Who ever can answer questions 8,9, and 10 will get 34 pts

6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

$a_1$ the horizontal distance between the first observer and the ballonist

$a_2$ the horizontal distance between the second observer and the ballonist

$\alpha _1$ and $\alpha _2$ the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

$S=a*h$ (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

$S=S_1+S_2$ (equation 2)

$S_1=a_1*h$

But we can write $S_1$ in terms of $\alpha _1$ , like this:

$\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}$

And for $S_2$ will be the same:

$S_2=\frac{h^{2} }{\tan(\alpha _2)}$

Replacing in the equation 2:

$S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})$

And replacing in the equation 1:

$h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}$

So, we can replace all the known data in the last equation:

$h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft$

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0

3 years ago

Please helppppppppppp help

yuradex [85]

13. 9x^2-36x+36
14. 4x^2+14x+20
Remember area formula for a square is Length times Width.
The area formula for a triangle is 1/2base times height.

5 0

3 years ago

Class records at rockwood college indicate that a student selected at random has probability 0.75 of passing french 101. for the

Kipish [7]

To get the probability of two individual events both occurring, you have to multiply the probabilities of their individual events occurring. Therefore in this problem, the probability that a student selected at random will pass both French 101 and French 102 is 0.683 (.75 x .91). The answer is already rounded to three decimal places.

4 0

4 years ago

Read 2 more answers

You cut 63 meters of rope into 9 equal pieces. How long is each equal piece of rope?

nirvana33 [79]

Each piece of rope will be 7 meters

5 0

3 years ago

Read 2 more answers

At a ski resort, 1/4 of the 300 skiers are beginners,and 1/4 of the 260 snowboarders are beginners.The resort staff used the dis

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

1/4 of the 300 skiers are beginners......1/4 of the 260 snowboarders are beginners..

so we want the total number of beginners..

the distributive property in this situation would be :

1/4(300 + 260) .......to solve this, u first have to get rid of the parenthesis. To do this, u multiple the number directly to the left of the parenthesis, by everything in the parenthesis.....u distribute it.

1/4(560).....now we multiply

560/4 = 140

OR

this way

1/4( 300 + 260) = 1/4(300) + 1/4(260) = 300/4 + 260/4 = 75 + 65 = 140

3 0

3 years ago