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skad [1K]
3 years ago
7

A flagpole is supported by a wire fastened 60 feet from its base. The wire is longer than the height it reaches on the flagpole.

Find the length of the wire.

Mathematics
1 answer:
maxonik [38]3 years ago
8 0

Answer:

135.5ft

Step-by-step explanation:

THIS COMPLETE THE QUESTION

flagpole is supported by a wire fastened 60 feet from its base. The wire is 14 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Let X be the length of the wire

Let y be the height of the pole

X= Y + 14

Y= X -14

We can form a right angle triangle form this, where X denote the Hypotenose, Y is the Opposite, and 60feet is the Adjacent.(CHECK THE ATTACHMENT FOR THE TRIANGLE)

Using Pythagoras theorem

X²= 60² + Y²

X² = 3600 + Y²

if we subsitute for Y we have

X² = 3600 + (X -14)²

X² = 3600 +X² -14X-14X+196

X²-X²+ 28X= 3600+196

28X= 3796

X= 3796/28

=135.5ft

hence length of the wire is 135.5ft

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Anettt [7]

Answer:

a) not proportional

b) proportional; k = -\frac{3}{5}

Step-by-step explanation:

a) for any proportional equation, the line must pass through the origin. The equation in a) is y = 4x + 1, and the '+1' is the y-intercept. This means that the line does not pass through the origin, so x and y cannot increase by the same amount (i.e. they are not proportional).

Another way to determine this is is to use the y = kx base. If you have an equation that fits that it's likely proportional.

Here, if the equation was only y = 4x then it'd be proportional because u can see that k = 4. This is not the equation though, and the 4x + 1 doesn't fit to the y = kx formula so it can't be proportional.

b) straight away you can see that there's no 'c' term (y = mx + c) which means the y-intercept is 0, so the line passes through the origin. While this does not immediately mean the line is proportional, you can make sure that it is by checking it fits with the y = kx equation.

y = -(3/5)x fits with y = kx, with k being -3/5

3 0
3 years ago
A train is going at 200/KM per hour
olya-2409 [2.1K]

Answer:

<u>It</u><u> </u><u>moved</u><u> </u><u>for</u><u> </u><u>1</u><u>5</u><u>2</u><u>.</u><u>7</u><u> </u><u>seconds</u>

Step-by-step explanation:

Time taken/ period, T :

{ \sf{T =  \frac{distance}{speed} }}

substitute the variables:

{ \sf{T =  \frac{8482}{(200 \times 1000)} }} \\  \\ { \sf{T =0.042 \: hours }}

In seconds:

{ \sf{T = (0.042 \times 3600) \: s}} \\ { \sf{T = 152.7 \: seconds}}

6 0
3 years ago
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For the pie chart shown, what is the maximum number of people who could have an income of $45,000 if the total number of people
vfiekz [6]
There is no pie chart shown, please attach one.
7 0
3 years ago
A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the
Stells [14]

Answer:

\frac{5}{3} in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box=L\times B\times H

Substitute the values then we get

Volume of box=V(x)=(8-2x)(15-2x)x=(15x-2x^2)(8-2x)

V(x)=120x-30x^2-16x^2+4x^3

V(x)=4x^3-46x^2+120x

Differentiate w.r.t x

V'(x)=12x^2-92x+120

V'(x)=0

12x^2-92x+120=0

3x^2-23x+30=0

3x^2-18x-5x+30=0

3x(x-6)-5(x-6)=0

(x-6)(3x-5)=0

x-6=0\implies x=6

3x-5=0\implies x=\frac{5}{3}

Again differentiate w.r.t x

V''(x)=24x-92

Substitute x=6

V''(6)=24(6)-92=52>0

Substitute x=5/3

V''(5/3)=24(5/3)-92=-52

Hence, the volume is maximum at x=\frac{5}{3}

Therefore, the side of the square ,x=\frac{5}{3} in cutout that gives the box the largest possible volume.

5 0
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Yuki888 [10]

Answer:

I believe the answer is x=7

Step-by-step explanation:

<em>3x</em> and<em> 4x-1 </em> are corresponding sides and so are <em>14</em> and <em>18</em>.

You cross multiply with the smaller triangle lengths at the top.

3x/(4x-1)= 14/18

Cross multiply to get

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54x=56x-14

Subtract 54x on the other side and add 14 to the other (or subtract 56x to the other side)

you get 14=2x and divide 14 by 2 to get x=7

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3 years ago
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