Please help quick will give brainliest

Answer:

[tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex]. This is the solution.

Step-by-step explanation:

The homogeneous differential equation is given by  

[tex]\frac{dy}{dx} = \frac{x^{2} + y^{2} }{2xy}[/tex]

⇒ [tex]\frac{dy}{dx} = \frac{1 + (\frac{y}{x} )^{2} }{2(\frac{y}{x} )}[/tex] ........ (1)

Now to solve this differential equation we assume that y = vx where v is another variable.

So, differentiating with respect to x we get [tex]\frac{dy}{dx} = v + x \frac{dv}{dx}[/tex]

Therefore, the above equation (1) becomes

[tex]v + x \frac{dv}{dx} = \frac{1 + v^{2} }{2v}[/tex] {Since [tex]v = \frac{y}{x}[/tex]}

⇒ [tex]x\frac{dv}{dx} = \frac{1 + v^{2} - 2v^{2}  }{2v}[/tex]

⇒ [tex]x\frac{dv}{dx} = \frac{1 - v^{2}}{2v}[/tex]

⇒ [tex]\frac{2v}{1 - v^{2} } dv = \frac{dx}{x}[/tex] {By separation of variables}

Now, integrating both sides we get,

[tex]\int {\frac{2v}{ 1- v^{2}}} \, dv = \int {\frac{dx}{x} } \, dx[/tex]

⇒ [tex]- \int {\frac{d(1 - v^{2} )}{1 - v^{2}}}  = \int {\frac{dx}{x} }[/tex]

⇒ [tex]- ln (1 - v^{2}) = ln x + c[/tex] {Where c is the integration constant}

⇒ [tex]ln [1 - (\frac{y}{x} )^{2} ] + ln x + c = 0[/tex] (Answer)

The quotient is: 4a-5

The remainder is: 0

Step-by-step explanation:

We need to divide -40a^6+50a^5 by -10a^5

The division is shown in figure attached.

The quotient is: 4a-5

The remainder is: 0

Keywords: Division of polynomials

Learn more about Division of polynomials at:

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The circumference of a circle whose radius is given would be =200.96cm.

How to calculate the circumference of a given circle?

To calculate the circumference of a given circle whose radius is given, the following steps should be taken as follows:

The formula for circumference = 2πr

where;

radius = 32cm

Circumference = 2× 3.14× 32

= 200.96cm.

The general term for the sequence [tex]a_{n}=(-1)^{n} 3 n[/tex]

Given sequence is -3, 6, -9, 12, -15

We have to find the general term of sequence

The terms in the sequence are found out by using the recursive definition:

[tex]a_{n}=(-1)^{n} 3 n[/tex]

Let us use this definition to find out the terms and check if it matches our given sequence

[tex]\begin{array}{l}{\text { For } n=1:-(-1)^{n} 3 n=(-1)^{1} \times 3 \times 1=-3} \\\\ {\text { For } n=2:-(-1)^{n} 3 n=(-1)^{2} \times 3 \times 2=1 \times 6=6} \\\\ {\text { For } n=3:-(-1)^{n} 3 n=(-1)^{3} \times 3 \times 3=-1 \times 9=-9} \\\\ {\text { For } n=4:-(-1)^{n} 3 n=(-1)^{4} \times 3 \times 4=1 \times 12=12} \\\\ {\text { For } n=5:-(-1)^{n} 3 n=(-1)^{5} \times 3 \times 5=-1 \times 15=-15}\end{array}[/tex]

Thus the general term is given by [tex]a_{n}=(-1)^{n} 3 n[/tex]

Answer:

x = 10

Step-by-step explanation:

The sides of an equilateral triangle are all 60°. Divide 60 by 6 and get 10

Yeah just divide 60÷6 which equals 10

You roll a 6-sided die. The probability of getting prime is 50%.

Solution:

Given, that we have rolled a 6 – sided die.

We have to find the P(prime) as percentage.

Now, It means that we have to find the probability of getting a prime number on the face.

