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zloy xaker [14]
3 years ago
9

You are skiing down a mountain with a vertical height of 800 feet. The distance from the top of the mountain to the base is 1600

feet. What is the angle of elevation from the base to the top of the mountain?
Mathematics
1 answer:
adoni [48]3 years ago
7 0

Answer:

θ  = 30^{0}

Step-by-step explanation:

Since the vertical height of the mountain is 800 feet, and the distance from the top to its base is 1600 feet. Let the angle of elevation be represented by θ, applying the required trigonometric function;

Sin θ = \frac{opposite}{hypotenuse}

Sin θ = \frac{800}{1600}

        = 0.5

θ = Sin^{-1} 0.5

θ  = 30^{0}

Thus, the angle of elevation from the base to the top of the mountain is 30^{0}.

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vovangra [49]

Answer:

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Step-by-step explanation:

The formula of a volume of a cube with side length a:

V=a^3

We have a = 6cm. Substitute:

V=6^3=216\ cm^3

\begin{array}{c|c}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}

216=2\cdot2\cdot2\cdot3\cdot3\cdot3=(2\cdot2)\cdot(2\cdot3)\cdot(3\cdot3)=4\cdot6\cdot9\\\\216=2\cdot2\cdot2\cdot3\cdot3\cdot3=2\cdot(2\cdot2\cdot3)\cdot(3\cdot3)=2\cdot12\cdot9\\\\216=2\cdot2\cdot2\cdot3\cdot3\cdot3=(2\cdot2\cdot2)\cdot3\cdot(3\cdot3)=8\cdot3\cdot9\\\vdots

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3 years ago
What will be the cost for 8 hours of work? 10 hours of work?​
andreyandreev [35.5K]

Answer:

<u>Cost = 25 + 50h</u>

cost for 8 hours of work = $425

cost for 10 hours of work = $525

Step-by-step explanation:

The question is as following:

A plumber charges $25 for a service call plus $50 per hour of service write an equation to represent the cost of hiring this plumber​.

what will be the cost for 8 hours of work? 10 hours of work?​

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

A plumber charges $25 for a service call plus $50 per hour

<u>Cost = 25 + 50h</u>

Where h is the number of hours of service

8 hours of work: h = 8

Substitute with h = 8 at the equation of cost

<u>Cost = 25 + 50* 8 = $425</u>

10 hours of work: h = 10

Substitute with h = 10 at the equation of cost

<u>Cost = 25 + 50 * 10  = $525</u>

6 0
3 years ago
A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a
sdas [7]

Answer:

y=-\dfrac{13}{49}x^2

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

y=ax^2+bx+c

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

-13=a(-7)^2+b(-7)+c

49a-7b+c=-13

(x,y) = (7,-13)

-13=a(7)^2+b(7)+c

49a+7b+c=-13

(x,y) = (0,0)

0=a(0)^2+b(7)+c

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so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13

49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13

we can solve these two equation using the elimination method, by simply adding the two equations

\quad\quad49a-7b=-13\\+\quad49a+7b=-13

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

\quad\quad 98a=-26

\quad\quad a=-\dfrac{13}{49}

Now we can plug this value of a in any of the two equations.

49a-7b=-13

49\left(-\dfrac{13}{49}\right)-7b=-13

-13-7b=-13

-7b=0

b=0

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

y=\left(-\dfrac{13}{49}\right)x^2+0x+0

y=-\dfrac{13}{49}x^2

49y=-13x^2

This our equation of the arch!

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