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4 years ago

How do you do this question?

Mathematics

2 answers:

beks73 [17]4 years ago

8 0

The length of a circular arc (s) is the product of the circle's radius and the central angle measure in radians.

... s = r·θ

Then the central angle measure in radians is ...

... θ = s/r

For your problem, you have s = 8π/9 and r = 1. Then the central angle AOC is

... ∠AOC = (8π/9)/(1) = 8π/9 . . . . radians

The relationship between radians and degrees is

... 180° = π radians

Multiplying this equation by 8/9 will tell us the degree measure of ∠AOC.

... 8/9×180° = (8/9)×π radians

... ∠AOC = (8/9)·180° = 160°

We know that this is the sum of the two (equal) central angles ∠AOB and ∠BOC, so we have

... 2×∠AOB = 160°

... ∠AOB = 160°/2 = 80°

_____

Here, you know that 8π/9 is the central angle in radians because the ratio of arc length to radius is the angle in radians.

Hitman42 [59]4 years ago

4 0

The central angle corresponding to AOB is half of the 8pi/9 radians mentioned, meaning that the central angle of AOB is 4pi/9.

Converting that to degrees:

4pi/9 180 degrees

-------- * -------------------- = 80 degrees.

1 pi

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3 years ago

En un triángulo obtusángulo, uno de los ángulos mide 20° mas que el otro. El tercer ángulo, mide el doble que el mayor de los do

Troyanec [42]

Answer:

La medida del primer ángulo es 30°, la medida del segundo ángulo es 50° y el tercer ángulo mide 100°.

Step-by-step explanation:

Siendo "x" el valor de un ángulo del triángulo obtusángulo, sabes que uno de los ángulos, llamado segundo ángulo, mide 20° más que el primero. Este segundo ángulo se representa como x + 20°.

Además, un tercer ángulo mide el doble que el mayor de los dos, que en este caso es el ángulo cuya expresión es x + 20°. Por lo que el doble de este será 2*(x + 20)°, que será la medida del tercer ángulo.

Teniendo en cuenta que la suma de los ángulos interiores de un triángulo es 180°. Entonces, es posible sumar los valores de cada uno de los ángulos e igualarlos a 180°:

x + x + 20° + 2*(x + 20°) = 180°

Resolviendo:

x + x + 20° + 2*x + 2*20° = 180°

x + x + 20° + 2*x + 40° = 180°

4*x + 20° + 40° = 180°

4*x + 60° = 180°

4*x = 180° - 60°

4*x = 120°

x = 120° ÷ 4

x = 30°

Entonces, la medida del primer ángulo es 30°. El segundo ángulo es calculado como x + 20° = 30° + 20° = 50° mientras que el tercer ángulo es 2*(x + 20°) = 2*(30° + 20°) = 2*(50°) = 100°

La medida del primer ángulo es 30°, la medida del segundo ángulo es 50° y el tercer ángulo mide 100°.

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3 years ago

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Marysya12 [62]

Answer:

Yes the integral can be evaluated by integration by parts as solved below.

Step-by-step explanation:

$\int x^{2}e^{2x}dx$

Taking algebraic function as first function and exponential function as second function we have

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Advocard [28]

Answer:

Step-by-step explanation:

First off, I'm assuming that when you said "directrices" you mean the oblique asymptotes, since hyperbolas do not have directrices they have oblique asymptotes.

If we plot the asymptotes and the foci, we see that where the asymptotes cross is at the origin. This means that the center of the hyperbola is (0, 0), which is important to know.

After we plot the foci, we see that they are one the y-axis, which is a vertical axis, which means that the hyperbola opens up and down instead of sideways. Knowing those 2 characteristics, we can determine that the equation we are trying to fill in has the standard form

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$

We know h and k from the center, now we need to find a and b. Those values can be found from the asymptotes. The asymptotes have the standard form

y = ± $\frac{a}{b}(x-h)+k$

Filling in our asymptotes as they were given to us:

y = ± $\frac{2}{1}(x-0)+0$ where a is 2 and b is 1. Now we can write the formula for the hyperbola!:

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$\frac{y^2}{4}-\frac{x^2}{1}=1$

4 0

4 years ago