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NeX [460]
3 years ago
15

Problem 15.2. A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s

along a great circle on the earth when the subtending angle has measure 1′ = "one minute" = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.
(a) Find the length of one nautical mile to the nearest 10 feet.

(b) A vessel which travels one nautical mile in one hours time is said to have the speed of one knot; this is the usual navigational measure of speed. If a vessel is traveling 26 knots, what is the speed in mph (miles per hour)?

(c) If a vessel is traveling 18 mph, what is the speed in knots?
Mathematics
1 answer:
Stels [109]3 years ago
8 0

Answer:

a) 6080 ft

b) 29.952 mph = 30 mph to 2s.f

c) 15.6 knots

Step-by-step explanation:

Length of an arc is given as (θ/360) × (2πr)

For a nautical mile, θ = 1' = (1/60)° = 0.01667°

Length of a nautical mile = (0.01667/360) × (2π × 3960) = 1.152 miles

1 mile = 5280 ft

1.152 miles = 5280×1.152 = 6082.1 ft = 6080 ft to the nearest 10 feet.

b) 1 knot = 1 nautical mile/hour

1 nautical mile/hour = 1.152 miles/hour (from part (a))

1 knot = 1.152 miles/hour

26 knots = 26 × 1.152 miles/hour = 29.952 mph = 30 mph to 2 s.f

c) 1.152 mph = 1 knot

18 mph = (18×1/1.152) knots = 15.625 knots

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Furkat [3]

Answer:  a(x) = x^2 + 40 x + 384

Step-by-step explanation:

Since, here the length of the rectangle is represented by the function l(x) = x + 24,

While the breadth of the rectangle is represented by the function w(x) = x + 16.

And, we know that the area of the rectangle = length of the rectangle l(x) × breadth of the rectangle.

a(x) = l(x) × w(x)

a(x) = (x + 24) × (x + 16)

a(x) = x^2 + 24 x + 16 x + 24\times 16

a(x) = x^2 + 40 x + 384


4 0
3 years ago
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kvv77 [185]

Answer:

  all are "yes"

Step-by-step explanation:

A polynomial is defined for all values of x. None are excluded. Every value listed is in the <em>domain</em> of f(x) = (x +1)².

4 0
3 years ago
sally has a pet snail that snail fell in the well the well is 16 feet deep. each day the snail climbs up 5 feet but each night i
vlada-n [284]

<em>Answer:</em>

<em>The net speed per 24 hours is 5 - 4 = 1 foot.  </em>

<em>1 ft / 24 hrs = 16 ft / x hrs  </em>

<em> </em>

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<em />

3 0
3 years ago
Veronica has been saving dimes and quarters. She has 94 coins in all and the total value is $19.30. How many dimes and how many
Stolb23 [73]

Answer:

Step-by-step explanation:

d + q = 94.....d = 94 - q

0.10d + 0.25q = 19.30

0.10(94 - q) + 0.25q = 19.30

9.4 - 0.10q + 0.25q = 19.30

-0.10q + 0.25q = 19.30 - 9.40

0.15q = 9.90

q = 9.90/0.15

q = 66 <===== there are 66 quarters

d + q = 94

d + 66 = 94

d = 94 - 66

d = 28 <==== there are 28 dimes

3 0
3 years ago
If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra
bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be l units.

Using pythagoras theorem, we can find out the value of l.

As per theorem:

Hypotenuse^{2} = Base^{2} + Height^{2}\\

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Lateral surface area of square prism = 4 \times Area of triangular surface

\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units

Surface Area of 5 surfaces of the square prism =

4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units

So, total surface area of composite figure:

240 + 480 = 720 sq units.

7 0
3 years ago
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