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True [87]
3 years ago
5

Given that ABCD is a rhombus, what is the value of x?

Mathematics
1 answer:
stealth61 [152]3 years ago
4 0

Answer:

Diagonals of a rhombus intersect at right angles

Therefore, \angle AOD=90

Now,in\: \bigtriangleup AOD

\angle OAD+\angle AOD+\angle ADO=180

x+90+3x+12=180 \leftarrow [combing \: like\: terms]

4x+102=180\\-102   \: -102 \leftarrow [subtracting \:102 ]

\frac{4x}{4} =\frac{78}{4} \leftarrow [dividing \: by\: 4]

x=19.5 \Longleftarrow

<u>OAmalOHopeO</u>

<u />

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Any help with this greatly appreciated.
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Put the equation in standard linear form.

x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}

Find the integrating factor.

\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5

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(t+5) x'(t) + x(t) = 5(t+5)e^{5t}

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(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt

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(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C

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\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}

3 0
2 years ago
A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
yanalaym [24]

Answer:

173.15 ft.  

Step-by-step explanation:

Please find the attachment.

Let L be the length of kite.  

We have been given that a kite is stuck in  36-ft tree. The angle of elevation from the kite and the ground is 12.

We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.

Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.

sin(12)=\frac{36}{L}    

L=\frac{36}{sin(12)}

L=\frac{36}{0.207911690818}  

L=173.1504364105882792\approx 173.15

Therefore, the length of kite is 173.15 ft.

4 0
3 years ago
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