Ask question

Ask question

All categories

3 years ago

10

Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation

to the top of the mountain and finds it to be 25°11'. Find the height of the mountain to the nearest foot if Bob is 19,427.5 feet from the center of the mountain at the base.
a.9135 ft
b.9235 ft
c.91,351 ft
d.913,515 ft

1 answer:

DerKrebs [107]3 years ago

5 0

Answer:

Option A.

Step-by-step explanation:

Distance between Bob and the center of the mountain at the base = 19,427.5 ft.

Angle of elevation to the top of the mountain = 25°11'

We know that

1 degree = 60 minutes

1/60 degree = 1 minute

$25^{\circ}11'=25^{\circ}+\frac{11}{60}{\circ}\Rightarrow 25^{\circ}+0.183^{\circ}=25.183^{\circ}$

Let the height of the mountain be h.

In a right angled triangle

$\tan\theta = \frac{opposite}{adjacent}$

$\tan(25.183^{\circ}) = \frac{h}{19427.5}$

$\tan(25.183^{\circ})\times 19427.5 = h$

$h=0.4702\times 19427.5$

$h=9134.8105$

$h\approx 9135$

Therefore, the height of the mountain to the nearest foot 9135. Option A is correct.

You might be interested in

The booster club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs , cheeseburgers o

LenKa [72]

Answer:

6*5=30

Hope this helped!

6 0

4 years ago

Read 2 more answers

What is the length of CD to the nearest tenth?

kiruha [24]

Answer: 9.4

Step-by-step explanation:

if you see on the screenshot if you draw a line between the 2 it mesures 9.4

8 0

3 years ago

The functions below describe the temperatures in two cities on the same day. Which city had the greater starting temperature? Wh

Tresset [83]

Answer:

They have the same rate of change.

Step-by-step explanation:

They both increase two degrees every hour.

4 0

3 years ago

WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?

tatyana61 [14]

Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

$\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).

Thus, let's set what is under both square roots to be greater than 0:

$\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7$

$\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2$

Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

Since $\sqrt{x + 2}$ is on the bottom of the fraction, we must say that $\sqrt{x + 2} \neq 0$ , since the denominator can't equal 0. Thus, we must exclude $\sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2$ from the domain.

Thus, our answer is Choice C, or $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

<em>If you are wondering why the choices begin with the $x |$ symbol, it is because this is a way of representing that $x$ lies within a particular set.</em>

6 0

3 years ago

Kelly and Greta are asked to write an equation for the scenario below. "One person was able to plant 4 trees in the same amount

Alina [70]

Answer:

$y=\dfrac{1}{4}x$

Kelly is correct.

Step-by-step explanation:

One person is able to plant 4 trees

Let x be the number of people

y be the number of trees

The situation is represented by

$1x=4y\\\Rightarrow y=\dfrac{1}{4}x$

5 people are able to plant 20 trees

$5x=5(4y)\\\Rightarrow 5x=20y\\\Rightarrow y=\dfrac{5x}{20}\\\Rightarrow y=\dfrac{1}{4}x$

So, the situation is represented by $y=\dfrac{1}{4}x$

Hence, Kelly is correct.

6 0

3 years ago

Read 2 more answers