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Gnom [1K]
3 years ago
8

Saint Petersburg, Russia and Anchorage, Alaska, both have approximately the same latitude of 60 degrees. That means you can reac

h Saint Petersburg from Anchorage by flying directly east, or directly west. Assume the earth is a sphere of radius 6371 km. (a) By heading directly east, what is the distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E)?
Mathematics
1 answer:
user100 [1]3 years ago
5 0

Answer:

Distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E) = 10,002.47 KM

Step-by-step explanation:

As earth is a sphere of radius 6371 km.

Therefore at 60 degree latitude, the radius of circle can be calculated as shown below:

= 6371 * Cos 60

= 3185.5 KM

Saint Petersburg is nearly 180 degree about Anchorage by flying directly east.

So Distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E) can be calculated as shown below:

= (180 * 2 * 3.1416 * 3185.5) / 360

= 10,002.47 KM

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I need help with this question
kifflom [539]

Answer:

(-1,9)

(0,3)

(1,-3)

(5,-27)

Step-by-step explanation:

Plug x values into the equation.

6 0
3 years ago
Factor 4a^2-25. Please
Dmitrij [34]

Answer:

(2 a - 5) (2 a + 5)

Step-by-step explanation:

Factor the following:

4 a^2 - 25

4 a^2 - 25 = (2 a)^2 - 5^2:

(2 a)^2 - 5^2

Factor the difference of two squares. (2 a)^2 - 5^2 = (2 a - 5) (2 a + 5):

Answer: (2 a - 5) (2 a + 5)

8 0
3 years ago
The denominator of a rational number is greater than its numerator by 5. If 5 is subtracted from the numerator and 4 is added to
nasty-shy [4]

Answer:

7/12.

Step-by-step explanation:

=x/x+5.

x-5/x+5+4=⅛

x-5/x+9=⅛

x-5=⅛(x+9)

x-5=⅛x+1⅛

x-⅛x=1⅛+5

⅞x=49/8

7x=49

x=7

thus the initial fraction is x/x+5= <u>7</u><u>/</u><u>1</u><u>2</u>

A rational number is a fraction

4 0
3 years ago
Consider the following system of equations. -10x2-10y2=-300 5x2+5y2=150 Which statement describes why the system has infinite so
scoundrel [369]

Answer:

The equations represent circles that result in the same graph.

Step-by-step explanation:

we have

-10x^{2}-10y^{2}=-300

Divide by -10 both sides

x^{2}+y^{2}=30 -----> equation A

This is the equation of a circle centered at origin with radius r=\sqrt{30} \ units

and

5x^{2}+5y^{2}=150

Divide by 5 both sides

x^{2}+y^{2}=30 -----> equation B

This is the equation of a circle centered at origin with radius r=\sqrt{30} \ units

equation A and equation B are equal

therefore

The system has infinite solutions, because the equations represent circles that result in the same graph.

4 0
3 years ago
Paul paid $ 25.50 for 3 cups of hot chocolate and cups of tea. The cost of each cup of tea was 2/3 the cost of each cup of hoy c
Allushta [10]

Let the cost of one cup of hot chocolate  be = x

Let the cost of one cup of hot tea be = y

Paul paid $ 25.50 for 3 cups of hot chocolate and 4 cups of tea.

Equation becomes = 3x+4y=25.50   ...(1)

As given, the cost of each cup of tea was 2/3 the cost of each cup of hot chocolate.

y=\frac{2x}{3}   .... (2)

Putting the value of y from (2) in (1)

3x+4(\frac{2x}{3})=25.50

=3x+\frac{8x}{3}=25.50

=\frac{9x+8x}{3}=25.50

=17x=76.5

x=4.5

y=\frac{2x}{3}

=\frac{2*4.5}{3}

y =3

Hence each cup of hot chocolate is $4.50

Each cup of tea is $3.

7 0
3 years ago
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