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3 years ago

5

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

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>

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Put the equation in standard linear form.

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

Find the integrating factor.

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

Multiply both sides by $\mu$ .

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

Now the left side the derivative of a product,

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

Integrate both sides.

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

On the right side, integrate by parts.

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

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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.

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3 years ago