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AfilCa [17]
3 years ago
7

A safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. A fire department's longest ladder is

110 feet. What is the maximum safe rescue height?

Mathematics
2 answers:
Bess [88]3 years ago
6 0

Answer:

104.6

Step-by-step explanation:

Julli [10]3 years ago
5 0

Answer:

The maximum safe rescue height is   104.6 feet above the height of  the ground.

Step-by-step explanation:

Consider a triangle ABC where C is the point where the rescue ladder is standing and  AB be the building  and Ladder making an angle of 72° as shown.

We have to find the height of the building.

Let x be the height of building

Using Trigonometric ratio,

\sin C=\frac{\text{Perpendicular}}{\text{Hypotenuse}}

\sin 72^{\circ}=\frac{AB}{BC}

\sin 72^{\circ}=\frac{x}{110}

x=110 \times \sin 72^{\circ}

x=104.6

So, the maximum safe rescue height is   104.6 feet above the height of

the ground.

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Simplify expression –5.6 + 8.2
Vedmedyk [2.9K]
2.6   because you substract


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3 years ago
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The function f(x) = 15(2)^x represents the growth of a frog population every year in a remote swamp. Elizabeth wants to manipula
weeeeeb [17]
Half one is 1/2;
half three is 3/2;
Thus, if f(x) represents annual growth, f(x)/2 shows it every half-year, like this:
\dfrac{f(x)}{2} = \dfrac{15\cdot 2^x}{2} \\  \\ 
\dfrac{f(x)}{2} = \dfrac{15}{2}\cdot 2^x

Written in plain text: f(x)=15/2*2^x
5 0
3 years ago
Read 2 more answers
I need help on listing the four points that have a distance of 8 from B, thank you!
dolphi86 [110]

Answers:

  • (12, 3)
  • (-4, 3)
  • (4, 11)
  • (4, -5)

A diagram is shown below.

===========================================================

Explanation:

First we locate point B at (4,3). The '4' in the x position means we've gone 4 units to the right of the origin, and the 3 in the y coordinate means we've gone 3 units up.

Now we need to find four points that are 8 units away from this central location. We'll ignore point A.

What we can do is add 8 to the x coordinate of point B to get x+8 = 4+8 = 12. Keeping the y coordinate the same, the point (12, 3) is exactly 8 units away from (4,3). Think of drawing a number line through those two points. Then we can note there are 8 spaces between (4,3) and (12,3). Or we can say "there are 8 spaces between 4 and 12" since that '3' doesn't really play much of a role in this case.

So (12,3) is one answer.

---------------------------------

Move back to point B(4,3)

Instead of adding 8 to the x coordinate, let's subtract 8 from it

x-8 = 4-8 = -4

Again the y coordinate is kept the same.

The point (-4, 3) is 8 units away from (4,3). The number line distance from -4 to 4 is 8 units.

So (-4,3) is another answer.

----------------------------------

Move back to point B

From this starting point, we can move 8 units up. Doing this means we add 8 to the y coordinate, while the x coordinate is kept intact.

(4,3) turns into (4,11) after doing so.

(4,11) is another answer.

---------------------------------

Move back to point B

From this point, we can move down 8 units to arrive at (4,-5). note how y-8 = 3-8 = -5. The x coordinate is kept the same.

(4,-5) is another answer.

----------------------------------

The four points we found were:

  • (12, 3)
  • (-4, 3)
  • (4, 11)
  • (4, -5)

which are four possible answers

Those points are found by going 8 units right, 8 units left, 8 units up and 8 units down in that order. Each time we started at point B as our center of operation. The use of the word "center" is done because we can form a circle of radius 8, and the center of the circle is at B(4,3). Any point on the circle's edge is exactly 8 units away from the center point B.

Refer to the diagram below. The four answers are the red points P,Q,R,S. The point T is another point that could be an answer, but it's not as easy to find compared to the four other points.

3 0
3 years ago
What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4, 3)?
Ostrovityanka [42]
<h2>Answer:   y = - ¹/₂ x + 5 </h2>

<h3>Step-by-step explanation: </h3>

<u>Find the slope of the perpendicular line</u>

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

                 ⇒  if the slope of this line = 2     (y = 2x + 2)

                      then the slope of the perpendicular line (m) = - ¹/₂

<u>Determine the equation</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                               ⇒  y - 3 =  - ¹/₂  (x - 4)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

                             since   y - 3 =  - ¹/₂  (x - 4)

                                              y = - ¹/₂ x + 5   (in slope-intercept form)

8 0
2 years ago
If x=10, write an expression in terms of x for the number 5,364
LenKa [72]

Answer:

(5,354 + x)

or

536.4*x

Step-by-step explanation:

We know that x = 10.

Now we want to write an expression (in terms of x) for the number 5,364.

This could be really trivial, remember that x = 10.

Then:  (x - 10) = 0

And if we add zero to a number, the result is the same number, then if we add this to 5,364 the number does not change.

5,364 = 5,364 + (x - 10) = 5,364 + x - 10

5,364 = 5,354 + x

So (5,354 + x) is a expression for the number 5,364 in terms of x.

Of course, this is a really simple example, we could do a more complex case if we know that:

x/10 = 1

And the product between any real number and 1 is the same number.

Then:

(5,364)*(x/10) = 5,364

(5,364/10)*x = 5,364

536.4*x = 5,364

So we just found another expression for the number 5,364 in terms of x.

5 0
3 years ago
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