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barxatty [35]
2 years ago
9

A 6-foot man walks on level ground toward a 60 foot flag pole. He notes different angles of elevation θ to the top of the pole w

hen he is different horizontal distances x away from the pole.
a) Express the man's horizontal distance from the base of the pole x (in feet) as a function of the angle of elevation θ in degrees. Type theta for θ.
b) Express the angle of elevation θ as a function of the man's horizontal distance to the base of the pole x.
Mathematics
1 answer:
krek1111 [17]2 years ago
5 0

Answer:

  a)  x = 54/tan(theta)

  b)  theta = arctan(54/x)

Step-by-step explanation:

a) The tangent ratio is the ratio of the side opposite an acute angle in a right triangle to the adjacent side. For the angle of elevation, the adjacent side is the distance x to the flagpole. The side opposite is the 54-foot difference between the top of the man's head and the top of the flagpole. So, we have ...

  tan(theta) = 54/x

Solving for x gives ...

  x = 54/tan(theta)

__

b) Solving the first equation in the previous part for theta involves the inverse tangent function:

  theta = arctan(54/x)

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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents th
Novay_Z [31]

Answer:

Step-by-step explanation:

I use  84+ CE

stat edit, then fill in the #s

then

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2'nd stat plot, on

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then click (4)(LinReg(ax+b))

then click enter 5 times

(y=-25.31428571x+1000.285714

y=-25.3x+1000.3

now, lets use computer:

y=-25.31(543)+1000.3

y=-12743.03

round to the biggest whole number )

this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing

now I get

y=-25.31428571x+51603.54286

y=-25.3x+51603.5

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y=-25.3(543)+51603.5

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7 0
2 years ago
Solve the system of equations – 5x + y = 56 and x + y = -4 by combining the<br> equations.
anygoal [31]

Answer:

Your solution is (-10, 6).

Step-by-step explanation:

Combining the equations is also known as substitution. This is done when you substitute one variable into another equation.

-5x + y = 56

x + y = -4

Let's change the second equation into one with one variable on each side.

y = -x - 4

Now, plug this into your first equation.

-5x + (-x - 4) = 56

Distribute the + sign.

-5x - x - 4 = 56

Combine the like terms.

-6x - 4 = 56

-6x = 60

Isolate x by dividing both sides by -6.

x = -10

Now plug this back into either equation.

-10 + y = -4

Add 10 to both sides to find y.

y = 6

Your solution is (-10, 6).

Check this by plugging in these values into the equation you have not checked yet.

-5(-10) + (6) = 56

50 + 6 = 56

56 = 56

Your solution is correct.

Hope this helps!

5 0
1 year ago
Read 2 more answers
La hormiguita Fidencia se encontro una hojita, la cargo y se llevo al hormiguero. Le dio a su amiguita 1/5 y ella se comió 1/3 d
vredina [299]

Answer:

The ant Fidencia ate more

Step-by-step explanation:

The question in English

The ant Fidencia found a leaf, the charge and took the anthill. She gave her friend 1/5 and she ate 1/3 of the leaf. Who ate more?

Her friend

Multiply (1/5) by (3/3)

(1/5)*(3/3)=3/15

Ant Fidencia

Multiply (1/3) by (5/5)

(1/3)*(5/5)=5/15

Compare

5/15 > 3/15 -----> two fractions with the same denominator the fraction with the highest numerator is greater

therefore

The ant Fidencia ate more

7 0
2 years ago
Michael went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 40 grams of sugar and
Fudgin [204]
40x+20y=300
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y= amount of juice bottles

Solving this equation, finding x&y will give you the number of each bottles!

I hope this helped!

~ Penny
8 0
2 years ago
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Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract
serg [7]

Answer:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Step-by-step explanation:

Given:

The equation to solve is given as:

x^2=-5x+8

Rearrange the given equation in standard form ax^2+bx +c =0, where, a,\ b,\ and\ c are constants.

Therefore, we add 5x-8 on both sides to get,

x^2+5x-8=0

Here, a=1,b=5,c=-8

The solution of the above equation is determined using the quadratic formula which is given as:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Plug in a=1,b=5,c=-8 and solve for x.

x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Therefore, the solutions are:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

4 0
2 years ago
Read 2 more answers
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