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2 years ago

A line with a slope of 0 passes through the point (6, 16). What is its equation in slope-intercept form?

Mathematics

1 answer:

satela [25.4K]2 years ago

8 0

Answer:

y = 0x + 16

Step-by-step explanation:

Slope of line m = 0

$(6,\:16)=(x_1,\:y_1)$

Equation of line in slope point slope form is given as:

$y-y_1 = m(x-x_1) \\\\\therefore y - 16 = 0(x - 6)\\\\\therefore y - 16 = 0x - 0\\\\\therefore y = 0x + 16\\\\$

This is the required equation in slope intercept form.

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Consider the implicit differential equation <img src="https://tex.z-dn.net/?f=%2849%20y%5E%7B3%7D%20%2B%2045%20xy%29%20dx%20%2B%

BaLLatris [955]

We're looking for an integrating factor $\mu(x,y)=x^py^q$ such that

$\mu\underbrace{(49y^3+45xy)}_M\,\mathrm dx+\mu\underbrace{(98xy^2+50x^2)}_N\,\mathrm dy=0$

is exact, which would require that

$(\mu M)_y=(\mu N)_x$
$(49x^py^{q+3}+45x^{p+1}y^{q+1})_y=(98x^{p+1}y^{q+2}+50x^{p+2}y^q)_x$
$49(q+3)x^py^{q+2}+45(q+1)x^{p+1}y^q=98(p+1)x^py^{q+2}+50(p+2)x^{p+1}y^q$
$\implies\begin{cases}49(q+3)=98(p+1)\\45(q+1)=50(p+2)\end{cases}\implies p=\dfrac52,q=4$

You can verify that $(\mu M)_y=(\mu N)_x$ if you'd like. With the ODE now exact, we have a solution $F(x,y)=C$ such that

$F_x=\mu M$
$F=\displaystyle\int(49y^3+45xy)x^{5/2}y^4\,\mathrm dx$
$F=10x^{9/2}y^5+14x^{7/2}y^7+f(y)$

$F_y=\mu N$
$50x^{9/2}y^4+98x^{7/2}y^6+f'(y)=98x^{7/2}y^2+50x^{9/2}y^4$
$f'(y)=0$
$\implies f(y)=C$

and so the general solution is

$F(x,y)=10x^{9/2}y^5+14x^{7/2}y^7=C$

8 0

3 years ago

If b√2 = 6, what does b equal? I don't know why I'm stuck on this problem, but could somebody help me?

kotegsom [21]

Answer:

Step-by-step explanation:

Divide both sides by the square root of 2. If you are looking for an exact answer that is rationalized, it would be found by multiplying 6/sqrt(2) * sqrt(2)/sqrt(2) to get

$b=\frac{6\sqrt{2} }{2}=3\sqrt{2}$

8 0

3 years ago

Read 2 more answers

What is (p) + (2p + 1) + (p+4)

AlladinOne [14]

Answer:

4p + 5

Step-by-step explanation:

Add all like terms:

p + 2p + p = 4p

1 + 4 = 5

4p + 5

3 0

2 years ago

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Question 4 A circle has a radius of 14 inches. What is the circumference of the circle? 77 inches Ов 147 inches C С 2876 inches

DiKsa [7]

Answer:

A=87.92

Step-by-step explanation:

2 x pie x r

2 times 3.14 times 14

6.28 times 14

=87.92

Use the same method to solve others

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2 years ago

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andreev551 [17]

Answer:

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Step-by-step explanation:

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2 years ago