How do you find the equation of a line with 2 points in Class 10?
Steps to find the equation of a line with 2 points mentioned below:
What is equation of line?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.
To determine a line's equation from two points following steps are there:
1. Determine the slope and used the slope formula.
Slope(m) = (y₂ - y₁) / (x₂ - x₁)
2. To determine the y-intercept, use the slope and one of the points(b).
The x and y in your equation y = mx + b may be replaced by one of your locations, and the m can be replaced by the slope you just computed. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.
3. Once you have the values for m and b, you can use them to solve for the line's equation in the slope-intercept form (y = mx + b).
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