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makkiz [27]
3 years ago
6

If 10x + 5y = 30 and -5x - 3y = 12, find the value of 5x + 2y

SAT
1 answer:
Firlakuza [10]3 years ago
8 0

Explanation:

Answers: (a) 12x – 15y

or 3(4x – 5y)

(b) 5pq (p + 2q) .

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A point charge q1 = -4. 00 nc is at the point x = 0. 60 m, y = 0. 80 m , and a second point charge q2 = +6. 00 nc is at the poin
Alekssandra [29.7K]

The net electric field is the vector sum of the components of the electric

field produced by the two charges.

The values of the magnitude and direction of the net electric field at the origin (approximate values) are;

  • 131.6 N/C
  • 12.6 ° above the negative x–axis

<h3>How are the net electric field magnitude and direction calculated?</h3>

The possible questions based on a similar question posted online are;

(a) The net electric field at the origin.

The electric field due to charge q₁ is given as follows;

\vec E_{1x} = \mathbf{ \dfrac{1}{4 \cdot \pi \cdot \epsilon_0} \cdot \dfrac{q_1}{\vec{r}^2_2}}

Which gives;

\vec{E}_{1x} =\mathbf{ \dfrac{\left(9 \times 10^9 \, N \cdot m/C^2 \right) \cdot \left(-4 \, nC \times \dfrac{10^{-9}C}{1 \, nC} \right)}{\left(1 \, m \right)^2}} \cdot cos\left(arctan\left(\dfrac{0.8}{0.6} \right) \right) =-21.6 \, N/C

\vec{E}_{1y} = \mathbf{\dfrac{\left(9 \times 10^9 \, N \cdot m/C^2 \right) \cdot \left(-4 \, nC \times \dfrac{10^{-9}C}{1 \, nC} \right)}{\left(1 \, m \right)^2}} \cdot sin\left(arctan\left(\dfrac{0.8}{0.6} \right) \right) = 28.8 \, N/C

Which gives;

\vec{E}_1 = \mathbf{21.6 \, N/C  \cdot \hat x +  28.8 \, N/C \hat y}

\vec{E}_{2x} = \dfrac{\left(9 \times 10^9 \, N \cdot m/C^2 \right) \cdot \left(6.00 \, nC \times \dfrac{10^{-9}C}{1 \, nC} \right)}{\left(1 \, m \right)^2} = 150 \, N/C

Therefore;

\vec  {E} = \left[ 21.6 \, N/C - 150 \, N/C \right] \left( \hat x \right) + \left(28.8 \, N/C \right) \left( \hat y \right)

\vec  {E} = \mathbf{\left( -128.4 \, N/C  \right) \left( \hat x \right) + \left(28.8 \, N/C \right) \left( \hat y \right)}

The magnitude of the net electric field is therefore;

E = \sqrt{(-128.4^2 + 28.8^2)} ≈ 131.6

  • The magnitude of the net electric field at the origin is E ≈<u> 131.6 N/C</u>

(b) The direction of the net electric field at the origin.

  • The \ direction \ is \ arctan \left(\dfrac{28.8}{-128.4} \right) \approx \underline{ 12.6^{\circ}} \ above \ the \ negative \ x-axis

Learn more about electric field strength here:

brainly.com/question/14743939

brainly.com/question/3591946

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What values of c and d would make the following expression represent a real number? i(2 3i)(c di) c = 2, d = 3 c = –2, d = 3 c =
Olegator [25]

Complete question:

<em>What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di) </em>

<em>choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2</em>

<em />

<em>Option D</em><em> is correct. </em> The value of c and d for the expression to be real are -3 and -2 respectively

Given the expression

i(2 + 3i)(c + di)

Expand the expression

=i(2 + 3i)(c + di)\\=(2i+3i^2)(c+di)\\=(2i+3(-1))(c+di)\\=(2i-3)(c+di)\\=2ic+2di^2-3c-3di\\=2ic-2d-3c-3di

Collect the like terms

=2ic-3di-2d-3c

For the resulting function to be real, then the imaginary part must be zero i.e.

2ic-3di=0\\2ci = 3di\\2c = 3d\\c=\frac{3d}{2}\\

If d = -2, then;

c=\frac{3(-2)}{2}\\c=\frac{-6}{2}\\c= -3

Hence the value of c and d for the expression to be real are -3 and -2 respectively.

Learn more here: brainly.com/question/4244460

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3 years ago
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