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3 years ago

Help me with this problem with steps. Please.

Mathematics

1 answer:

enyata [817]3 years ago

3 0

I found this on Yahoo answers 18 different sets.

There are 6 faces, so that's 6 sets.

If we draw two parallel diagonals on two opposite faces, their endpoints are another set of four coplanar points. There are 3 pairs of opposite faces, and each has two such sets of diagonals, giving us another 6 sets.

Now consider the four diagonals of the cube. They all meet at a single point in the center of the cube. Therefore, any pair of them represent a pair of intersecting lines and so define a plane. So any pair of these diagonals produces yet another set of four coplanar vertices.

There are four such diagonals, and there are
4C2 = 4! / (2! 2!) = 4 * 3 / 2 = 6 different combinations comprised of two of them, so that's another 6.

That gives us a total of 18 different such sets of four coplanar vertices of the cube. No other combinations of four vertices are coplanar.

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4 years ago

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A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find t

Evgesh-ka [11]

Answer:

Part a) $120\pi\ \frac{rad}{min}$

Part b) $960\pi\ \frac{in}{min}$

Step-by-step explanation:

we have

60 rev/min

Part a) Find the angular speed in radians per minute

we know that

One revolution represent 2π radians (complete circle)

$1\ rev=2\pi \ rad$

To convert rev to rad, multiply by 2π

$60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}$

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=8\ in$ ----> given problem

substitute

$C=2\pi(8)$

$C=16\pi\ in$

Remember that

One revolution subtends a length equal to the circumference of the circle

$1\ rev=16\pi\ in$

To convert rev to in, multiply by 16π

$60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}$

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3 years ago

James sees 4 fewer birds than lily. lily sees 9 birds. how many birds does james see?

Alenkasestr [34]

Answer:

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Step-by-step explanation

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(X^2+x-6)(2x^2+4x) factor completely

MissTica

Answer:

$2x\left(x-2\right)\left(x+3\right)\left(x+2\right)$

Step-by-step explanation:

Lets go ahead and take a step by step approach to solving your problem.

First we must start by factoring $x^2+x-6$ .

To do this, we must break the expression into groups! Although I will also provide a definition to help you understand! For $ax^2+bx+c$ we need to find u, v > $u\cdot \:v=a\cdot \:c$ and $u+v=b$ which we will group into $\left(ax^2+ux\right)+\left(vx+c\right)$ .

The values we have are... $a=1,\:b=1,\:c=-6$ and $u\cdot v=-6,\:u+v=1$ .

Now we need the factors of 6 which are 1, 2, 3 and 6. We also need the negative factors which you get simply by multiplying the positives by -1 or just reversing them.

Now we need to check for every two factors if u + v = 1.

$\mathrm{Check}\:u=1,\:v=-6: \:u\cdot v=-6,\:u+v=-5 \Rightarrow \mathrm{False}$