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anyanavicka [17]
3 years ago
7

A plane flies due south for 600 miles. It turns and flies 250 miles ,35 degrees east of south. How far is the plane from it’s or

igin. Step by step..Explanation.Please..

Mathematics
1 answer:
Mariulka [41]3 years ago
6 0

The distance of plane from the origin is 357.14 miles

<u>Explanation:</u>

Given:

distance traveled southwards, y = 600 miles

Distance traveled east of south, z = 250 miles

Angle, θ = 35°

Distance of plane from the origin, x = ?

The figure is attached for reference:

tan θ = Perpendicular / base

tan θ = distance travelled east of south / x

tan 35° = 250 / x

we know,

tan 35° = 0.7

So,

0.7 = \frac{250}{x} \\\\x = \frac{250}{0.7} \\\\x = 357.14 miles

Therefore, the distance of plane from the origin is 357.14 miles

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Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
Point E is between points D and F and DE=27 and EF =34.
asambeis [7]
If e is between them, then the distances DE and EF add to the total, DF. So the answer is just 27 + 34 which is 61, A

4 0
4 years ago
I need help the question is solve the equation n+75=155​
SashulF [63]
All you need to do for this is 155-75 which would be 80 :) hope this helps
5 0
3 years ago
Read 2 more answers
The equation y=2x+3 represents the cost y (in dollars) of mailing a package that weighs x pounds. a. Graph the equation. b. Usin
FinnZ [79.3K]

Answer:

B. Slightly more than $5

Step-by-step explanation:

y = 2x + 3

Firstly we check variables to make sure we understand.

y = dollars

x = pounds

On the scale, it says 1.126 lb. Which means 1.126 pounds.

And so, x = 1.126

y = 2x + 3

y = 2(1.126) + 3

y = 2.252 + 3

y = 2.252

The graph for part a and park b. It is underneath. I wrote 1.1, because it is rounded down from 1.126 lb, which is part b. The one with one line and no dots is part a.

4 0
2 years ago
Needs to be solved in 10 min. I don't under stand.
GarryVolchara [31]

4a. 150*6=900 g

4b. 450/150=3 eggs

5a. 11.96/4=$2.99/bag

5b. 2.99*9=$26.91 for 9 bags

Hope this helps!

8 0
4 years ago
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