Answer:
The length of AD is 5 units
Step-by-step explanation:
Verify that y=e^xy is an implicit solution of the differential equation (1-xy)y'=y^2
Yes, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
Here,
The differential equation (1-xy)y' = y^2
And, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2.
What is Differential equation?
A differential equation is a mathematical equation that relates some function with its derivatives.
Now,
To show y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2, we have to find the solution of differential equation.
The differential equation is;
[tex](1-xy)y'=y^2\\\\\\\\[/tex]
[tex](1-xy) \frac{dy}{dx} = y^2[/tex]
[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]
It is form of [tex]\frac{dx}{dy} + Px = Qy[/tex],
Where, P is the function of y and Q is the function of x.
Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]
The solution is;
[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]
[tex]xy = lny + c[/tex]
Take c = 0, we get;
[tex]xy = lny\\\\y = e^{xy}[/tex]
Hence, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
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Equivalent expression
4 x 6 x 7
Answer:
168
Step-by-step explanation:
4x6=24
24x7=168
HELP ME PLEASE TY
Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.
Explain the concept of rational numbers.?It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.
It is possible when decimals and numbers have worked effectively.
In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.
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On a map with a scale 1 : 100,000, the distance between two cities is 12 cm. What would be the distance between these two cities on a different map with a scale 1 : 300,00?
Answer:
36 cm
Step-by-step explanation:
A square room has a floor area of 144 square feet. the hieght of the room is 6 feet what is the area of one wall
The area of one wall of the room is 72 square feet.
What is the area of a square?The area of a square is given by -
A{S} = a²
where -
{a} is side of square.
Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.
It is given that -
floor area = 144
a² = 144
a = √(144)
a = √(12 x 12)
a = 12
The area of the wall will be equivalent to -
A{W} = h x a
A{W} = 6 x 12
A{W} = 72 square feet.
Therefore, the area of one wall of the room is 72 square feet.
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What is the value of a?
Answer:
15 units
Step-by-step explanation:
By using the Pythagoras Theorem,
C^2 = A^2 + B^2
Substitute in the given values,
25^2 = a^2 + 20^2
625 = a^2 + 400
625 - 400 = a^2 + 400 - 400
a^2 = 225
[tex]a = \sqrt{225} [/tex]
= 15
Hope this too helped! ^^
I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.
I need help on my math
1/5 of x is 14
What is the x
How much will a person pay for 6.8 pounds of bananas at a price of $0.79 per pound?
Answer:
A person will pay $5.37
Step-by-step explanation:
6.8 pounds of bananas x $0.79 per pound = $5.37.
I hope this helps and have a blessed day! :)
Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.
Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by Continuous random variables.
What is Continuous Random Variable ?
A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.
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Laci and leon are saving money to go to an amusement park. laci has $1 more than 4 times the amount of money leon has. together, they have $76. write an equation to determine how much money they have together. 4x 1 = 76 x 4x − 1 = 76 4x − 1 = 76 x 4x 1 = 76
Answer:
Leon has $15 and Laci has $61
Step-by-step explanation:
Let x = the amount Leon has. So 4 times that plus $1 would be 4x+1. Our equation is:
x + (4x+1) = 76
Combine like terms
5x + 1 = 76
Subtract 1 from both sides
5x = 75
Divide both sides by 5
x = 15. This is Leon. Laci is 4(15) +1, or 61.
A survey from the Department of Motor Vehicles was given to residents in the city of Smallville. The results showed that 80% held a valid driver’s license. Of the individuals who held a value driver’s license, 10% has at least one traffic violation, whereas 30% who did not have a valid driver’s license has at least one traffic violation. What percent of Smallville residents have at least one traffic violation?
A. 14%
B. 28%
C. 38%
D. 40%
Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.
As given,
A=Person has a driver license
A'=Person does not have a driver license
P(A)=0.80
P(A')=0.20
For A, 10% has at least one traffic violation
For A', 30% had at least one traffic violation.
Probability with at least one traffic violation
=Probability of( A and one traffic violation +A' and one traffic violation)
=0.80(0.10)+0.20(0.30)
=0.08+0.06
=0.14
=14%
Therefore, percent of the residents with at least one traffic violation is 14%.
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can someone help me with 13 and 14 please and fast
Answer:
24 25 26
Step-by-step explanation:
guess and check..................
-7,5 + 4,2 =?
-0,9 * 2,7 =?
