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katen-ka-za [31]
4 years ago
5

Interstellar Travel. Our fastest current spacecraft travel away from Earth at a speed of roughly 50,000 kilometers per hour. At

this speed, how long would it take to travel the 4.4 light year distance to Alpha Centauri, the nearest star system to our own?
Mathematics
1 answer:
Citrus2011 [14]4 years ago
7 0
Answer: It will take about 21,689 years.

To start, we need to know that there are 9.5 x 10^12 kilometers in a light year. Next, lets divide that by 50,000 (or 5 x 10^4) to find the number of hours that it will take to travel that distance.

9.5 x 10^12 5 x 10^4 = 1.9 x 10^8 hours

We could further divide that be 24 to find the number of days and then by 365 to find the number of years.

1.9 x 10^8 / 24 / 365 = 21,689 years

It will take about 21,689 years.
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Solving right triangles
Sav [38]
<h2>1. Answer:</h2>

A right triangles is a triangle having a 90 degree side. According to the figure, the sides of this triangle are expressed in inches. Therefore, we can find the missing sides and angles as follows:

<u>m∠B:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

m \angle B + 51^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle B = 39^{\circ}}

<u>CA and AB:</u>

We must use the law of sines as follows:

\frac{CA}{sin39^{\circ}}=\frac{9}{sin51^{\circ}} \\ \\ \therefore CA=\frac{9sin39^{\circ}}{sin51^{\circ}} \\ \\ \therefore \boxed{CA=7.3in}

\frac{AB}{sin90^{\circ}}=\frac{9}{sin51^{\circ}} \\ \\ \therefore AB=\frac{9sin90^{\circ}}{sin51^{\circ}} \\ \\ \therefore \boxed{AB=11.6in}

<h2>2. Answer:</h2>

According to the figure, the sides of this triangle are expressed in meters. Therefore, we can find the missing sides and angles as follows:

<u>m∠A:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

m \angle A + 53^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle A = 37^{\circ}}

<u>CA and CB:</u>

We must use the law of sines as follows:

\frac{CA}{sin53^{\circ}}=\frac{5}{sin90^{\circ}} \\ \\ \therefore CA=\frac{5sin53^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CA=4.0m}

\frac{CB}{sin37^{\circ}}=\frac{5}{sin90^{\circ}} \\ \\ \therefore CB=\frac{5sin37^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CB=3.0m}

<h2>3. Answer:</h2>

According to the figure, the sides of this triangle are expressed in miles. Therefore, we can find the missing sides and angles as follows:

<u>m∠B:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

m \angle A + 28^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle B = 62^{\circ}}

<u>CB and AB:</u>

We must use the law of sines as follows:

\frac{CB}{sin28^{\circ}}=\frac{29.3}{sin62^{\circ}} \\ \\ \therefore CB=\frac{29.3sin28^{\circ}}{sin62^{\circ}} \\ \\ \therefore \boxed{CA=15.6mi}

\frac{AB}{sin90^{\circ}}=\frac{29.3}{sin62^{\circ}} \\ \\ \therefore AB=\frac{29.3sin90^{\circ}}{sin62^{\circ}} \\ \\ \therefore \boxed{AB=33.2mi}

<h2>4. Answer:</h2>

According to the figure, the sides of this triangle are expressed in miles. Therefore, we can find the missing sides and angles as follows:

<u>m∠A:</u>

The sum of the three interior angles of any triangle is 180°, therefore:

m \angle A + 24^{\circ} + 90^{\circ} = 180^{\circ} \\ \\ \boxed{m \angle A = 66^{\circ}}

<u>CA and CB:</u>

We must use the law of sines as follows:

\frac{CA}{sin66^{\circ}}=\frac{14}{sin90^{\circ}} \\ \\ \therefore CA=\frac{14sin66^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CA=12.8mi}

\frac{CB}{sin24^{\circ}}=\frac{14}{sin90^{\circ}} \\ \\ \therefore CB=\frac{14sin24^{\circ}}{sin90^{\circ}} \\ \\ \therefore \boxed{CB=5.7mi}

8 0
3 years ago
X + 2y – 4z = 1<br> -2x – 4y + 4z = 6<br> -4x – 3y – 4z = 21
elena55 [62]

Answer:

x = - 1

y = - 3

z = -2

Step-by-step explanation:

Please see steps in the image attached here.

6 0
3 years ago
What is the value of the underlined digit? 587
Nadya [2.5K]
There is no underlined dogit
8 0
3 years ago
Read 2 more answers
Molly now blends 6 ml of blue paint with 5 ml of white paint. She decides that she likes this color and wants to make more. If s
Stella [2.4K]

9514 1404 393

Answer:

  48 mL

Step-by-step explanation:

The amount of white paint she added is 40/5 = 8 times the amount she already had. So, Molly needs to add 6·8 = 48 ml of blue paint to her mix.

6 0
3 years ago
Natasha packs a single layer of a prism with 5 cubes. Each cube measures 1 centimeter long on each edge. If 5 layers completely
Nastasia [14]

Answer:25

Step-by-step explanation

5 x 5 = 25. Got this problem correct on Imagine Math.

5 0
3 years ago
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