A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches.
2 answers:
Answer:
Radius = 75 inches .
Step-by-step explanation:
Given : A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches.
To find : what is the length of the radius of the circle.
Solution : We have given
Central angle = 90°
Arc of length = 117.75 inches.
Arc length = .
Plug the values
Theta = 90 , pi = 3.14 , arc length = 117.75 .
117 .75 = .
117 .75 =
On multiplying both sides 4
117.75 * 4 = 2 * 3.14 * radius .
471 = 6 .28 * radius .
On dividing both sides by 6.28
radius = .
Radius = 75 inches .
Therefore, Radius = 75 inches .
You might be interested in
Answer:
The correct option is;
x ≥ 6; h⁻¹(x) = 6 +√(x - 22)
Step-by-step explanation:
Given the function, h(x) = x² - 12·x + 58
We can write, for simplification;
y = x² - 12·x + 58
Therefore;
When we put x as y to find the inverse in terms of x, we get;
x = y² - 12·y + 58
Which gives;
x - x = y² - 12·y + 58 - x
0 = y² - 12·y + (58 - x)
Solving the above equation with the quadratic formula, we get;
0 = y² - 12·y + (58 - x)
a = 1, b = -12, c = 58 - x
Therefore;
We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;
At minimum, h'(x) = 0 = 2·x - 12
x = 12/2 = 6
Therefore;
h(6) = 6² - 12×6 + 58 = 22
Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing
Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22) and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6
The correct option is x ≥ 6; h⁻¹(x) = 6 +√(x - 22).
Check the picture below.
we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangle FPZ and triangle FPY are both congruent, so their sides are also congruents, thus PY = PZ.
