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wel
3 years ago
12

HURRICANES A category 3 hurricane reaches speeds up to 20.88 kilometers per hour. The distance from Cuba to Key West is 145 kilo

meters. Write and solve a multiplication equation to find how long it would take a category 3 hurricane to travel from Cuba to Key West.
Mathematics
1 answer:
White raven [17]3 years ago
8 0
Let us assume that the time taken by the category 3 hurricane to travel from Cuba to Key West = X minutes
Speed of the category 3 hurricane is given as 20.88 km/hr
So the category 3 hurricane can travel 20.88 km in 1 hour.
The distance between Cuba and Key West = 145 km
Then
20.88 km is travelled by the category 3 hurricane in = 60 minutes
145 km from Cuba to Key west is travelled by the category 3 hurricane in = X minutes
So,
X = [(145 * 60)/20.88] minutes
   = 416.66 minutes
   = 17 hours and 36 minutes
Time taken by the category 3 hurricane to reach Key West from Cuba is 17 hours and 36 minutes.
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Towers A and B are located 5 miles apart. A ranger spots a fire at a 42-degree angle from tower A. Another fire ranger spots the
lord [1]

Answer: The fire is 3.5 miles from tower B

Step-by-step explanation: Please refer to the attached diagram. The triangle in the attached diagram illustrates the clues given in the question. Both rangers are standing at points A and B respectively with a distance of 5 miles between them, which is line AB. Also, one ranger spots a fire from a tower at an angle of 42 degrees, which is point A. Another ranger spots the same fire from another tower, but from an angle of 64 degrees, which is point B. The fire is at point C on the triangle. Now we have a triangle with only one side known (5 miles) and three angles known (the third angle is computed as 180 - {64+42} which equals 74) which are 64 degrees, 42 degrees and 74 degrees.

The distance from the fire to tower B is calculated using the law of sines. (Note that this is not a right angled triangle, hence we cannot use trigonometric ratios). The law of sines is expressed as follows;

a/SinA = b/SinB or

a/SinA = c/SinC

Depending on the sides and angles we are given and the ones we are to calculate.

The distance from the fire to tower B is line BC, labeled as a in our diagram. Using the law of sines

a/SinA = c/SinC

(Note also that a is directly facing angle A, c is directly facing angle C, and so on)

a/SinA = c/SinC

a/Sin 42 = 5/Sin 74

By cross multiplication we now have

a (Sin 74) = 5 (Sin 42)

Divide both sides of the equation by Sin 74 and we now arrive at

a = 5 (Sin 42)/Sin 74

a = 5 (0.6691)/0.9613

a = 3.3455/0.9613

a = 3.4802

{rounded to the nearest tenth of a mile, a equals 3.5}

Therefore the distance from tower B to the fire is approximately 3.5 miles

3 0
3 years ago
4. Match the polynomial in the left column with its descriptive feature in the
FromTheMoon [43]

Complete question is;

Match the polynomial in the left column with its descriptive feature in the

right column

A.) x³ + 3x² - 2x + 7

B.) 3a³ b ^(6)

C.) 3x⁴ – 9x³ + 5x^(8)

D.) 7a³ b ² + 18ab² c – 9a³

E.) 2x^(5) – 9x³ + 8x^(7)

F.) 4x^(8) – 7x² + 9

G.) x² − 7

I. 9th degree monomial

II. Constant term of −7

III. 7th degree polynomial

IV. Leading coefficient of 4

V. Four terms

VI. 5th degree polynomial

VII. Equivalent to 5x^(8) + 3x⁴ – 9x³

Answer:

A) For polynomial x³ + 3x² - 2x + 7 : Option V - 4 Terms

B) For polynomial 3a³ b ^(6) : option I - 9th degree monomial

C) For the polynomial 3x⁴ – 9x³ + 5x^(8) : Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) For the polynomial 7a³b² + 18ab²

c – 9a³ : Option VI - 5th degree polynomial.

E) For the polynomial 2x^(5) – 9x³ + 8x^(7) : Option III - 7th degree polynomial.

F) for the polynomial 4x^(8) – 7x² + 9 : Option IV - Leading coefficient of 4

F) For the polynomial x² − 7 : Option II - Constant term of −7

Step-by-step explanation:

A) Most appropriate matching descriptive feature for the polynomial x³ + 3x² - 2x + 7 is Option V - 4 Terms

B) Most appropriate matching descriptive feature for the polynomial 3a³ b ^(6) is option I - 9th degree monomial. This is because the sum of the powers of a and b is 9.

C) Most appropriate matching descriptive feature for the polynomial 3x⁴ – 9x³ + 5x^(8) is Option VII - Equivalent to 5x^(8) + 3x⁴ – 9x³

D) Most appropriate matching descriptive feature for the polynomial 7a³ b ² + 18ab² c – 9a³ is Option VI - 5th degree polynomial. This is because the highest sum of powers attached to a and b in a figure is 2 + 3 = 5.

E) Most appropriate matching descriptive feature for the polynomial 2x^(5) – 9x³ + 8x^(7) is Option III - 7th degree polynomial. This is because the highest power of x is 7.

F) Most appropriate matching descriptive feature for the polynomial 4x^(8) – 7x² + 9 is Option IV: Leading coefficient of 4. This is because the coefficient attached to the largest power of x is 4.

G) Most appropriate matching descriptive feature for the polynomial

x² − 7 is Option II - Constant term of −7

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Answer:

Variable (or coefficients)

Step-by-step explanation:

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2 years ago
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Show two different ways to solve (3x + 6) = 4x + 3. {= Show your work.​
yKpoI14uk [10]

Answer: Work below.

3x+6 = 4x+3

6-3 = 4x - 3x

3 = x

or

3x+6 = 4x+3

3x - 4x = 3 - 6

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3 years ago
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