[tex]-7,5 + 4,2 = -3.3[/tex]
[tex]-0,9 \cdot 2,7 = -2.43[/tex]
The equation for line r can be written as y= 1/2 x+8. Line s, which is perpendicular to line r, includes the point (2, – 7). What is the equation of line s?
Answer:
y = -2x - 3
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2
using m = -2, x = 2, y = -7
y = mx + b
-7 = (-2)(2) + b
-7 = -4 + b
b = -3
y = -2x - 3
What is the solution to -3/4 X +2<-7
Answer:
Pretty sure it’s x>12
Step-by-step explanation:
Answer x > 12
thats the whole thing
Continuation of Qn on part ii)
Answer:
Step-by-step explanation:
an exterior angle of a triangle is 105 degree and one of its interior opposite angle is 35 degree less than the other .calculate the measure of both interior angle
The value of both the interior angles of the triangle is calculated as 70° and 35°.
What is the exterior angle property?If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.
When an equivalent angle is chosen to take at each vertex of the triangle, this same exterior angles always add up to 360°.Each exterior angle equals 180° minus the interior angle. If the relating interior angle is given, this formula can be used. Exterior angle = Sum of opposite angles on the inside. When the exterior angle's distant interior opposite angles are given, this formula can be used to find it.Now, as per the given question;
The exterior angle of a triangle is 105°.
Let one of the interior angle is 'x'.
Then, the other interior angle is 35 degree less; x - 35°.
By the exterior angle property.
Sum of interior angles = exterior angle
x + x - 35° = 105°
2x = 105° + 35°
2x = 140°
x = 70°
The other interior angle is; x - 35°
= 70° - 35°
= 35°
Therefore, the two interior angles of the triangles are estimated as 70° and 35°.
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Write an equation and solve.
For a ride on a rental scooter, Justin paid a $2 fee to start the scooter plus 12 cents per
minute of the ride. The total bill for Justin's ride was $20.84. For how many minutes did
Justin ride the scooter?
Answer:
2+0.12x=time on scooter bill
x is minutes and x is 157 minutes on the scooter
Step-by-step explanation:
Use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 4 6 ln(x) dx, 1 n = 6
The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.
Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.
The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.
Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.
Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).
Now,
a=1,b=4,Δx =(b-a)/n =3/6 =1/2
f(x)=4√(ln(x))
trapezoidal rule:
∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1)) +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]
∫4√(ln(x)) dx =10.365336
midpoint rule :
∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]
∫4√(ln(x)) dx =(1/2)[4√(ln(1.25)) +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]
∫4√(ln(x)) dx =10.724182
simpsons rule:
∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+ 2*f(3)+ 4*f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1)) +4*4√(ln(1.5)) + 2*4√(ln(2)) +4*4√(ln(2.5)) +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]
∫4√(ln(x)) dx =10.527905
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Graph the following system of equations.
3x + 6y = 6
2x + 2y = 6
What is the solution to the system?
A)There are infinitely many solutions.
B)There is one unique solution, (4, -1).
C)There is one unique solution, (6, -2).
D)There is no solution.
The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is
B) There is one unique solution, (4, -1).
What is a solution for a system of equations?The solutions for a system of equation is the intersecting points between them
We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.
Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.
The system of equations has no solution when they are parallel to each other.
So, now we'll graph this system of equations and observe where they lie in XY coordinate.
Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).
We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).
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Help please :)
create your own unit rate example in which you have to determine the unit rate of two fractions with different units. explain what the two fractions are, write the scenario, and calculate the unit rate. do not forget your units and remember to show your work!
no trolling!
Mansi can cover 1 mile of the distance in just 12 minutes.
How to calculate the unit rate?The unit rate can be expressed in any unit for instance minute per mile, miles/hour, etc
There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.
Lets consider Mansi covers 3 miles in 36 minutes, her unit rate in minutes per mile is expressed as:
Unit rate = 36min/3miles
Unit rate = 12 minutes/mile
Here,
This shows that Mansi can cover 1 mile of the distance in just 12 minutes.
