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3241004551 [841]
3 years ago
15

Lily is standing at horizontal ground level with the base of the Sears Tower. The angle formed by the ground and the line segmen

t from her position to the top of the building is 15.7°. The Sears Tower is 1450 feet tall. Find Lily's distance from the Sears Tower to the nearest foot.
Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
This is the concept of trigonometry, the distance of Lily from the tower will be given by:
tan theta=[opposite]/[adjacent]
opposite=1450 ft
adjacent=x ft
theta=15.7
thus;
1450/x=tan15.7
hence;
x=1450/tan15.7
x=5,158.54 ft
x=5,159 (to the nearest foot)
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Point A is located at (-4, -13). Point B is located at (-4, 3). What is the distance between point A
12345 [234]

Answer:

the distance is 16

Step-by-step explanation:

Hi there!

We are given point A (-4,-13) and point B (-4,3). We need to find the distance between those two points

the distance formula is given as \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} where (x_{1},y_{1}) and (x_{2}, y_{2}) are points

we are given 2 points, which is what we need for the formula. However, let's label the values of the points to avoid any confusion

x_{1}=-4

y_{1}=-13

x_{2}=-4

y_{2}=3

now substitute those values into the formula. Remember: the formula uses SUBTRACTION.

\sqrt{(-4--4)^2+(3--13)^2}

simplify

\sqrt{(-4+4)^2+(3+13)^2}

now add the values inside the parenthesis that are under the radical

\sqrt{(0)^2+(16)^2}

raise everything under the radical to the second power

\sqrt{0+256}

add under the radical

\sqrt{256}

now take the square root of 256

\sqrt{256}=16

so the distance between point A and point B is <u>16</u>

Hope this helps! :)

8 0
3 years ago
Can someone explain how you solve proofs?
kap26 [50]

Answer:

Yeahh

Step-by-step explanation:

Write the statement in one side and give the reasons on other side.

And then proof it by accurate reason

6 0
3 years ago
Ab over 2 equal 2a minus 1,express a in terms of b
sasho [114]

\frac{ab}{2} = 2a - 1

2(\frac{ab}{2}) = 2(2a - 1) <em>multiplied both sides by 2 </em>

ab = 4a - 2 <em>distributed the 2 on the right side</em>

ab - 4a = -2 <em>subtracted 4a from both sides</em>

a(b - 4) = -2 factored out "a" from the left side

a = \frac{-2}{b - 4} <em>divided (b - 4) on both sides</em>

Answer: a = \frac{-2}{b - 4}

6 0
3 years ago
A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t
Solnce55 [7]

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

h=-16t^2+200t

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

350=-16t^2+200t

The last is a quadratic equation, which can be put in the form at^2+bt+c=0 and solved applying the formula:

t=\frac{-b+-\sqrt{b^2-4ac} }{2a}

So, let's put the equation on the form at^2+bt+c=0 adding 16t^2 and subtracting 200t to each side of the equation; the result is:

16t^2-200t+350=0

So, we note that a=16, b=-200, and c=350.

Then,

t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10

t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

4 0
3 years ago
can someone help me!! Use algebraic rules of equations to predict the solution type to the system of equations. Include all of y
xz_007 [3.2K]

Answer:

x + y = 4 Equation 1

y = 2x -1 Equation 2

-2x + y = -1

x + y = 4

Subtract

You will get

- 3x = -5

Divide by -3

-3x / -3 = - 5 /-3

x = 5/3

Substitute x into equation 1

x + y = 4

x = 5/3

5/3 + y = 4

y = 4 - 5/3

y = 7/3

x = 5/3 y = 7/3

Hope this helps.

4 0
3 years ago
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