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AlexFokin [52]
4 years ago
13

Name all rays with the endpoint k

Mathematics
1 answer:
Alex_Xolod [135]4 years ago
4 0
Number is already correct.

but the other two answer are...

2. KL and KV

3. Another name for VL is LV
You might be interested in
The expressions A, B, C, D, and E are left-hand sides of trigonometric identities. The expressions 1, 2, 3, 4, and 5 are right-h
Semenov [28]

Answer:

A.\ \tan(x) \to 2.\ \sin(x) \sec(x)

B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)

C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)

D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)

E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}

Step-by-step explanation:

Given

A.\ \tan(x)

B.\ \cos(x)

C.\ \sec(x)csc(x)

D.\ \frac{1 - (cos(x))^2}{cos(x)}

E.\ 2\sec(x)

Required

Match the above with the appropriate identity from

1.\ \sin(x) \tan(x)

2.\ \sin(x) \sec(x)

3.\ \tan(x) + \cot(x)

4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}

5.\ \sec(x) - \sec(x)(\sin(x))^2

Solving (A):

A.\ \tan(x)

In trigonometry,

\frac{sin(x)}{\cos(x)} = \tan(x)

So, we have:

\tan(x) = \frac{\sin(x)}{\cos(x)}

Split

\tan(x) = \sin(x) * \frac{1}{\cos(x)}

In trigonometry

\frac{1}{\cos(x)} =sec(x)

So, we have:

\tan(x) = \sin(x) * \sec(x)

\tan(x) = \sin(x) \sec(x) --- proved

Solving (b):

B.\ \cos(x)

Multiply by \frac{\cos(x)}{\cos(x)} --- an equivalent of 1

So, we have:

\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}

\cos(x) = \frac{\cos^2(x)}{\cos(x)}

In trigonometry:

\cos^2(x) = 1 - \sin^2(x)

So, we have:

\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}

Split

\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}

Rewrite as:

\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)

Express \frac{1}{\cos(x)}\ as\ \sec(x)

\cos(x) = \sec(x) - \sec(x) * \sin^2(x)

\cos(x) = \sec(x) - \sec(x)\sin^2(x) --- proved

Solving (C):

C.\ \sec(x)csc(x)

In trigonometry

\sec(x)= \frac{1}{\cos(x)}

and

\csc(x)= \frac{1}{\sin(x)}

So, we have:

\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}

Multiply by \frac{\cos(x)}{\cos(x)} --- an equivalent of 1

\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}

\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}

Express \frac{1}{\cos^2(x)}\ as\ \sec^2(x) and \frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}

\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}

\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}

In trigonometry:

tan^2(x) + 1 =\sec^2(x)

So, we have:

\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}

Split

\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}

Simplify

\sec(x)csc(x) = \tan(x) + \cot(x)  proved

Solving (D)

D.\ \frac{1 - (cos(x))^2}{cos(x)}

Open bracket

\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}

1 - \cos^2(x) = \sin^2(x)

So, we have:

\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}

Split

\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}

\frac{sin(x)}{\cos(x)} = \tan(x)

So, we have:

\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)

\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x) --- proved

Solving (E):

E.\ 2\sec(x)

In trigonometry

\sec(x)= \frac{1}{\cos(x)}

So, we have:

2\sec(x) = 2 * \frac{1}{\cos(x)}

2\sec(x) = \frac{2}{\cos(x)}

Multiply by \frac{1 - \sin(x)}{1 - \sin(x)} --- an equivalent of 1

2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}

2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}

Open bracket

2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}

Express 2 as 1 + 1

2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}

Express 1 as \sin^2(x) + \cos^2(x)

2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}

Rewrite as:

2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}

Expand

2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}

Factorize

2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}

Factor out 1 - sin(x)

2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}

Express as squares

2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}

Split

2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}

Cancel out like factors

2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)} --- proved

3 0
3 years ago
Reduce 15/24 what's the answer
Taya2010 [7]
15 ÷ 3 = 5,
24 ÷ 3 = 8,
 so it's 5/8
7 0
3 years ago
The tables below show the values of y corresponding to different values of x:
Brums [2.3K]
In functions, two x's cant exist. It will create an undefined (straight down) line.

To figure out if there it is a function or not from a graph, do the pencil test. Take your pencil (or finger) and drag it across the graph vertically. If your pencil hits two points at once (on the same x-axis, or straight up/down), its not a function.

Therefore, both tables are not a function, or B.
7 0
4 years ago
The volume of the cylinder above is 2,119.5^m3 what is the radius of the cylinder​
Y_Kistochka [10]

Answer:

7.5

Step-by-step explanation:

Pi * r^2 * 12 = 2119.5

r^2 = 56.25

r = sqrt(56.25) = 7.5

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What is The Division expression To
Shkiper50 [21]

Answer:

4/3

Step-by-step explanation:

The number of items / How many people you need to spit it between

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