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3 years ago

Which line is a slop that is positive

Mathematics

2 answers:

NISA [10]3 years ago

7 0

Answer:

the correct answer i believe is A. :)

dexar [7]3 years ago

4 0

Answer: A

Step-by-step explanation:

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Find all the solutions for the equation:

Contact [7]

$2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0$

Divide both sides by $x^2\,\mathrm dx$ to get

$2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}$

Substitute $v(x)=\dfrac{y(x)}x$ , so that $\dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}$ . Then

$x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}$

The remaining ODE is separable. Separating the variables gives

$\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x$

Integrate both sides. On the left, split up the integrand into partial fractions.

$\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}$

$\implies v^2+2v+1=a(v^2+1)+(bv+c)v$

$\implies v^2+2v+1=(a+b)v^2+cv+a$

$\implies a=1,b=0,c=2$

Then

$\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v$

On the right, we have

$\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C$

Solving for $v(x)$ explicitly is unlikely to succeed, so we leave the solution in implicit form,

$\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C$

and finally solve in terms of $y(x)$ by replacing $v(x)=\dfrac{y(x)}x$ :

$\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}$

7 0

3 years ago

PLEASE HELP ASAP! WILL GIVE BRAINLEIST!<br> Find the area of the shaded region. Use pi = 3.14

Semmy [17]

Answer:

Step-by-step explanation:

Square

The side length of the square = 8 cm

The area of the square = s^2

The area of the square = 8^2 = 64

Circle

r = d/2

r = 8/2

r = 4

Area of the circle = pi r^2

Area of the circle = 3.14 * 16

Area of the circle = 50.24

Shaded Area

Area of the Shaded area = area Square - Area Circle

= 64 - 40.24

= 23.76

4 0

3 years ago

Please help on this one?

rodikova [14]

Answer:

$\large\boxed{A.\ \dfrac{4}{x-9}}$

Step-by-step explanation:

$\dfrac{4(x-2)}{(x-2)(x-9)}\\\\\text{canceled}\ (x-2)\\\\=\dfrac{4}{x-9}$

4 0

3 years ago

Bob is performing an experiment to learn more about probability. He has a box of pink, yellow, blue, and white ribbons. He rando

shtirl [24]

Answer:

The relative frequency of picking a white ribbon is 0.1

The relative frequency of picking a white ribbon is 0.3

It is most likely that the number of blue ribbons in the box is the highest.

It is most likely that the number of pink ribbons in the box is the lowest.

Step-by-step explanation:

3 0

3 years ago

Sam is fencing in his property. The length is 12 feet less than twice the width. If the total amount of fence needed is 216 feet

DaniilM [7]

Answer:

L = 68 ft

Step-by-step explanation:

To find the perimeter of something you need to add up all the sides

In this case I am assuming Sam's property is a square/rectangle

Which means the formula for the perimeter is P = 2L + 2W

If L = 2W - 12 and P = 216, we can use these values and plug them into our perimeter equation to solve for w and then solve for l

216 = 2(2W -12) + 2W → ditributing the 2 to the (2w - 12) gives us
216 = 4W - 24 + 2W → combing like terms gives us
216 = 6W - 24 → adding 24 to both sides gives us
240 = 6W → dividing both sides by 6 gives us
40 ft = W

With the width being solved, we can now plug that value into our length equation

L = 2(40) - 12 → distributing the 2 to the 40 gives us
L = 80 - 12 → combing like terms give us
L = 68 ft

3 0

3 years ago