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ehidna [41]
3 years ago
8

Which equation is equivalent to x + 8 = 21? (x + 8) × 4 = 21 (x + 8) × 4 = 21 ÷ 4 (x + 8) × 4 = 21 × 2 (x + 8) × 4 = 21 × 4

Mathematics
1 answer:
Drupady [299]3 years ago
7 0

Answer:

(x + 8) × 4 = 21 × 4

Explanation:

x + 8 = 21

21 - 8 = 13

(13 + 8) × 4 = 21 × 4

21 × 4 = 21 × 4

84 = 21 × 4

84 = 84

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A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1), and back to the origin under
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Step-by-step explanation:

If C is the path the particle follows, then work done is \int_{C}^{}F.dx.

According to the question the force F=z^{2}i+5xyj+4y^2k and all four points are in the plane z=\frac{1}{4}y.

therefore, if S is the at surface with boundary C, so that S is the portion of the plane z=\frac{1}{4}y over the rectangle D=[0,2]\times [0,4].

Now,

curlF=\begin{vmatrix}i &j  &k \\  \frac{\partial }{\partial x}&\frac{\partial }{\partial y}  &\frac{\partial }{\partial z} \\  z^{2}&5xy  &4y^{2} \end{vmatrix}=8yi+2zj+5yk

By the Stoke's theorem:

\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA

=\iint_{D}^{}\left ( \frac{39}{8}y \right )dA\, \, \, \, \, \, \, \, \, Since\, \, z=\frac{1}{4}y\\\\=\int_{0}^{2}\int_{0}^{4}\frac{39}{8}y\, \, \, dy\, dx\\\\

\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \,  dx\\\\=39\times 2\\\\=78 \, N

8 0
4 years ago
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