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3 years ago

Factor completely the expression: 2x^3 - 2x^2 - 12.

Mathematics

1 answer:

Gnom [1K]3 years ago

3 0

Answer:

2(x^3-x^2-6)

Step-by-step explanation:

2 out of 2x^3 - 2x^2 - 12

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Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

2 years ago

What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?

swat32

The answer would be 1017.88 in³. Use the volume for cones ( 1/3 times pi times radius times height) so 1/3*3.14*9*12 in which would be 1017.88 in³ hope it helps!

4 0

2 years ago

Read 2 more answers

3 over 18 as a percent please help

Ratling [72]

3/8 as a percentage is 37.5%

3 0

2 years ago

Read 2 more answers

rectangular solid that is 6-cm-by-6 cm-by-6 cm is painted on all six faces. then the solid is cut into cubes that measure 2 cm o

Nitella [24]

If you check the picture below

the rectangular solid is a 6x6x6, so all sides are equal thus is a cube

is painted on all faces, so the only part that's painted is the faces, ok
then you split it like in the picture, you have all 6 faces painted there,

now, let's say each of those 6 faces are cut in 2cm

how many of those 2cm pieces will each have? so get that amount for each and sum them up, that's how many of the cubes have one face painted

only the cubes that are part of the face, which was painted, are the ones that have a painted face themselves

keep in mind that each face is a 6x6 rectangle
notice the 2nd picture below