At what point in the first quadrant does the line with the equation y=x+2 intersect the circle with radius 6 and center (0,2)

In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?

Ainat [17]

Answer:

$A_{Circle} \approx 39.24\: units^2$

Step-by-step explanation:

Square ABCD is inscribed in a circle with center P such that BC = 5 units.

BD will be diagonal of the square as well as diameter of the circle.

$BD = BC\times\sqrt 2$

$\implies BD = 5\sqrt 2$

-> Diameter of the circle $(d) = 5\sqrt 2$

-> Radius of the circle $(r) = 2.5\sqrt 2=3.535\: units$

$A_{Circle} =\pi(r)^2$

$\implies A_{Circle} =3.14(3.535)^2$

$\implies A_{Circle} =39.2381465$

$\implies A_{Circle} \approx 39.24\: units^2$

8 0

2 years ago

Two trains leave towns 471 miles apart at the same time and travel toward each other. One train travels 21 miles per hour slower

nadya68 [22]

Let the slower train's velocity be x-21

Let the faster train's velocity be x

We know that the approach speed is the sum of both speeds, so x+x -21= 2x-21.

The approach rate is given by Distance/time = 471/3 = 157mpH

x+x-21=157

2x=157+21

2x=178

x=89mph

The slower train is travelling 89-21 = 68mph

The faster train is travelling 89mph.

7 0

1 year ago

What is the value of x ?

statuscvo [17]

Here, Sin Ф = P / H
Sin 31 = x / 430
0.515 = x /430
x = 430 * 0.515
x = 221.45

In short, Your Answer would be 221.45

Hope this helps!

8 0

3 years ago

Solve 9x^2- 17x- 85 = 0 Give your solutions correct to 3 significant figures.

dybincka [34]

Answer:

$x =\frac{17}{18} +\frac{1}{18} \sqrt{3349}$ OR $x =\frac{17}{18} +\frac{-1}{18} \sqrt{3349}$

Step-by-step explanation:

9x2−17x−85=0

For this equation: a=9, b=-17, c=-85

9x2+−17x+−85=0

Step 1: Use quadratic formula with a=9, b=-17, c=-85.

$x =\frac{-b + \sqrt{b^{2}-4ac } }{2a}$

$x =\frac{-(-17)+\sqrt{(-17)^{2} -4(9)(-85)} }{2(9)}$

$x =\frac{17}{18} +\frac{-1}{18} \sqrt{3349}$

4 0

2 years ago

Write the data set that is shown on the dot plot in ascending order.

Lady_Fox [76]

Answer:

Step-by-step explanation:

1,2,3,3,3,3,5,6,7,10,10,10,11,11,12,12,13,13,

14,15

5 0

3 years ago