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Bogdan [553]
3 years ago
6

A radio transmission tower is 170 feet tall. How long should a guy wire be if it is attached 15 feet from the top and makes a 27

degree angle with the ground?
Mathematics
1 answer:
MatroZZZ [7]3 years ago
6 0
The wire is attached 155 feet off the ground.sine(27) = 155 / hypotenuse hypotenuse = 155 / sine (27)hypotenuse =155 / 0.45399hypotenuse = <span> <span> <span> 341.42
</span></span></span>This means the guy wire is 341.42 feet long.

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Convert 22 to a numeral in base 2.
musickatia [10]
The answer is 10110

===============================================

Explanation:

Divide 22 over 2. Use long division to find the quotient and remainder
22/2 = 11 remainder 0 <<--- this remainder will be used later. Call it A, so A = 0

Now repeat for the value 11, which was the quotient above
11/2 = 5 remainder 1 <<--- this remainder will be used later. Call it B, so B = 1

Repeat again for the quotient we just got
5/2 = 2 remainder 1 <<--- this remainder will be used later. Call it C, so C = 1

Repeat again
2/2 = 1 remainder 0 <<--- this remainder will be used later. Call it D, so D = 0

Repeat again
1/2 = 0 remainder 1 <<--- this remainder will be used later. Call it E, so E = 1

The last quotient above is 0, so we stop here. If we tried to keep going, then we'd get nothing but 0 remainders forever.

The remainders we got above were:
A = 0
B = 1
C = 1
D = 0
E = 1

The idea is to read the remainders in reverse order in which we found. So we start with E and work back to A
E = 1
D = 0
C = 1
B = 1
A = 0

So 22 base 10 = 10110 base 2

5 0
3 years ago
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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len
Rama09 [41]

The length of a curve <em>C</em> parameterized by a vector function <em>r</em><em>(t)</em> = <em>x(t)</em> i + <em>y(t)</em> j over an interval <em>a</em> ≤ <em>t</em> ≤ <em>b</em> is

\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt

In this case, we have

<em>x(t)</em> = exp(<em>t</em> ) + exp(-<em>t</em> )   ==>   d<em>x</em>/d<em>t</em> = exp(<em>t</em> ) - exp(-<em>t</em> )

<em>y(t)</em> = 5 - 2<em>t</em>   ==>   d<em>y</em>/d<em>t</em> = -2

and [<em>a</em>, <em>b</em>] = [0, 2]. The length of the curve is then

\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt

=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt

=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt

=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt

=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}

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Line f has a slope of -3. what is the slope of the line that is parallel to line f
andre [41]

Answer:

A line parallel has the same slope, so -3

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Oksanka [162]

Answer:

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Step-by-step explanation:

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mafiozo [28]

Answer:

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Step-by-step explanation:

Divide 7x>-35 by 7

Divide - 5x>-50 by - 5

Since we divide by a negative whe change the inequality sign.

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