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Bogdan [553]
3 years ago
6

Find the circulation of Bold Upper F equals 5 x Bold i plus 7 z Bold j plus 6 y Bold k around the closed path consisting of the

following three curves traversed in the direction of increasing t.
Mathematics
1 answer:
ch4aika [34]3 years ago
4 0

Answer:

The circulation of the given vector is (5/2)x² + 7yz + 6yz + C

Step-by-step explanation:

Given that F = 5xi + 7zj + 6yk

The circulation of F is given as

Integral of F.dr

dr = idx + jdy + kdz

F.dr = (5xi + 7zj + 6yk).(idx + jdy + kdz)

= 5xdx + 7zdy + 6ydz

Integral of F.dr = Integral of (5xdx + 7zdy + 6ydz)

= (5/2)x² + 7yz + 6yz + C

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Amp is the number in front of sine so its 1/2 aka D :)
8 0
2 years ago
Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
Shtirlitz [24]

Answer:

The endpoints of the latus rectum are (12, -7) and (-8, -7).

Step-by-step explanation:

A parabola with vertex at point C(x, y) = (h,k) and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

(x-h)^{2} = 4\cdot p \cdot (y-k) (1)

Where:

y - Independent variable.

x - Dependent variable.

p - Distance from vertex to the focus.

h, k - Coordinates of the vertex.

The coordinates of the focus are represented by:

F(x,y) = (h, k+p) (2)

The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that h = 2, k = -2 and p = -5, then the latus rectum is between the following endpoints:

By (2):

F(x,y) = (2, -2-5)

F(x,y) = (2,-7)

By (1):

(x-2)^{2} = -20\cdot (-7+2)

(x-2)^{2} = 100

x - 2 = \pm 10

There are two solutions:

x_{1} = 2 + 10

x_{1} = 12

x_{2} = 2-10

x_{2} = -8

Hence, the endpoints of the latus rectum are (12, -7) and (-8, -7).

4 0
2 years ago
Factor y 2 + 10z - 10y - yz. 1. (z - y)(y - 10) 2. (y - z)(y - 10) 3. (y - z)(10 - y)
Iteru [2.4K]

Answer:

y²+10z-10y-yz

Reaaranging the terms

=y²-yz+10z-10y

taking common

=y(y-z)+10(y-z)

=(y+10)(y-z) is the right option

i hop this will help you :)

5 0
4 years ago
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