How is the formula for the circumference of a circle derived? Drag and drop the correct word into each box to complete the expla
nation.
2 answers:
Answer:
diameter
circumference
diameter
Step-by-step explanation:
First, find the length of the diameter (d) and the length of the circumference of the circle (c).
Next, divide the length of the circumference c by the length of the diameter d and set up an equation
where the ratio equals to (the definition of
)
Then, solve the equation for the circumference c:
Finally, substitute 2 times the radius for the diameter
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Answer:
m(arc ZWY) = 305°
Step-by-step explanation:
8). Formula for the angle formed outside the circle by the intersection of two tangents or two secants is,
Angle formed by two tangents =
=
=
= 40°
9). Following the same rule as above,
Angle formed between two tangents =
125 =
250 =
250 = m(arc ZWY) - 55
m(arc ZWY) = 305°
Therefore, measure of arc ZWY = 305° will be the answer.
10). m(arc BAC) =
=
=
= 74°
Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
