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3 years ago

15

A number times teo divided by four

1 answer:

leonid [27]3 years ago

5 0

Answer:

(x*10)/4

Step-by-step explanation:

I think "teo" means ten, so x times 10, divided by 4.

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The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart

azamat

Answer:

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio $\big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)}$ to create an equation with the two angles.

$\displaystyle \text{tan(45)} = \frac{h}{x}$
$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Let's take these two equations and solve for x in both of them.

<h2> $\textbf{Equation I}$ </h2>

$\displaystyle \text{tan(45)} = \frac{h}{x}$

tan(45) = 1, so we can rewrite this equation.

$\displaystyle 1=\frac{h}{x}$

Multiply x to both sides of the equation.

$\displaystyle x = h$

<h2> $\textbf{Equation II}$ </h2>

$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Multiply x + 200 to both sides and divide h by tan(30).

$\displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}$

Subtract 200 from both sides of the equation.

$\displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200$

Simplify h/tan(30).

$x=\sqrt{3}h - 200$

<h2> $\textbf{Equation I = Equation II}$ </h2>

Take Equation I and Equation II and set them equal to each other.

$h=\sqrt{3}h-200$

Subtract √3 h from both sides of the equation.

$h-\sqrt{3}h=-200$

Factor h from the left side of the equation.

$h(1-\sqrt{3}) =-200$

Divide both sides of the equation by 1 - √3.

$\displaystyle h=\frac{-200}{1-\sqrt{3} }$

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

$\displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}$
$\displaystyle h=\frac{-200+200\sqrt{3} }{1-3}$
$\displaystyle h =\frac{-200+200\sqrt{3} }{-2}$

Simplify this equation.

$\displaystyle h=100+100\sqrt{3}$
$h=273.20508075$

The height of the lighthouse is about 273 meters.

5 0

3 years ago

Read 2 more answers

A, b, and c are collinear, and B is between a and c. The ratio of AB to AC is 1:2. If A is at (7,-1) and B is at (2,1) what are

Nutka1998 [239]

Answer:

C(-3,3)

Step-by-step explanation:

Given

A = (7,-1)

B = (2,1)

AB:AC = 1:2

Required

Determine the coordinates of C

Since, B is between A and C; we need to determine ratio BC as follows;

$AB:AC = 1:2$

Convert to division

$\frac{AB}{AC} = \frac{1}{2}$

<em>AC = AB + BC;</em>

$\frac{AB}{AB + BC} = \frac{1}{2}$

Cross Multiply

$2 * AB = 1 * (AB + BC)$

$2 AB = AB + BC$

$2AB - AB = BC$

$AB = BC$

Divide both sides by BC

$\frac{AB}{BC} = 1$

Rewrite as

$\frac{AB}{BC} = \frac{1}{1}$

Write as ratio

$AB:BC = 1:1$

Next is to determine the coordinates of C as follows;

Because B is between both points. we have:

$B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$m:n = AB:BC = 1:1$

$B(x,y) = B(2,1)$

$A(x_1,y_1) = A(7,-1)$

So; we're solving for x2 and y2

$B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

Solving for x2;

$x = \frac{mx_2 + nx_1}{m+n}$

$2 = \frac{1 * x_2 + 1 * 7}{1+1}$

$2 = \frac{x_2 + 7}{2}$

Cross Multiply

$2 * 2 = x_2 + 7$

$4 = x_2 + 7$

$x_2 = 4 - 7$

$x_2 = -3$

Solving for y2;

$y = \frac{my_2 + ny_1}{m+n}$

$1 = \frac{1 * y_2 + 1 * -1}{1+1}$

$1 = \frac{y_2- 1}{2}$

Cross Multiply

$2 * 1 = y_2 - 1$

$2 = y_2 - 1$

$y_2 = 2 + 1$

$y_2 = 3$

<em>Hence, the coordinates of C are: C(-3,3)</em>

4 0

4 years ago

If RITA walked 13,200 feet to her friends house and Fabian rode his bike 4 miles, who walked further

iren2701 [21]

Rita walked 13,200 feet
fabian rode=4miles(4 x 5280)=21,120 feet
answer=Fabian walked further

6 0

3 years ago

Read 2 more answers

Given the line 2 x - 3 y - 5 = 0, find the slope of a line that is perpendicular to this line. A.3/2

Sliva [168]

Answer:

Step-by-step explanation:

2x - 3y = 5

-3y = -2x + 5

y = (2/3)x - 5

the perpendicular slope is -3/2

the answer is c

3 0

4 years ago

Read 2 more answers

Ple help me whats the slope?

mestny [16]

Answer:

-4/3

Step-by-step explanation:

that is the answer...no explanation needed

7 0

3 years ago

Read 2 more answers