On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6

Number of possible outcomes = 6

We have to get a prime number on rolling a die

The prime numbers in possible outcomes are 2, 3, 5

So number of favorable outcomes = 3

[tex]\text {Probability of an event as percentage }=\frac{\text { favourable number of outcomes }}{\text { total number of outcomes }} \times 100[/tex]

[tex]\text {Probability of getting prime number on face of die }=\frac{3}{6} \times 100[/tex]

[tex]\begin{array}{l}{\text { P(prime) }=\frac{1}{2} \times 100} \\\\ {\text { P(prime) }=50 \%}\end{array}[/tex]

Hence, probability of getting prime is 50%.

Answer:

Equation:  2x + 10y = 98

y-intercept:  (0, 9.8)

Step-by-step explanation:

The easiest possible way to solve thios problem follows:

Keep the form of the given line 2x + 10y = 7, replacing the '7' with the constant 'c:'

2x + 10y = c

Now take the coordinates of the given point (4, 9) and substitute them into the above equation, to find c:

2(4) + 10(9) = c

Then 8 + 90 = c, and c = 98

Then the desired equation is 2x + 10y = 98

To find the y-intercept, let x = 0 and solve for y.  We get

10y = 98, so that y = 9.8.  The y-intercept is thus (0, 9.8).

The y-intercept of the line parallel to 2x + 10y = 7 and containing the point (4, 9) is 8.6.

The y-intercept of a parallel line can be found using the equation y = mx + b, where m is the slope and b is the y-intercept. Since the given line 2x + 10y = 7 is in the form Ax + By = C, we need to rearrange it to the slope-intercept form. Therefore, the equation becomes: 10y = -2x + 7 → y = (-2/10)x + 7/10. The slope of the given line is -2/10, which means any line parallel to it will also have a slope of -2/10. Now we can use the point-slope form to find the equation of the parallel line that passes through the point (4, 9):

y - y1 = m(x - x1) → y - 9 = (-2/10)(x - 4)

Expanding and simplifying the equation, we get:

y - 9 = (-2/10)x + 8/10 → y = (-2/10)x + 8/10 + 9 → y = (-2/10)x + 86/10

Therefore, the equation of the parallel line that contains the point (4, 9) is y = (-2/10)x + 86/10. The y-intercept of this line is 86/10 or 8.6.

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Using two unit multiplier 628 km is equal to 62800000 cm

Solution:

628 kilometer to centimeter

We will go from kilometers to meters to centimeters.

Start by putting 628 km over 1:

[tex]\frac{628 km}{1}[/tex]

We want to get rid of km and bring in m.

We know that 1000 m = 1 km.

Since km is in the numerator, we will make the  first unit multiplier by putting 1 km in the  denominator and 1000 m in the numerator, so the  km will cancel. So we multiply by the unit multiplier,

[tex]\frac{628 km}{1} \times \frac{1000m}{1km}[/tex]

Now the km's will cancel:

[tex]\frac{628}{1} \times \frac{1000m}{1}[/tex]

Now we want to get rid of m and bring in cm.

We know that 100 cm = 1 m.

Since meter is in the numerator, we will make the  first unit multiplier by putting 1 meter in the  denominator and 100 cm in the numerator, so the  meter's will cancel. So we multiply by the unit  multiplier

[tex]\frac{100cm}{1m}[/tex]

[tex]\frac{628}{1} \times \frac{1000m}{1} \times \frac{100cm}{1m}[/tex]

We cancel the m's and we end up with:

[tex]628 \times 1000 \times 100 cm[/tex]

= 62800000 cm

Thus 628 km is equal to 62800000 cm

Final answer:

To convert 628 kilometers to centimeters, multiply by the conversion factors for kilometers to meters and then meters to centimeters, leading to 62,800,000 centimeters.

Explanation:

To convert 628 kilometers to centimeters, we need to apply two unit multipliers. The first conversion factor is 1 kilometer = 1000 meters, and the second conversion factor is 1 meter = 100 centimeters.

First, we convert kilometers to meters:

628 km × 1000 m/km = 628,000 meters

Then, we convert meters to centimeters:

628,000 m × 100 cm/m = 62,800,000 centimeters

Therefore, 628 kilometers is equal to 62,800,000 centimeters.

Answer:

0

Step-by-step explanation:

If the answer is between 0 to 0.49, the best estimate is 0.

If the answer is between 0.5-1.49, the best estimate is 1.

If the answer is 1.5 or greater, the best estimate is 2.

Without giving the fractions 1/10 and 1/12 a common denominator, we know the answer is between 2/12 and 2/10.

