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mariarad [96]
2 years ago
10

A man travels at 42 degrees northwest, and ends up 8.5 miles west of his starting point. How far did he travel?

Mathematics
1 answer:
Zarrin [17]2 years ago
6 0

Answer:

The man traveled 12.70 miles.

Step-by-step explanation:

We can find the distance traveled by the man knowing:

d_{W}: the distance at the west = 8.5 miles

\theta_{NW}: the northwest angle = 42°

Then by using the following trigonometric identity we have:

sin(\theta) = \frac{d_{W}}{d_{NW}}

d_{NW} = \frac{d_{W}}{sin(\theta)} = \frac{8.5 miles}{sin(42)} = 12.70 miles

Therefore, the man traveled 12.70 miles.

I hope it helps you!                                    

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D=sqrt((x2-x2)^2+)y2-y1)^2)
D=sqrt((1-0)^2+(2-6)^2
D=sqrt(1+16)
D=sqrt 17
radius = sqrt 17
(h, k) is the center and r is the radius
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5 0
3 years ago
What is the sum of the arithmetic sequence 3, 9, 15…, If there are 34 terms?
snow_tiger [21]

Answer:

first we find the common difference.....do this by subtracting the first term from the second term. (9 - 3 = 6)...so basically, ur adding 6 to every number to find the next number.

we will be using 2 formulas....first, we need to find the 34th term (because we need this term for the sum formula)

an = a1 + (n-1) * d

n = the term we want to find = 34

a1 = first term = 3

d = common difference = 6

now we sub

a34 = 3 + (34-1) * 6

a34 = 3 + (33 * 6)

a34 = 3 + 198

a34 = 201

now we use the sum formula

Sn = (n (a1 + an)) / 2

S34 = (34(3 + 201))/2

s34 = (34(204)) / 2

s34 = 6936/2

s34 = 3468 <=== the sum of the first 34 terms:

6 0
3 years ago
The sum of two numbers is 23. The difference of the numbers is 7.4. What are the two numbers?​
Brums [2.3K]
X+y=23
X-y=7.4

X+y=23
y=23-X

X-y=7.4
(23-y)-y=7.4
23-2y=7.4
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Y=7.8

X+y=23
X+7.8=23
X=15.2

Therefore the two numbers are 7.8 & 15.2

5 0
2 years ago
(3/5)^2 + 4 x 3 - 2<br><br><br><br><br> Please help :)
Molodets [167]

Answer:

10 \frac{9}{25}

Step-by-step explanation:

\bigg(  \frac{3}{5} \bigg)^{2}  + 4 \times 3 - 2 \\  \\  =  \frac{9}{25}  + 12 - 2 \\  \\  =  \frac{9}{25}  + 10 \\  \\  =  \frac{9 + 10 \times 25}{25}  \\  \\  =  \frac{9 + 250}{25}  \\  \\  =  \frac{259}{25}  \\  \\  = 10 \frac{9}{25}

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2 years ago
In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio o
Kruka [31]

Answer:

1/14:5/7:3/14

Step-by-step explanation:

Since orange=15

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Coconut milk=50

50+15+5

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So

Orange=15/70

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Apple=5/70

Divide both by 5

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Coconut milk=50/70

Divide both by 10

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So the ratio of apple to coconut to orange

1/14:5/7:3/14

8 0
2 years ago
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