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Gre4nikov [31]
3 years ago
13

Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind i

s blowing at a 45 angle from due east. What is the actual speed of the plane with the wind?
Mathematics
1 answer:
ch4aika [34]3 years ago
8 0
The actual speed of the plane with the wind:
v² = ( 150 + 50 · cos 45°)² + ( 50 · sin 45°)²
v² = ( 150 + 35.355 )² + 35.355²
v² = 34,356.467 + 1,249.976
v = √35,606.452
v = 188.7 mph
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Attached below is the problem that I worked out. And I checked my answer simply by plugging it in

8 0
2 years ago
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
kozerog [31]

Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

xₙ = y + d(a-1)

2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

x₃* r * r

= x₃*r² = x₅

divide both sides by x₃ to isolate the r²

x₅/x₃ = r²

square root both sides

√(x₅/x₃) = ±r

One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.

Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence

8 0
3 years ago
Juan says that 8, 1 3/4, and -12 are all integers. Is he correct? Explain your answer. Please help me fast
monitta
No, he is not right.

Integer is a number that can be written without a fractional component, and 1 3/4 doesn't.

Here's an image for you to better understand. 


8 0
3 years ago
Read 2 more answers
-8 times 0.09 times -0.5
Black_prince [1.1K]
The answer is 0.36. I don't think u need to explain why, right ;)
8 0
3 years ago
Read 2 more answers
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