Answer:
a) ,
, b)
,
, c)
,
.
Step-by-step explanation:
The equation of the circle is:
After some algebraic and trigonometric handling:
Where:
Finally,
a) ,
.
b) ,
.
c) ,
Where:
The solution is
The parametric equations are:
Sarah bought a binder for $7.25 and six folders that totaled $9.05 how much did each folder cost
2 answers:
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Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.
Answer:
The other endpoint is (-33, 17)
Step-by-step explanation:
The rule of the mid-point of a segment whose endpoints are
(,
) and (
,
) is
In our question
∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)
∴ = -15 and
= x
∴ = 13 and
= y
∵ The coordinates of the mid-point of this segment are (-24, 15)
∴ = -24 and
= 15
→ Use the rule of the mid-point to find x and y
∵
→ Multiply both sides by 2
∴ -48 = -15 + x
→ Add 15 to both sides
∴ -33 = x
∵
→ Multiply both sides by 2
∴ 30 = 13 + y
→ Subtract 13 from both sides
∴ 17 = y
∴ The other endpoint is (-33, 17)