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Alexeev081 [22]
2 years ago
8

A circle has a radius with endpoints at(2,5) and (-1,-4).Find the circumference and area of the circle.

Mathematics
1 answer:
ratelena [41]2 years ago
7 0

Answer:

circumference is 59.6075

area is 282.743

Step-by-step explanation:

   To find the circumference and area of the circle, we need to first find the radius. This can be achieved using the distance formula.

   The distance formula goes as follows: for any two points on an coordinate plane, the distance can be calculated using a certain method. This method is the derived from the Pythagorean Theorem. Basically, you find the distance from right to left and square it, and then find the distance from up to down and square it. You add these two values together and then square root the whole thing. I know, its complicated.

   To apply this to your problem, we do 2-(-1) to find the distance from right to left (x-distance) and then we do 5-(-4) to find the distance from up to down (y-distance). 2-(-1)=3 and squaring that we get 9. 5-(-4)=9 and squaring that we get 81. Adding these two values together, we get 90 and square rooting it we get \sqrt{90}.

   The formula for circumference of a circle is 2Pi * radius and plugging in our values we get 2Pi * \sqrt{90} which gives us approximately 59.6075.

   The formula for area of a circle is Pi * radius^2 and plugging in our values we get Pi * \sqrt{90} ^2 which gives us approximately 282.743.

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If the company provides 1 1/4 vacation days to its employees every month,how many vacation days does an employee get every year?
FromTheMoon [43]
We know there are 12 months in a year so we would multiply 1 1/4 by 12. We can write 1 1/4 as 1.25 (to make it easier to multiply). 12x1.25=15
Your answer is 15 vacation days in one year
5 0
3 years ago
Use the functions f(x)=2x and g(x)=x^2+1 to find the value of each expression
Alinara [238K]

Answer:

1.  20

2. 23

3. 6

Step-by-step explanation:

We have that:

f(x) = 2x

g(x) = x² + 1

f(g(x)) is the composite function of f and g. So

f(g(x)) = f(x²-1) = 2(x²+1) = 2x² + 2

1. f(g(3))

f(g(x)) = 2x² - 2 = 2(3)² + 2 = 18 + 2 = 20

2. f(3)+g(4)

f(3) = 2(3) = 6

g(4) = 4² + 1 = 17

f(3) + g(4) = 6 + 17 = 23

3. f(5) - 2g(1)​

f(5) = 2(5) = 10

g(1) = (1)² + 1 = 2

f(5) - 2g(1) = 10 - 2*2 = 10 - 4 = 6

6 0
3 years ago
Find the area of the triangle formed by the origin and the points of intersection of parabolas y=− 1/3 (x−1)^2+8 and y=x^2−2x−3.
Kobotan [32]

Answer:

The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.

Step-by-step explanation:

The two parabolas are y = - \frac{1}{3}(x - 1)^{2} + 8 and y = x² - 2x - 3.

Now, solving those two equations we will get the points of intersection.

So, - \frac{1}{3}(x - 1)^{2} + 8 = x^{2} - 2x - 3

⇒ - (x - 1)² + 24 = 3x² - 6x - 9

⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9

⇒ 4x² - 8x - 32 = 0

⇒ x² - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ (x - 4)(x + 2) = 0

So, x = 4 or - 2.

Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).

Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).

Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.

So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)

8 0
2 years ago
Given h(x) = 5x + 3. what is the value of h(-11)
alexira [117]

Answer:

h(-11)=-52

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
PLEASE HELP QUICK I HAVE 10 MINUTES
Vlad1618 [11]

Answer:

56.58j = c

Step-by-step explanation:

c = cost

5 0
2 years ago
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