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Pachacha
2 months ago
8

In △ABC , m∠A=53°,m∠B=17°, and a=27. Find the perimeter of the triangle.

Mathematics
1 answer:
lawyer [12.5K]2 months ago
6 0
Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.

The angle C calculates to 180-53-17=110°

Thus, we have 27/sin53=b/sin17=c/sin110

This leads to b=27sin17/sin53, c=27sin110/sin53

The perimeter is defined as a+b+c, so

p=27+27sin17/sin53+27sin110/sin53 units

p≈68.65 units (rounded to the nearest hundredth of a unit)
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1 month ago
superstore and cheap store are two supermarkets that sell boxes of the same type of cereal each supermarket has a special offer
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Step-by-step explanation:

Cheapstore:

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£4 corresponds to 600g

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600g divided by 10 results in 60g, which when multiplied by 3 yields 180g, added to 600g

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8 0
2 months ago
Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche
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Response:

The height of the water when it reaches 4 inches is \frac{3}{8\times \pi} inch/s.

Detailed Explanation:

Flow rate of water from the cone = R=\frac{3}{2} inch^3/s

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}

r = h/2

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\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s

The height of the water when it is 4 inches deep is \frac{3}{8\times \pi} inch/s.

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