Answer:
818.4 in²
Step-by-step explanation:
shaded region = area of sector - area of triangle
area of sector = area of circle × fraction of circle
A = π × 27.8² × ≈ 1011.65 in²
area of triangle = 0.5 × 27.8 × 27.8 × sin150° ≈ 193.21 in²
shaded region = 1011.65 - 193.21 ≈ 818.4 in²
Answer:
Total area equation = tex]w(w+6)=91[/tex]
b/2 = 3
Dimensions of the patio: width = 7 feet, length = 13 feet
Step-by-step explanation:
The area of a rectangle is given the formula:
where
is the width
is the length
We know from our problem that the area of the patio is 91 square feet, so . We also know that the length is 6 feet longer then the width, so
.
Replacing values in our area equation
Expanding the left side:
Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is , so its coefficient is 6. Now, half its coefficient or
. Finally,
.
To complete the square we need to add 9 to both sides of the equation:
Notice that the left side is a perfect square trinomial (both and 9 are perfect squares), so we can express it as:
Now that we completed the square, we can solve our equation
- Take square root to both sides
- Subtract 3 from both results
Since length cannot be negative, is the solution of our equation.
We now know that the width of our rectangular patio is 7 feet, so we can find its length:
We can conclude that half the coefficient of the width is , the width of the patio is 7 feet, and its length is 13 feet.
answer:
Step-by-step explanation:
On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).
now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is , where (p,q) is the turning point. now we substitute the turning point
, now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.
0 = a(3.15 - 0.76)^2 + 57
-57 =a(2.39)^2
-57 = a(5.7121)
-57/5.7121 =a
-9.9788169 = a then we substitute a to get the quadratic equation therefore f is