I NEED HELP The measure of an angle is 74.6°. What is the measure of its supplementary angle?

Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators

Nata [24]

Answer:

The solution is $y=-\frac{12}{12x-30x^2+1}$ .

Step-by-step explanation:

A first order differential equation $y'=f(x,y)$ is called a separable equation if the function $f(x,y)$ can be factored into the product of two functions of $x$ and $y$ :

$f(x,y)=p(x)h(y)$

where $p(x)$ and $h(y)$ are continuous functions.

We have the following differential equation

$y'=(1-5x)y^2, \quad y(0)=-12$

In the given case $p(x)=1-5x$ and $h(y)=y^2$ .

We divide the equation by $h(y)$ and move $dx$ to the right side:

$\frac{1}{y^2}dy\:=(1-5x)dx$

Next, integrate both sides:

$\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C$

Now, we solve for $y$

$-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}$

We use the initial condition $y(0)=-12$ to find the value of C.

$-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}$

Therefore,

$y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}$

4 0

3 years ago

Hello can someone help me pls

beks73 [17]

Hello. I do not know this answer on the spot. But there is an app called mymath and you can download it on any apple or android device that will give you the answer to any of the variables in the equation. Hope it helps

4 0

2 years ago

Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0

timama [110]

The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

<h3>What is the distance between a point and a line?</h3>

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

$\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

$\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units$

Learn more about the distance between a point and a line here;

brainly.com/question/11558698

#SPJ1

7 0

2 years ago

On a recent trip to a local orchard, the Morgan family picked four different kinds of apples - Braeburn, Cortland, Fuji, and Rom

ivanzaharov [21]

Answer:

Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.

Step-by-step explanation:

Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.

We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:

$B+C+F+R=360...(1)$

We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:

$B=2F...(2)$

We are told that Morgan family picked twice as many Cortland as Rome, that is:

$C=2R...(3)$

We are told that Morgan family picked 50% more Fuji than Rome, that is:

$F=1.5R...(4)$

Upon substituting equation (4) in equation (2), we will get:

$B=2(1.5)R$

$B=3R$

Now, each apple in in terms of Rome apples, so we will get:

$3R+2R+1.5R+R=360$

Let us solve for R.

$7.5R=360$

$\frac{7.5R}{7.5}=\frac{360}{7.5}$

$R=48$

Therefore, Morgan family picked 48 Rome apples.

Upon substituting $R=48$ in (3), we will get:

$C=2R\Rightarrow 2(48)=96$

Therefore, Morgan family picked 96 Cortland apples.

Upon substituting $R=48$ in (4), we will get:

$F=1.5R\Rightarrow 1.5(48)=72$

Therefore, Morgan family picked 72 Fuji apples.

Upon substituting $F=72$ in (2), we will get:

$B=2F\Rightarrow 2(72)=144$

Therefore, Morgan family picked 144 Braeburn apples.

3 0

3 years ago

Find the coefficient:

guapka [62]

Answer:

1/3

Step-by-step explanation:

Ask me in the comments of you need an explanation.

:)

3 0

3 years ago

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