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velikii [3]
4 years ago
14

On a trip from Indianapolis, Indiana, to Houston, Texas, Mr. Sanchez averaged a speed of 63 mi/h. The total distance of the trip

was 1071 mi. Write and solve the equation to determine how many hours (h) it took mr. Sanchez to drive from Indianapolis to Houston.
Mathematics
1 answer:
m_a_m_a [10]4 years ago
3 0

Distance/Speed = Time

Distance=1,071   Speed=63    Time=x

1,071/63 = x

17 = x

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10. Two lighthouses are located on a north-south line.
Kamila [148]

The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)

The distance between both lighthouses is 5783.96 m

I've added an attachment that represents the scenario.

From the attachment, we have:

\mathbf{\angle A = 180^o - 120^o\ 43'}

Convert to degrees

\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}

\mathbf{\angle A = 180^o - (120^o +0.717^o)}

\mathbf{\angle A = 180^o - (120.717^o)}

\mathbf{\angle A = 59.283^o}

\mathbf{\angle B = 39^o43'}

Convert to degrees

\mathbf{\angle B = 39^o + \frac{43}{60}^o}

\mathbf{\angle B = 39^o + 0.717^o}

\mathbf{\angle B = 39.717^o}

So, the measure of angle S is:

\mathbf{\angle S = 180 - \angle A - \angle B} ---- Sum of angles in a triangle

\mathbf{\angle S = 180 - 59.283 - 39.717}

\mathbf{\angle S = 81}

The required distance is distance AB

This is calculated using the following sine formula:

\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }

Where:

\mathbf{AS = 3742}

So, we have:

\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}

Make AB the subject

\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}

\mathbf{AB= 5783.96}

Hence, the distance between both lighthouses is 5783.96 m

Read more about bearing and distance at:

brainly.com/question/19017345

5 0
2 years ago
What’s the circumference of this shape?xx
VikaD [51]

The hypotenuse of the triangle would be the diameter of the semi circle.

Using the Pythagorean theorem you can find that.

8^2 + 6^2 = x^2

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The diameter is 10, now find the circumference.

Circumference = diameter x PI = 10 x 3.14 = 31.4

Since it is a semi circle, the circumference would be 1/2 of that.

31.4 / 2 = 15.7

The perimeter would be 8 + 6 + 15.7 = 29.7

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