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vivado [14]
2 years ago
15

Find the value of x ​

Mathematics
1 answer:
givi [52]2 years ago
3 0

Answer:

110°

Step-by-step explanation:

In triangle AOB

OA = OB (radii of same circle)

m\angle OAB = m\angle OBA =20\degree

m\angle AOB = 180\degree - (20\degree +20\degree)

m\angle AOB = 180\degree - 40\degree

m\angle AOB = 140\degree

m\widehat {ACB} =m\angle AOB = 140\degree

(measure of minor arc is equal to corresponding central angle)

x\degree = \frac{1}{2} (360\degree - 140\degree)

(inscribed angle theorem)

x\degree = \frac{1}{2} \times 220\degree

\huge\purple {x = 110}

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If 5 x 6 = 30 you can figure out 8 x 6 by adding 6 three times to 30!

30 + 6 = 36

36 + 6 = 42

42 + 6 = 48 <-- the answer is 48!
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If the measure 3= (2y+20) degrees, and the measure of 5= (210-4y) degrees, what is the measure of 4?
Sidana [21]

Answer:

110°

Step-by-step explanation:

y = 25

Angle 5 equals Angle 4 because of the Alternate Angles Postulate.

Angle 4 equals 110°

6 0
2 years ago
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irakobra [83]

Answering pretty sure yes

Step-by-step explanation:

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3 years ago
Find the simple interest paid for 8 years on a $850 loan at 7.5% per year.
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3 years ago
Let R be the region in the first quadrant of the​ xy-plane bounded by the hyperbolas xyequals​1, xyequals9​, and the lines yequa
Tema [17]

Answer:

The area can be written as

\int\limits_1^2 \int\limits_1^3 u(\frac{1}{v} - v \, ln(v)) \, du \, dv = 0.2274

And the value of it is approximately 1.8117

Step-by-step explanation:

x = u/v

y = uv

Lets analyze the lines bordering R replacing x and y by their respective expressions with u and v.

  • x*y = u/v * uv = u², therefore, x*y = 1 when u² = 1. Also x*y = 9 if and only if u² = 9
  • x=y only if u/v = uv, And that only holds if u = 0 or 1/v = v, and 1/v = v if and only if v² = 1. Similarly y = 4x if and only if 4u/v = uv if and only if v² = 4

Therefore, u² should range between 1 and 9 and v² ranges between 1 and 4. This means that u is between 1 and 3 and v is between 1 and 2 (we are not taking negative values).

Lets compute the partial derivates of x and y over u and v

x_u = 1/v

x_v = u*ln(v)

y_u = v

y_v = u

Therefore, the Jacobian matrix is

\left[\begin{array}{ccc}\frac{1}{v}&u \, ln(v)\\v&u\end{array}\right]

and its determinant is u/v - uv * ln(v) = u * (1/v - v ln(v))

In order to compute the integral, we can find primitives for u and (1/v-v ln(v)) (which can be separated in 1/v and -vln(v) ). For u it is u²/2. For 1/v it is ln(v), and for -vln(v) , we can solve it by using integration by parts:

\int -v \, ln(v) \, dv = - (\frac{v^2 \, ln(v)}{2} - \int \frac{v^2}{2v} \, dv) = \frac{v^2}{4} - \frac{v^2 \, ln(v)}{2}

Therefore,

\int\limits_1^2 \int\limits_1^3 u(\frac{1}{v} - v \, ln(v)) \, du \, dv = \int\limits_1^2 (\frac{1}{v} - v \, ln(v) ) (\frac{u^2}{2}\, |_{u=1}^{u=3}) \, dv= \\4* \int\limits_1^2 (\frac{1}{v} - v\,ln(v)) \, dv = 4*(ln(v) + \frac{v^2}{4} - \frac{v^2\,ln(v)}{2} \, |_{v=1}^{v=2}) = 0.2274

4 0
3 years ago
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