The statement that fills in the blank in the last line of proof is : ∠n ≅ ∠p
<h3>
Parallelogram</h3>
Given that the figure described in the question is a parallelogram the angles in the figure are supplementary angles. Supplementary angles that add up to 180° but not less than 90° and angles ∠n ≤ 180° and ∠p≤180°
Hence we can conclude that the correct option that fills in the blank in the last line of proof is ∠n ≅ ∠p
Learn more about parallelogram : brainly.com/question/3050890
<u>Attached below is the missing part of the question </u>
<em>A partial proof was constructed given that MNOP is a parallelogram. Parallelogram M N O P is shown. By the definition of a parallelogram, MN ∥ PO and MP ∥ NO. Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary. Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary. Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary. Therefore, __________________ because they are supplements of the same angle</em>
Everyone knows that cats are nocturnal.
The frequency of waves are determined by the amount of waves that pass a specific point in a certain period of time and Radio stations broadcast their signals at different frequencies so that the range of radio frequencies can be used by many stations.
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;
- 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}}](https://tex.z-dn.net/?f=%5Cvec%20E_%7B1x%7D%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7B1%7D%7B4%20%5Ccdot%20%5Cpi%20%5Ccdot%20%5Cepsilon_0%7D%20%5Ccdot%20%5Cdfrac%7Bq_1%7D%7B%5Cvec%7Br%7D%5E2_2%7D%7D)
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](https://tex.z-dn.net/?f=%5Cvec%7BE%7D_%7B1x%7D%20%3D%5Cmathbf%7B%20%5Cdfrac%7B%5Cleft%289%20%5Ctimes%2010%5E9%20%5C%2C%20N%20%5Ccdot%20m%2FC%5E2%20%5Cright%29%20%5Ccdot%20%5Cleft%28-4%20%5C%2C%20nC%20%5Ctimes%20%5Cdfrac%7B10%5E%7B-9%7DC%7D%7B1%20%5C%2C%20nC%7D%20%5Cright%29%7D%7B%5Cleft%281%20%5C%2C%20m%20%5Cright%29%5E2%7D%7D%20%5Ccdot%20cos%5Cleft%28arctan%5Cleft%28%5Cdfrac%7B0.8%7D%7B0.6%7D%20%5Cright%29%20%5Cright%29%20%3D-21.6%20%5C%2C%20N%2FC)
![\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](https://tex.z-dn.net/?f=%5Cvec%7BE%7D_%7B1y%7D%20%3D%20%5Cmathbf%7B%5Cdfrac%7B%5Cleft%289%20%5Ctimes%2010%5E9%20%5C%2C%20N%20%5Ccdot%20m%2FC%5E2%20%5Cright%29%20%5Ccdot%20%5Cleft%28-4%20%5C%2C%20nC%20%5Ctimes%20%5Cdfrac%7B10%5E%7B-9%7DC%7D%7B1%20%5C%2C%20nC%7D%20%5Cright%29%7D%7B%5Cleft%281%20%5C%2C%20m%20%5Cright%29%5E2%7D%7D%20%5Ccdot%20sin%5Cleft%28arctan%5Cleft%28%5Cdfrac%7B0.8%7D%7B0.6%7D%20%5Cright%29%20%5Cright%29%20%3D%2028.8%20%5C%2C%20N%2FC)
Which gives;
![\vec{E}_1 = \mathbf{21.6 \, N/C \cdot \hat x + 28.8 \, N/C \hat y}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D_1%20%3D%20%5Cmathbf%7B21.6%20%5C%2C%20N%2FC%20%20%5Ccdot%20%5Chat%20x%20%2B%20%2028.8%20%5C%2C%20N%2FC%20%5Chat%20y%7D)
![\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](https://tex.z-dn.net/?f=%5Cvec%7BE%7D_%7B2x%7D%20%3D%20%5Cdfrac%7B%5Cleft%289%20%5Ctimes%2010%5E9%20%5C%2C%20N%20%5Ccdot%20m%2FC%5E2%20%5Cright%29%20%5Ccdot%20%5Cleft%286.00%20%5C%2C%20nC%20%5Ctimes%20%5Cdfrac%7B10%5E%7B-9%7DC%7D%7B1%20%5C%2C%20nC%7D%20%5Cright%29%7D%7B%5Cleft%281%20%5C%2C%20m%20%5Cright%29%5E2%7D%20%3D%20150%20%5C%2C%20N%2FC)
Therefore;
![\vec {E} = \mathbf{\left( -128.4 \, N/C \right) \left( \hat x \right) + \left(28.8 \, N/C \right) \left( \hat y \right)}](https://tex.z-dn.net/?f=%5Cvec%20%20%7BE%7D%20%3D%20%5Cmathbf%7B%5Cleft%28%20-128.4%20%5C%2C%20N%2FC%20%20%5Cright%29%20%5Cleft%28%20%5Chat%20x%20%5Cright%29%20%2B%20%5Cleft%2828.8%20%5C%2C%20N%2FC%20%5Cright%29%20%5Cleft%28%20%5Chat%20y%20%5Cright%29%7D)
The magnitude of the net electric field is therefore;
E =
≈ 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.
Learn more about electric field strength here:
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