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3 years ago

A circle has a sector with area 45/4 pi and central angle of 9/10 pi radians. What is the area of the circle?

Mathematics

1 answer:

Nikitich [7]3 years ago

6 0

Answer:

the area of the circle: 25π

Step-by-step explanation:

45/4 π = 11.25π

9/10π = 0.9π

11.25π / 0.9π = x / 2π .... 360° = 2π

x = (11.25π x 2π) / 0.9π = 25π

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Lucy was playing a card with two friends. They were playing with a deck of 21 cards. Lucy dealt 1/3 of the deck to each person.

Rama09 [41]

If each of them got 1/3 of the deck then they would each get 7 cards

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3 years ago

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A secant and a tangent to a circle intersect in a 42-degree angle. The two arcs of the circle intercepted by the secant and the

Amanda [17]

Answer:

The measure of the third arc is $150\°$

Step-by-step explanation:

step 1

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

in this problem

Let

x----> the greater arc of the circle intercepted by the secant and the tangent

y----> the smaller arc of the circle intercepted by the secant and the tangent

$42\°=\frac{1}{2}(x-y)$

$84\°=(x-y)$ ----> equation A

$\frac{x}{y}=\frac{7}{3}$

$x=\frac{7}{3}y$ -----> equation B

Substitute equation B in equation A and solve for y

$84\°=(\frac{7}{3}y-y)$

$84\°=(\frac{4}{3}y)$

$y=3*84\°/4=63\°$

Find the value of x

$x=\frac{7}{3}(63\°)=147\°$

step 2

Find the measure of the third arc

Let

z------> the measure of the third arc

we know that

$x+y+z=360\°$ -----> complete circle

substitute the values and solve for z

$147\°+63\°+z=360\°$

$z=360\°-(147\°+63\°)=150\°$

3 0

3 years ago

La funcion que representa el beneficio obtenido por una empresa si vende x unidades de uno de sus productos es f(x)= -70x^2+2800

DerKrebs [107]

Answer:

$20$

Step-by-step explanation:

La función es

$f(x)=-70x^2+2800x-45000$

Diferenciando con respecto a $x$ obtenemos

$f'(x)=-140x+2800$

Igualar con cero

$0=-140x+2800\\\Rightarrow x=\dfrac{2800}{140}\\\Rightarrow x=20$

Doble derivada de la función

$f''(x)=-140$

Entonces, la función es máxima cuando el número de unidades vendidas, $x=20$ ,

3 0

3 years ago

What is the sum of 1 2/5 and 5 3/4

Art [367]

Answer:

$7\frac{3}{20}$

Step-by-step explanation:

Hey there!

Well to add this we need to pu it in improper form.

7/5 + 23/4

Now we need to find the LCM.

5 - 5, 10, 15, 20, 25, 30

4 - 4, 8, 12, 16, 20, 24, 28

So the LCD is 20.

Now we need to change the 5 and 4 to 20.

5*4 = 20

7*4 = 28

28/20

4*5=20

23*5=115

115/20

Now we can add 28 and 115,

= 143/20

Simplified

7 3/20

Hope this helps :)

4 0

3 years ago

Read 2 more answers

A small box of cereal contains 10 cups of cereal. A medium box of the same cereal contains 30% more cereal than the small box. H

mario62 [17]

Answer:

13 cups

Step-by-step explanation:

If the small box has 10 cups, then:

(small) 10 cups = 100%

(medium) x cups = 130%

Now, cross multiply:

10 (130) = x (100)

1300 = 100x

x = 13

Another way to solve this is by turning 30% into a decimal:

30/100 = 0.3

10 (0.3) = 3

Now you have 30% of the 10 cups, but you need 30% more than the small box, so:

10 + 3 = 13 cups

6 0

3 years ago