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3 years ago

2. Gabby, the teller, counted

Mathematics

2 answers:

Ad libitum [116K]3 years ago

8 0

Answer:

295 was the total

Step-by-step explanation:

nika2105 [10]3 years ago

3 0

Answer:

https://answers.yahoo.com/question/index?qid=20100709054241AAMrcI7

Step-by-step explanation:

look at this website!

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-5y+6>26 does the inequality sign flip?

tigry1 [53]

Answer:

Yes

Step-by-step explanation:

3 0

3 years ago

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A lamina occupies the part of the disk x2 + y2 ≤ 25 in the first quadrant. Find its center of mass if the density at any point i

goblinko [34]

Answer:

The center of mass is located at coordinates $(x_0,y_0) = (\frac{15}{8}, \frac{15\pi }{16})$

Step-by-step explanation:

Consider the disk $x^2+y^2\leq 25$ and its' portion located at the first quadrant. We are being said that the density $\rho$ is proportional to the distance of the point to the x-axis. Given a point of coordinates (x,y), its' distance to the x-axis is y. Therefore, we know that the density function $\rho(x,y) = k\cdoty$ for some constant k, whose value is not relevant. Let (x_0,y_0) be the center of mass and let D be the region occupied by the lamina. The center of mass's coordinates fulfill the following equations:

$x_0 = \frac{\int_{D}x\cdot\rho(x,y)dA}{M}$

$y_0 = \frac{\int_{D}y\cdot\rho(x,y)dA}{M}$

where M is the mass of the region, which in this case is given by $M=\int_D \rho(x,y)dA$ .

Let us calculate the mass of the lamina. For this, we will use the polar coordinates. Recall that they are given by the change of coordinates $x=r\cos \theta, y = r\sin \theta$ , where r and theta are the new parameters. Given a point (x,y) in the plane, r is the distance from (x,y) to the origin and theta is the angle formed between the line that joins the origin and the point, and the x-axis. We want to describe the region D in terms of the new parameters. Replacing the values of x,y in the given inequality, we get that $(r\cos\theta)^2+(r\sin\theta)^2$ . Since $\cos^2\theta + \sin^2\theta = 1$ and r>0 we get that r<=5. On the other side, in order to describe the whole region of the first quadrant, we need to sweep the angle theta from 0 to $\frac{\pi}{2}$ . With that, we can calculate the mass of the lamina as follows

M = $\int_D \rho(x,y)dA = \int_D ky dA = \int_{0}^{\frac{\pi}{2}}\int_{0}^5 k r \sin \theta \cdot r drd\theta = k (\frac{5^3}{3}-0)\int_{0}^{\frac{\pi}{2}} \sin \theta d\theta =k \cdot \frac{5^3}{3}$

In here, the extra r appears as the jacobian of the change of coordinates (the explanation of why this factor occurs is beyond the scope of this answer. Please refer to the internet for further explanation).

Then, we need to calculate the following integrals.

$\int_{D}x\cdot\rho(x,y)dA = k\int_D xy dA = k \int_{0}^{\frac{\pi}{2}}\int_{0}^5 r\cos \theta \cdot r\sin \theta r dr d\theta =k(\frac{5^4}{4}-0) \int_0^{\frac{\pi}{2}}\frac{\sin(2\theta)}{2}d\theta = k\cdot \frac{5^4}{8}$ (recall $\cos(\theta)\sin\theta = \frac{\sin(2\theta)}{2}$ ).

Then, $x_0=\frac{k \cdot \frac{5^4}{8}}{k \cdot \frac{5^3}{3}}= \frac{15}{8}$

On the other hand:

$\int_{D}y\cdot\rho(x,y)dA = k\int_D y^2 dA = k \int_{0}^{\frac{\pi}{2}}\int_{0}^5 r\cdot r^2\sin^2 \theta dr d\theta = k(\frac{5^4}{4}-0) \int_{0}^{\frac{\pi}{2}}\frac{1-\cos(2\theta)}{2}d\theta = k \cdot \frac{5^4\pi}{16}$

(recall $\sin^2(\theta) = \frac{1-\cos(2\theta)}{2}$

Then, $y_0 = \frac{k \cdot \frac{5^4\pi}{16}}{k \cdot \frac{5^3}{3}} = \frac{15\pi }{16}$

To check that the answer makes sense, the center of mass must lie in the disk, that is, it should satisfy the equation. We can easily check that $(\frac{15}{8})^2+ (\frac{15\pi }{16})^2=12.19$

5 0

3 years ago

In circle C, what is the value of x?

Anna71 [15]

Answer:x=22 degrees

Step-by-step explanation:

We are given a circle C.

Centre is at C

A line passes through the centre makes angle x and 68 on either side

A triangle is formed with angles x, 68 and another angle at the circumference.

Since the line passing through the centre is diameter of the circle, we have

the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)

In the triangle sum of three angles

=90+x+68 =180

x =22 degrees

5 0

3 years ago

Only 3 questions! Please help, this is TIMED!

Bas_tet [7]

Answer:

D. π

Step-by-step explanation:

Period = 2π/v

2sinxcosx=sin(2x)

Therefore, T = 2π/2 = π

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3 years ago

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The following list gives the number of pets for each of 13 students.

podryga [215]

The mode's of this set of data are 1,2, and 4.

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3 years ago