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zalisa
2 months ago
13

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
2 answers:
Inessa [12.5K]2 months ago
5 0
Let
x denote the distance the boat has traveled, while
y represents the distance from the boat to the lighthouse.

The equations we can derive are:
tan 18°33' = 200 / (x + y)
and
tan 51°33' = 200 / y

To find y from the second equation:
y = 200 / tan 51°33'

Next, by rearranging the first equation and substituting for y, we get:
x = 200 / tan 18°33' - 200 / tan 51°33'
x = 458.81 ft

Thus, the distance the boat covered is 458.81 ft before it halted.
PIT_PIT [12.4K]2 months ago
4 0

Response: 437.21 ft

Detailed explanation:

Initially, convert all minutes into degrees.

18°33’ converts to 18.55°

51°33’ converts to 51.55°

At the moment the boat is first seen:

Tan(x) = opposite/adjacent

Tan(18.55°) = 200/x

Solving gives x = 200/tan(18.55)

x = 596.01 ft

When the boat comes to a stop:

Tan(51.55) = 200/x

x = 158.80 ft

Calculating the distance traveled:

596.01 - 158.80 = 437.21

It's quite straightforward once the pattern is grasped!

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Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.
Zina [12379]

Answer:

1. Both directions

2. Only in one direction

Step-by-step explanation:

    The reason Statement 1 can occur both ways is that if Bo and Mel are connected, it holds true forward and backward.

The reasoning for Statement 2 being one-directional is that if the sprinklers are operating, then the grass is wet will be valid since it's stating ONLY that the sprinklers are on. If it were to reverse and the grass is wet ONLY because of the sprinklers, then it's incorrect as rain could also cause the grass to be wet. Thus, there are numerous possibilities for the grass being wet, which explains the answers.

4 0
2 months ago
The numbers 1, 2, 3, and 4 have weights 0.1, 0.2, 0.3, and 0.4 respectively. Compute the weighted average. (to the nearest tenth
PIT_PIT [12445]

Response:

3.0

Detailed breakdown:

1(0.1) + 2(0.2) + 3(0.3) + 4(0.4) equals 3.0

3 0
1 month ago
Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative Start
babunello [11817]

Response:

Second option: (2.2, -1.4)

Third option: (2.2, -1.35)

Detailed explanation:

The missing graph has been provided.

The attached image illustrates the graphing of the following system of linear equations:

\left \{ {{y=-\frac{7}{4}x+\frac{5}{2}} \atop {y=\frac{3}{4}x-3}} \right.

Notice the intersection of the lines.

According to the definition, if lines in a system of equations intersect, then there is only one solution. This implies that the intersection point is the solution to that system. This can be expressed as:

(x,y)

Represented by "x" for the x-coordinate and "y" for the y-coordinate.

Here, it's noticeable that:

- The x-coordinate of the intersection point lies between  x=2 and x=3.

- The y-coordinate of the intersection point is situated between  y=-1 and y=-2.

Therefore, you can conclude that the forthcoming points (Refer to the options given in the exercise) are potential approximations for this system:

(2.2, -1.4)\\\\\\(2.2, -1.35)

7 0
3 months ago
Read 2 more answers
Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, p
PIT_PIT [12445]

Answer:

B ≤ 11 bags

Step-by-step explanation:

Alonso starts with $21. After purchasing eggs for $2.50, he has $21 - $2.50 left = $18.50

Thus, the remaining money for avocados is $18.50.

Each 3 bags of avocados cost $5, making the price for 1 bag $(5/3)

Consequently, if B represents the quantity of avocado bags purchased by Alonso, it could be expressed as:

B ≤ $18.50 ÷ $(5/3)

B ≤ 11.1

B ≤ 11

B ≤ 11 bags

8 0
1 month ago
Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3). Round your answer to the ne
tester [12383]

Answer: 20 units

Step-by-step explanation:

The formula for calculating the distance between two coordinates P(a,b) and Q(c,d) is as follows:-

PQ=\sqrt{(d-b)^2+(c-a)^2}

Initially provided: The coordinates of the quadrilateral's vertices are C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

The distance between vertices C (−2, 1) and D (2, 4) is as follows:-

CD=\sqrt{(4-1)^2+(2-(-2))^2}\\\\\Rightarrow\ CD=\sqrt{(3)^2+(4)^2}\\\\\Rightarrow\ CD=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ CD=5\text{ units}

Distance between points D (2, 4) and E (5, 0) is calculated as:-

DE=\sqrt{(4-0)^2+(2-5)^2}\\\\\Rightarrow\ DE=\sqrt{(4)^2+(-3)^2}\\\\\Rightarrow\ DE=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ DE=5\text{ units}

Distance between coordinates E (5, 0) and F (1, −3) is given by:-

EF=\sqrt{(-3-0)^2+(1-5)^2}\\\\\Rightarrow\ EF=\sqrt{(-3)^2+(-4)^2}\\\\\Rightarrow\ EF=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ EF=5\text{ units}

Distance from C (−2, 1) to F (1, −3) is as follows:-

FC=\sqrt{(-3-1))^2+(1-(-2))^2}\\\\\Rightarrow\ FC=\sqrt{(-4)^2+(3)^2}\\\\\Rightarrow\ FC=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ FC=5\text{ units}

The total perimeter of the quadrilateral is calculated as = CD + DE + EF + FC

=5+5+5+5=20\text{ units}

3 0
2 months ago
Read 2 more answers
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