2/12 is less than 2/10. 2/10 is 0.2, which is less than 0.5.

Since the final answer is less than 0.5, the best estimate is 0.

Answer:

3h-9/2

Step-by-step explanation:

3/4(4h-6)=3h-18/4

simplify

3h-9/2

Answer:

3(3h-3/2) in its simplified form.

Step-by-step explanation:

Given the equation 3/4(4h-6),

First we will open the bracket up by multiplying through by 3/4 to have;

3h - 9/2

Since 3 is common at both sides of the resulting equation, we will factor it out to have;

3(h-3/2).

Since we cannot simplify further, then the expression 3/4(4h-6) is also equivalent to 3(h-3/2).

Danielle earned $969 last week if she sold $4,400 in electronics merchandise

Given that, Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.  

She also earns a base salary of $650 per week.  

We have to find how much did she earn last week if she sold $4,400 in electronics merchandise?  

Now, we know that, earned amount = base salary + commission

Given that she earns a 7.25% commission on everything she sells

So commission earned for selling $ 4400 is given as:

commission earned = 7.25 % of 4400

[tex]\text { commission earned }=\frac{7.25}{100} \times 4400=7.25 \times 44=319[/tex]

Earned amount = base salary + commission = 650 + 319 = 969

Hence, she earned $969 last week

Answer:

PLEASE PROVIDE MORE INFORMATION

Step-by-step explanation:

Multiply the current price by 1 + percentage of increase.

3.50 x 1.11 = 3.89

The new price will be $3.89

Answer:

u^2/11v

Step-by-step explanation:

11u^2/121v=u^2/11v

Because 11/121=1/11.

Answer:

B

Step-by-step explanation:

Note (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= - 4x² - 6x - 1 - (- x² - 5x + 3) ← distribute parenthesis by - 1

= - 4x² - 6x - 1 + x² + 5x - 3 ← collect like terms

= - 3x² - x - 4 → B

HERE IS THE ANSWER 85

Answer:

33

Step-by-step explanation:

substitute 4 in the place of x.

multiply 4 by 7 then add 5 and your answer is 33.

Answer:

Either x  = + i/2 or  x = i/2 is the solution for the given quadratic equation.

Step-by-step explanation:

Here, the given quadratic equation is:[tex]4x^2 + 1 = 0[/tex]

Now, comparing the given equation with standard Quadratic Form, [tex]ax^2 + bx + c = 0[/tex]

we get,a  = 4, b =0 and c = 1

Now, the Quadratic Formula is given as:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

So, here the solution for the given expression is:

[tex]x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies  x = \frac{0 \pm4i}{8}\\\implies x  =  \frac{0 + 4i}{8} = \frac{i}{2} \\or,  x  =  \frac{0 - 4i}{8} = \frac{-i}{2}[/tex]

Hence, either x  = + i/2 or  x = i/2 is the solution for the givenquadratic equation.

Answer:

.49

Step-by-step explanation:

So pretty much all you have to do is divide 8,526 by 42 which gives you .49, I know its pretty hard on paper but using a handy algebra calculator I was able to do it for ya :)

Answer:

We can conclude that Δ XYZ ≅ Δ RST by AAS postulate

Step-by-step explanation:

Δ XYZ and Δ RST are congruents by AAS postulate because:

1. Their non-included sides YZ and ST are equal (10 units = 10 units).

2. Their angles ∠Y and ∠S are equal.

3. Their angles ∠X and ∠R are equal.

4.Their non-included sides XZ and RT are equal.

Now, we can conclude that Δ XYZ ≅ Δ RST by AAS postulate.

b) ii) The value of y when x is 2.5 is -1.5

How to find the value of y

b) ii) The value of y when x is 2.5 is read from the graph to be approximately -1.8  

An mage  is attached to show how to read the value.

This can be solved by substitution

For x = 2.5

y = (2.5)² - (2.5) - 3 = 1.75

Answer:

Step-by-step explanation:

The current weather in a strange place is known to be 0 degrees, after a couple of hours, the weather has dropped 15 degrees, making the day much more colder than usual. What's the degree after the weather has dropped?

Solution:

0-15=-15

The integer -15 can be used to describe a situation of temperature falling below freezing point or owing someone money. In these situations, zero represents the freezing point or balanced position (no debt) respectively.

