Answer:
The probability that a randomly placed point falls within the smaller, inner circle is 25/64
Step-by-step explanation:
The remaining part of question is attached
Solution
The area of smaller circle is
The area of large circle is
Area of the shaded region
Area of large circle - area of small circle
Probability that the point falls in the region of smaller circle is
Answer:
The answers are given below.
Step-by-step explanation:
7. EFGH is a rectangle. Slope of HE is
So, the slope of EF is
=
8 .PQRS is a square.
So, m∠QSR = 45°
[since the diagonals bisect the internal angles of a square]
9. m∠PTQ = 90°
[since the diagonals of a square intersect each other at right angles]
10. RT = 24 unit ,
so,
PR = unit
= 48 unit [since the diagonals of a square bisect each other]
So, SQ = PR = 48 unit
[since the diagonals of a square are equal]
11. Yes, a squae is a rectangle
12. Since RSTU is a rectangle,
so, ∠RUS + ∠SUT = 90°
⇒3x + 6 + 5x - 4 = 90°
⇒x = 11°
So, ∠RUS = 3x + 6 = 39°
Answer:
Part 1)
225 feet.
Part 2)
7 seconds.
Step-by-step explanation:
The height h(t) of the ball above the ground after <em>t</em> seconds is modeled by the function:
Part 1)
We want to determine the maximum height of the ball.
Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.
The vertex of a parabola is given by:
In this case, <em>a</em> = -16, <em>b</em> = 104, and <em>c</em> = 56.
Find the <em>x-</em> (or rather <em>t-</em>)<em> </em>coordinate of the vertex. So:
In other words, the ball reaches its maximum height after 3.25 seconds.
To find the maximum height, substitute this value back into the function. Hence:
The maximum height of the ball is 225 feet in the air.
Part 2)
We want to find the amount of time it took for the ball to hit the ground.
When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for <em>t: </em>
We can simplify a bit. Divide both sides by -8:
We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.
-14 and 1 works! Therefore, split the second term into -14 and 1:
Factor out a 2<em>t</em> from the first two terms and group the last two terms:
Factor by grouping:
Zero Product Property:
Solve for each case:
Since time cannot be negative, we can ignore the first case.
Therefore, it takes seven seconds for the ball to hit the ground.