The boat's travel from when it was first noticed until it stopped is 554.89 ft.
<h3>What is trigonometry?</h3>
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
Learn more about trigonometry here:
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Answer:
V = 339.3 cm³; L = 203.9 cm²; A = 317.0 cm²
Step-by-step explanation:
a) Volume
The formula for the volume (V) of a cone is
V = ⅓πr²h
V = ⅓π × 6² × 9
V = ⅓π × 36 × 9
V = 108π cm³
V ≈ 339.3 cm³
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Curved surface area
The formula for the lateral surface area (L) of a cone is
L = πr√(r² + h²)
L = π×6√(36 + 81)
L = 6π√[9(4 + 9)]
L = 6π√(9 × 13)
L = 18π√13 cm²
L ≈ 203.9 cm²
===============
b) Base surface area
The base is a circle, so the formula for base surface area (B) is
B = πr²
B = π×6²
B = 36π cm²
B ≈ 113.1 cm²
=====
Total surface area
A = L + B
A = 18π√(13 +36π)
A = 18π(2 + √13) cm²
A ≈ 203.9 + 113.1
A ≈ 317.0 cm²
Answer:
$80,000
Step-by-step explanation:
<u>Define the variables</u>:
Let x = "fish-flavored" chicken company investment (in dollars)
Let y = spray-on vitamins company investment (in dollars)
If Allen invested a total of $100,000:
⇒ x + y = 100000
Given:
- 3% profit on "fish-flavored" chicken investment
- 1% profit on pray-on vitamins investment
- Total profit = $2,600
⇒ 0.03x + 0.01y = 2600
Rewrite the first equation to make y the subject:
⇒ y = 100000 - x
Substitute into the second equation and solve for x:
⇒ 0.03x + 0.01(100000 - x) = 2600
⇒ 0.03x + 1000 - 0.01x = 2600
⇒ 0.02x + 1000 = 2600
⇒ 0.02x = 1600
⇒ x = 80000
Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.
Answer:
Answer Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis explanation the given figure has vertices p(1,2),q(2,1),r(3,2),s(3,3)recall that for counterclockwise rotation about the origin, (x,y)\rightarrow (-x,-y)when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will become p1( - 1, - 2),q1( - 2, - 1),r1( - 3, - 2),s1( - 3, - 3)next, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,p'(1, - 2),q'(2, - 1),r'(3, - 2),s'(3, - 3)
Step-by-step explanation:
Answer: 1 and 3
Step-by-step explanation:
4•3=12 and 2•3=6
