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3 years ago

Factor completely. x^3 + 2x^2 + x + 2

Mathematics

1 answer:

slega [8]3 years ago

8 0

$x^3 + 2x^2 + x + 2=\\
x^2(x+2)+1(x+2)=\\
(x^2+1)(x+2)$

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

9 months ago

The sum of two numbers is 76 and their difference is 52. Find the two numbers.<br> Please explain

Yanka [14]

Step-by-step explanation:

hope it helps first find one number and then multiply one number by 2

6 0

2 years ago

Can someone help with an explanation? This is finding Surface Area.

Y_Kistochka [10]

The answer should be 95in^2

Explanation:

You’re essentially just finding the area of all the shapes on the triangle and adding them together.

Area of a triangle = 1/2•b•h
Area of a square = l•w or just s2

The area of the triangles given what we have in the diagram can be found with
1/2•5•7 = 17.5

There are 4 triangles so you multiply 17.5 by 4 which gives 70

The base of the triangle (the square) = 25

70+25=95

7 0

2 years ago

A classroom board is 23 inches wide and 17 inches tall. Juan

natima [27]

Answer:

80 inches

Step-by-step explanation:

12 x 7=34

23 x 2=46

34+46=80 inches

6 0

2 years ago

The equation V equals pi r squared h, where r represents radius and h represents height, is used to find the volume of a _______

baherus [9]

Answer:

Volume of a cylinder.

Step-by-step explanation:

The given equation is :

$V=\pi r^2 h$

Where

r is the radius

h is the height

This equation is used to find the volume of a cylinder.

For example, a cylinder having radius of 7 units and height of 10 units, its volume will be :

$V=\dfrac{22}{7}\times 7^2\times 10\\\\V=1540\ \text{unit}^2$

So, the given equation is used to find the volume of a cylinder.

7 0

2 years ago