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Firdavs [7]
3 years ago
15

A radio transmission tower is feet tall. How long should a guy wire be if it is to be attached feet from the top and is tomake a

n angle of with the ground
Mathematics
1 answer:
Bond [772]3 years ago
3 0

Answer:

<em> Length of guy wire is 590.6 ft</em>

Step-by-step explanation:

The complete question is

A radio transmission tower is  210  feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of  20°  with the ground. Give your answer to the nearest tenth of a foot.

height of tower = 210 ft

8 ft fro the top leaves 210 - 8 = 202 ft to the ground

This is an angle of elevation problem

the opposite is 202 ft

hypotenuse = ?

angle is  20°  

using sin ∅ = opp/hyp

sin  20°  = 202/hyp

0.342 = 202/hyp

hyp = 202/0.342 = <em>590.6 ft   this is the length of the guy wire</em>

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A pie is made using 2 cups of sugar for every 3 cups of flour. Max knows he needs 15 cups of flour to make enough pies. How many
PolarNik [594]

Answer: 10 cups of sugar

Step-by-step explanation:

Cups of sugar : Cups of flour

                    2 : 3

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Cross multiply

3? = 15 × 2

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Divide both sides by 3

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He needs 10 cups of sugar.

8 0
3 years ago
Place the numbers 40 and 100 into the proportion. (Whole)(percents) ----------- (Part) what goes where?
Ksivusya [100]

Answer:

Step-by-step explanation:

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40/100 = 40%

4 0
3 years ago
John played a note on his tuba that vibrated the air 120 times per second. If you play the note for 4 seconds, how many times in
Zigmanuir [339]

480

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4 0
3 years ago
Read 2 more answers
Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.
Mice21 [21]

Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

Step-by-step explanation:

Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

Taking 8y^{4} common:

\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)

Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)

Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

Hence, <em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

5 0
3 years ago
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