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3 years ago

What rule would you allow to test weather (x,y) is on line l

Mathematics

1 answer:

n200080 [17]3 years ago

8 0

Answer:

Step-by-step explanation:

If a point (x, y) lies on a straight line, coordinates of the point will satisfy the equation.

Slope of a line passing through two points C(4, 5) and D(8, 10),

m = $\frac{y_2-y_1}{x_2-x_1}$

m = $\frac{10-5}{8-4}$

m = $\frac{5}{4}$

Equation of the line passing through C(4, 5) and slope m = $\frac{5}{4}$

y - y' = m(x - x')

y - 5 = $\frac{5}{4}(x-4)$

y = $\frac{5}{4}x-5+5$

y = $\frac{5}{4}x$

If point B(4, 0) lies on the line CD,

0 = $\frac{5}{4}(4)$

0 = 5

Which is not true.

Therefore, point B doesn't lie on line CD.

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Step-by-step explanation:

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3 years ago

Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a

Aloiza [94]

Answer:

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

Step-by-step explanation:

Given equation is $x^{3}+y^{3}+z^{3}=3xyz$ ………………(1)

we use derivative formula $\frac{d}{dx}(x^{n}) = n x^{n-1}$

$\frac{d}{dx}(x^{3)} = 3 x^{2}$

$\frac{d}{dx}(z^{3)} = 3 z^{2}$

And also apply 'u v' formula

$\frac{d}{dx}(uv}) = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)$

Differentiating equation (1) partially with respective to 'x' , we treated 'y' as constant.

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))$ ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)$

again simplification, we get

$3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}$

taking common ' $\frac{∂z}{∂x}$ on left on side , we get

$(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}$

dividing ' $(3z^{2}- 3yx)$ on both sides, we get

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

<u>Final answer</u>:-

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

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3 years ago

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blsea [12.9K]

He has 17 quarters and 18 pennies.
Because 17*0.25=4.25 and 18*0.01=0.18.
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