A situation that can be modeled by the integer -15 could be the temperature outside on a very cold day in winter. If we are expressing the temperature in degrees Fahrenheit, for instance, a temperature of -15 could represent a day that is 15 degrees below the freezing point, which is 32 degrees Fahrenheit. In this situation, the integer zero represents the freezing point. So, if the temperature is -15, it means the temperature is 15 degrees below the freezing point.

Another example could be a debt. If you owe someone $15, then your balance can be represented by -15. In this case, zero represents the point where you do not owe any money, it is the neutrally balanced point of your financial situation.

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Answer:

In pictures.

Step-by-step explanation:

2x-6y=12

-6y=-2x+12

y=2/6x-2

Now the equation is in standard form.

Table in attachments.

Graph in attachments.

Sorry, I made a mistake somewhere and got 2 different lines.

This answer might not be right.

Answer:

400,000

Step-by-step explanation:

Lets do the inverse of division which is multiplication so we are going to multiply 2,000 by 200 and get 400,000 and you can check by dividing 400,000 by 2,000 and you would get 200

Answer:

D: All of the above.

Step-by-step explanation:

A. All simple machines are useful in some way, weather that be making it easier to lift heavy objects, activating other machines, or something else.

B. Any simple machine must be, well, simple. i. e. have few moving parts.

Take the lever, for example. It has only one moving part, yet it is still very useful.  

C. They can be used to do work. Simple machines can be put together to make something that can do work.

Imagine a windmill that generates power, which then is taken by a motor attached to an Archimedes screw. All of these machines are simple, yet they are still used to do work.

Answer:

Step-by-step explanation:

Slope: -3

Y-Intercept: -21

x: 0, 1,

y: -21, -24

h(x)=−3x−21 is the closest answer

We can use the points (-6, 2) and (-4, 13) to solve.

Slope formula: y2-y1/x2-x1

= 13-2/-4-(-6)

= 11/2

______

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Answer:

The length of the farm is 310 yards and the width is 105 yards

Step-by-step explanation:

The correct question is

The Williams have a farm that is in a rectangular shape. The length of the farm is one hundred yards more than twice the width. The whole perimeter of the farm is 830 yards

Find the dimensions of the farm

Let

x ----> the length of the rectangular farm

y ----> the width of the rectangular farm

we know that

The perimeter of the farm (rectangle) is equal to

[tex]P=2(x+y)[/tex]

we have

[tex]P=830/ yd[/tex]

so

[tex]830=2(x+y)[/tex]

simplify

[tex]415=(x+y)[/tex] -----> equation A

[tex]x=2y+100[/tex] ----> equation B

substitute equation B in equation A

[tex]415=(2y+100+y)[/tex]

solve for y

[tex]415=(3y+100)[/tex]

[tex]3y=415-100[/tex]

[tex]3y=315[/tex]

[tex]y=105\ yd[/tex]

Find the value of x

[tex]x=2y+100[/tex]

[tex]x=2(105)+100=310\ yd[/tex]

therefore

The length of the farm is 310 yards and the width is 105 yards

The diagonal of a square measured 7 square root of 2 cm. Then the length of side of square is 7 cm

Solution:

Given that,

The length of diagonal of a square is [tex]7 \sqrt{2}[/tex] cm

The figure is attached below

So length of diagonal = AC = [tex]7 \sqrt{2}[/tex] cm

Let the length of sides of the square be ‘a’

Since, the diagonal and the sides are forming a right angled triangle

So, we can use Pythagoras theorem,

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

In triangle ABC, AC forms the hypotenuse and BC is the perpendicular and AB is the base

So above Pythagoras theorem definition,

[tex](\mathrm{BC})^{2}+(\mathrm{AB})^{2}=(\mathrm{AC})^{2}[/tex]

[tex]\begin{array}{l}{(a)^{2}+(a)^{2}=(7 \sqrt{2})^{2}} \\\\ {2 a^{2}=98} \\\\ {a^{2}=98 \div 2=49} \\\\ {a=\sqrt{49}=7}\end{array}[/tex]

Hence, the length of the square is 7 cm

Answer:

The answer is A.

Step-by-step explanation:

Just took the test. You are welcome.