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Alex_Xolod [135]
3 years ago
12

The circumference of circle B is 48. The circumference of circle A is 12. How many times greater is the area of circle B to the

area of circle A
Mathematics
1 answer:
nata0808 [166]3 years ago
7 0
Circumference = 2(pi)(radius)

Circle 1: 48=2(pi)(radius)
              24/pi = radius

Circle 2: 12 = 2(pi)(radius)
                6/pi = radius



Area = (pi)(radius)^2

Circle 1: A = (pi) (24/pi)^2
                  = 576 / pi

Circle 2:  A = (pi) (12/pi)^2
                  = 144 / pi

576/144 = 4 times greater
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Alla [95]

Answer:

10x^3-70x+60=0

x=1, x=2.

Step-by-step explanation:

x is the number (in millions) of cameras produced

The price is  p=100 - 10x²

Profit= 60 (in millions)

It costs 30 to make a camera.

So we have:

Profit=x(price-cost)

60=x( [100-10x²] - 30)

60=100x-10x^3 -30x

60=70x-10x^3

10x^3-70x+60=0

⇒x^3 -7x+6=0 is the equation we were looking for.

Solving:

The independent term of the equation is 6.

the divisors of 6 are {1,-1, 2,-2, 3,-3, 6,-6}

Substituting each divisor in the equation we have:

x=1

(1)^3 -7(1)+6=0

1-7+6=0

0=0

⇒x=1 is a solution.

x=-1

(-1)^3 -7(-1)+6=0

-1+7+6=0

12=0 this is not true

⇒x=1 is not a solution.

x=2

(2)^3 -7(2)+6=0

8-14+6=0

0=0

⇒x=2 is a solution.

x=-2

(-2)^3 -7(-2)+6=0

-8+14+6=0

12=0 this is not true

⇒x=-2 is not a solution.

x=3

(3)^3 -7(3)+6=0

27-21+6=0

12=0 this is not true

⇒x=2 is not a solution.

x=-3

(-3)^3 -7(-3)+6=0

-27+21+6=0

0=0

⇒x=-3 is a solution.

x=6

(6)^3 -7(6)+6=0

216-42+6=0 this is not true

⇒x=6 is not a solution.

x=-6

(-6)^3 -7(-6)+6=0

-216+42+6=0 this is not true

⇒x=-6 is not a solution.

The solutions of the equation are x=-3,x=1,x=2.

However, it is not possible to produce -3 millions of cameras.

So the only possible solutions are x=1 and x=2.

4 0
3 years ago
Read 2 more answers
Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordl
Karo-lina-s [1.5K]

Full Question

Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 18 to establish the order in which they will be serviced.

What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?

What is the probability that two phones of each type are among the first six serviced?

Answer:

a. 0.149

b. 0.182

Step-by-step explanation:

Given

Number of telephone= 18

Number of cellular= 6

Number of cordless = 6

Number of corded = 6

a.

There are 18C6 ways of choosing 6 phones

18C6 = 18564

From the Question, there are 3 types of telephone (cordless, Corded and cellular)

There are 3C2 ways of choosing 2 out of 3 types of television

3C2 = 3

There are 12C6 ways of choosing last 6 phones from just 2 types (2 types = 6 + 6 = 12)

12C6 = 924

There are 2 * 6C6 * 6C0 ways of choosing none from any of these two types of phones

2 * 6C6 * 6C0 = 2 * 1 * 1 = 2.

So, the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced is

3 * (924 - 2) / 18564

= 3 * 922/18564

= 2766/18564

= 0.149

b)

There are 6C2 * 6C2 * 6C2 ways of choosing 2 cellular, 2 cordless, 2 corded phones

= (6C2)³

= 3375

So, the probability that two phones of each type are among the first six serviced is

= 3375/18564

= 0.182

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Lunna [17]

Given:

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.

Pilot's speed in still air is 315 miles per hour.

To find:

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Solution:

Let the speed of wind be x miles per hour.

Speed with wind = 315+x miles per hour

Speed against wind = 315-x miles per hour

We know that,

Time=\dfrac{Distance}{Speed}

According to the question,

\dfrac{450}{315+x}=\dfrac{360}{315-x}

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By cross multiplication, we get

5(315-x)=4(315+x)

5(315)-5x=4(315)+4x

5(315)-4(315)=4x+5x

(5-4)315=9x

Divide both sides by 9.

\dfrac{(1)315}{9}=x

35=x

Therefore, the speed of wind is 35 miles per hour.

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