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makkiz [27]
2 years ago
11

Write the equation of the line that passes through the points (7, -4) and (-1,3), first in point-slope form, and then in

Mathematics
1 answer:
RoseWind [281]2 years ago
5 0

Step-by-step explanation:

first we need to calculate the slope, which is needed in both equation forms.

the slope is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

I always prefer to go from left to right (but it works exactly the same way in the opposite direction), so I go from (-1, 3) to (7, -4).

x changes by +8 (from -1 to +7).

y changes by -7 (from +3 to -4).

so, the slope is -7/+8 = -7/8

when (7, -4) is used (I think you have a typo in the problem description up there), the point-slope form is

y - y1 = m(x - x1)

with (x1, y1) being the point coordinates, and m bring the slope

y - -4 = -7/8 × (x - 7)

or simplified

y + 4 = -7/8(x - 7)

the slope-intercept form is

y = mx + n

m being the slope, n being the y-intercept (y value for x=0).

we know already

y = -7/8 x + n

we also use the coordinates of a point here to solve for n :

-4 = -7/8 × 7 + n = -49/8 + n

-32/8 = -49/8 + n

17/8 = n

so, the full equation is

y = -7/8 x + 17/8

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2 years ago
Use the surface integral in​ Stokes' Theorem to calculate the circulation of the field Bold Upper F equals x squared Bold i plus
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Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]

Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]

Curl f(x) = (0,0,4)

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Thus, The circulation of the field f(x) over curve C is Zero

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