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3 years ago

Name three coplanar points

Mathematics

1 answer:

horsena [70]3 years ago

3 0

Answer:

The three coplannar points are

Points A, B & D in Plane O

Points A, B & C in Plane P.

Step-by-step explanation:

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The lenght of an arc in a circle with radius 8 inches is 3.2π. determine the measure of the arc

aleksandrvk [35]

Answer:

Step-by-step explanation:

32pi×360/2pi(8)=72

central angle= arc length 360/2pi×r

8 0

3 years ago

Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

What is the rate of change of the linear relationship modeled in the table (-2,5) (-1,4) (0,3) (1,2)

poizon [28]

The rate of change of the linear relationship is -1.

Explanation:

It is given that there is a linear relationship between all these points, these points lie on a straight line.

The equation to find the slope passing through two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(-2,5)$ and $(-1,4)$ , we get,

$\begin{aligned}m &=\frac{4-5}{-1+2} \\&=\frac{-1}{1} \\&=-1\end{aligned}$

Thus, the slope is -1.

Thus, the rate of change of the linear relationship is -1.

8 0

3 years ago

Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the

sammy [17]

Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

Here, we firstly would calculate the volume of the pile

Mathematically, that will be;

V = 1/3 * pi * r^2 * h

from the question, h = 14.2

Mathematically, r = d/2

r = 34.4/2 = 17.2 m

So the volume will be:

V = 1/3 * 3.142 * 17.2^2 * 14.2

V = 4,399.7719 m^3

To find the number of sanders to be filled,

we simply divide the volume obtained by the volume a sander can take

That will be;

4,399.7719/6.9

= 637.6 which is 638

4 0

3 years ago

Describe how k affects the graph of the function f(x)= -3/5(10)^x

Shalnov [3]

Answer:

1437.33

Step-by-step explanation:

8 0

3 years ago