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3 years ago

What is the measure of the angle x?

Mathematics

1 answer:

navik [9.2K]3 years ago

4 0

AOB = 2 . x
2x = 60°
x = 30°

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What is the slope if the form is y=-x-6

Irina-Kira [14]

The slope will be -1

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2 years ago

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The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the portions of the x-axis that jo

oksano4ka [1.4K]

Answer:

Required center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

Step-by-step explanation:

Given semcircles are,

$y=\sqrt{1-x^2}, y=\sqrt{16-x^2}$ whose radious are 1 and 4 respectively.

To find center of mass, $(\bar{x},\bar{y})$ , let density at any point is $\rho$ and distance from the origin is r be such that,

$\rho=\frac{k}{r}$ where k is a constant.

Mass of the lamina=m= $\int\int_{D}\rho dA$ where A is the total region and D is curves.

then,

$m=\int\int_{D}\rho dA=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}rdrd\theta=k\int_{}^{}(4-1)d\theta=3\pi k$

Now, x-coordinate of center of mass is $\bar{y}=\frac{M_x}{m}$ . in polar coordinate $y=r\sin\theta$

$\therefore M_x=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\sin\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\sin\thetadrd\theta$

$=3k\int_{0}^{\pi}\sin\theta d\theta$

$=3k\big[-\cos\theta\big]_{0}^{\pi}$

$=3k\big[-\cos\pi+\cos 0\big]$

$=6k$

Then, $\bar{y}=\frac{M_x}{m}=\frac{2}{\pi}$

y-coordinate of center of mass is $\bar{x}=\frac{M_y}{m}$ . in polar coordinate $x=r\cos\theta$

$\therefore M_y=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\cos\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\cos\theta drd\theta$

$=3k\int_{0}^{\pi}\cos\theta d\theta$

$=3k\big[\sin\theta\big]_{0}^{\pi}$

$=3k\big[\sin\pi-\sin 0\big]$

$=0$

Then, $\bar{x}=\frac{M_y}{m}=0$

Hence center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

3 0

3 years ago

What is the slope of the line?

Ede4ka [16]

Answer:

-1

Step-by-step explanation:

Remember, slope is rise/run

Start from a point on the line and count up and over until you reach another point on the line.

For example, start from (0,-2), count up and left until you get to (-2,0). This gets you 2/2, which reduces to 1.

Since the line represents a negative slope, the slope is -1.

7 0

3 years ago

Simplify. Assume that all variables are positive.

Alja [10]

I'm confused... Should there be more pictures? This in incomplete...

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2 years ago

What is the total resistance of a parallel circuit that has two loads? Load one has a resistance of 10 ohms. Load two has a resi

Romashka-Z-Leto [24]

Answer:

The total resistance is $7.0588\Omega$

Step-by-step explanation:

Attached please find the circuit diagram. The circuit is composed by a voltage source and two resistors connected in parallel: $R_1=10\Omega$ and $R_2=24\Omega$ .

First step: find the total current

For finding the current that the voltage source can provide, you must find the current consumed by each load and then add both. To do that, take first into account that the voltage is the same for both resistors ( $R_1$ and $R_2$ ).