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Tju [1.3M]
2 years ago
7

AB and DC are parallel.

Mathematics
1 answer:
bekas [8.4K]2 years ago
6 0

Answer:

  583 cm²

Step-by-step explanation:

To find the area of triangle BCD, we need to know the length of segment BD. That can be found from the law of sines:

  BD/sin(A) = BA/sin(D)

  BD = (sin(A)/sin(D))BA = sin(70°)/sin(74°)·(39 cm) ≈ 38.1249 cm

Then the area of BCD is ...

  A = 1/2(DB)(DC)sin(BDC)

Angle BDC, together with the marked angles, makes a total of 180°.

 ∠BDC = 180° -74° -70° = 36°

  A = 1/2)(38.1249 cm)(52 cm)sin(36°) ≈ 582.64 cm² ≈ 583 cm²

_____

<em>Additional comment</em>

The angle relation we used comes from the fact that consecutive interior angles where a transversal crosses parallel lines are supplementary. That means angle DAB and ADC are supplementary. Angle ADC is the sum of angles ADB and BDC, so we have ...

  ∠DAB +∠ADB +∠BDC = 180°

  ∠BDC = 180° -∠DAB -∠ADB

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Step-by-step explanation:

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Step-by-step explanation:

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What is the total resistance of a parallel circuit that has two loads? Load one has a resistance of 10 ohms. Load two has a resi
Romashka-Z-Leto [24]

Answer:

The total resistance is 7.0588\Omega

Step-by-step explanation:

Attached please find the circuit diagram. The circuit is composed by a voltage source and two resistors connected in parallel: R_1=10\Omega and R_2=24\Omega.

First step: find the total current

For finding the current that the voltage source can provide, you must find the current consumed by each load and then add both. To do that, take first into account that the voltage is the same for both resistors (R_1 and R_2).

  • I_{R_1}=\frac{V_S}{R_1}
  • I_{R_2}=\frac{V_S}{R_2}

The total current is:

I_{TOTAL}=I_{R_1}+I_{R_2}=\frac{V_S}{R_1}+\frac{V_S}{R_2}=\frac{R_2\cdot V_S+R_1\cdot V_S}{R_1\cdot R_2}

I_{TOTAL}=V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}

Now, the total resistance (R_{TOTAL}) would be the voltage divided by the total current:

R_{TOTAL}=\frac{V_S}{I_{TOTAL}}

If you replace I_{TOTAL} by the expression obtained previously, the total resistance would be:

R_{TOTAL}=\frac{V_S}{V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}}

After simplifying the terms you should get:

R_{TOTAL}=\frac{R_1\cdot R_2}{R_1 + R_2}}

Now, you must replace the values of the resistors:

R_{TOTAL}=\frac{(10\Omega )\cdot (24\Omega)}{10\Omega + 24\Omega}}=\frac{120}{17}\Omega=7.0588\Omega

Thus, the total resistance is 7.0588\Omega

3 0
3 years ago
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