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PLS EXPLAIN THIS ITS URGENT HOW DO YOU DO THISSSS
Answer:
It means you will have to match the name with the correct numbers on the right hand side.example:Animal bread
food dog
answeranimal— dog
food — bread
The real question answer:Zero slope — ( 16,3), (16,-80)Negative slope — (-5,-20), (-11,-20)undefined slope— (-1000,2500), (500,4000)Positive slope— (0,4,25), (1,25,1,75)Incase you aren't still convinced, you can try using the slope formula to solve it yourself .
slope = Y2 - Y1
————
X2 - X1
Hope this helpsGood luck ✅
Need an explanation, thx
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula and equate to the given slope
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(a)
(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )
[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then
[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )
y + 4 = 6 ( subtract 4 from both sides )
y = 2
ordered pair is (0, 2 )
(b)
(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )
[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then
[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )
3(x + 2) = 21 ( divide both sides by 3 )
x + 2 = 7 ( subtract 2 from both sides )
x = 5
ordered pair is (5, 5 )
(c)
(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )
[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then
[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )
- 5(1 - x) = - 20 ( divide both sides by - 5 )
1 - x = 4 ( subtract 1 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
ordered pair is (- 3, 5 )
(e)
(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )
[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then
[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )
- 7(2 - y) = 14 ( divide both sides by - 7 )
2 - y = - 2 ( subtract 2 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
ordered pair is (- 6, 4 )
the formula for the circumference of a circle is c equals 2 pi r. if the circumference is31.4 centimeters, what is the diameter of the circle? (let pi equals 3.14)
Answer: Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm². Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.
Step-by-step explanation:
A woman has a total of $9,000to invest. She invests part of the money in an account that pays7%per year and the rest in an account that pays9%per year. If the interest earned in the first year is$710, how much did she invest in each account? She invested $___ at 7% and $___ at 9%.
She invested $5,000 at 7% and $4,000 at 9%
How much is invested at each rate of return?
The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%
total interest at 7%=interest rate*amount invested
interest rate=7%
amount invested=x
total interest at 7%=7%*x=0.07x
total interest at 9%=9%*(9000-x)
total interest at 9%=810-0.09x
total interest on both accounts=0.07x+810-0.09x
total interest on both accounts=810-0.02x
total interest earned=$710
710=810-0.02x
0.02x=810-710
0.02x=100
x=100/0.02
x=amount invested in the account which earns 7%=$5,000
amount invested at 9%=$9000-$5000
amount invested at 9%=$4,000
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Which is equivalent to 6
41/4
Answer:
16 1/4
Step-by-step explanation:
4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4
Add the 6 and you get 16 1/4
1. Find the sum.
76,749
5 565
23
+
The sum is
(Simplify your answer. Type a whole number.)
Answer:
82,337
Step-by-step explanation:
76,749
5565
+ 23
82,337
Hope it helps!!!
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Assume $x is deposited into a savings account. Blank Bank offers an annual rate of r% for y years. Thank Bank offers a rate of ry% for 1 year. Which earns more interest?
Blank bank as well as Thank bank earn equal interest.
In this question, Blank Bank offers an annual rate of r% for y years.
and Thank Bank offers a rate of ry% for 1 year.
Assuming $x is deposited into a savings account, we need to determine which bank earn more interest.
We know that, Interest = principal × rate × time
Now we convert the rates to decimals and to do that we divide by 100.
So, the annual rate of the Blank bank = 0.0r
And the annual rate of the Thank Bank = 0.0ry
Using above formula of interest,
For Blank bank, the interest would be,
I_B = x × 0.0r × y
I_B = xy(0.0r)
I_B = 0.0rxy ....................(1)
here, we find the interest for 'y' years
And for the Thank Bank, the interest would be,
I_T = x × 0.0ry × 1
I_T = I_B = 0.0rxy ....................(2)
From (1) and (2),
I_B = I_T
Both the banks earn equal interest.
Therefore, Blank bank as well as Thank bank earn equal interest.
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What did lambert call the difference between the angle-sum of a triangle and 180 degrees?
Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
Who is Lambert?Johann Heinrich Lambert (26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made significant contributions to mathematics, physics (particularly optics), philosophy, astronomy, and map projections. Lambert pioneered the use of hyperbolic functions in trigonometry. He also proposed theories about non-Euclidean space. Lambert is credited with being the first to demonstrate that is irrational by employing a generalized continued fraction for the function tan x. Euler believed the conjecture but was unable to prove it was irrational, and it is speculated that Aryabhata believed it as well in 500 CE. Lambert also developed theorems about conic sections that simplified the calculation of comet orbits.Lambert refers to the defect as the difference between the angle-sum of a triangle and 180 degrees.Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
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8th grade Mathematics
A line has a slope of -3 and a y-intercept of 3.
What is the slope of the line?
O. -9
O. -1
O. 1
O. 9
I appreciate all of your answers even if they are wrong, thanks!! :)
Answer:
1
Step-by-step explanation: