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marta [7]
3 years ago
13

(6z 2 - 4z + 1)(8 - 3z).

Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0
Distributive property
a(b+c)+ab+ac
a(b-c)=ab-ac

(6z^2-4z+1)(8-3z)
move for nicety
(8-3z)(6z^2-4z+1)
distribute
8(6z^2-4z+1)-3z(6z^2-4z+1)=
48z^2-32z+8-18z^3+12z^2-3z=
-18z^3+48z^2+12z^2-32z-3z+8=
-18z^3+60z-35z+8
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A. In two or more complete sentences, explain how to find the exact value of sec 13pi/6 including quadrant location
Sergio039 [100]

Answer:

A. The exact value of sec(13π/6) = 2√3/3

B. The exact value of cot(7π/4) = -1

Step-by-step explanation:

* Lets study the four quadrants

# First quadrant the measure of all angles is between 0 and π/2

  the measure of any angle is α  

∴ All the angles are acute  

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between π/2 and π

  the measure of any angle is π - α

∴ All the angles are obtuse

∴ The value of sin(π - α) only is positive

  sin(π - α) = sin(α)  ⇒ csc(π - α) = cscα

  cos(π - α) = -cos(α)   ⇒ sec(π - α) = -sec(α)

  tan(π - α) = -tan(α)   ⇒ cot(π - α) = -cot(α)

# Third quadrant the measure of all angles is between π and 3π/2

  the measure of any angle is π + α  

∴ All the angles are reflex  

∴ The value of tan(π + α) only is positive

  sin(π + α) = -sin(α)  ⇒ csc(π + α) = -cscα

  cos(π + α) = -cos(α)   ⇒ sec(π + α) = -sec(α)

  tan(π + α) = tan(α)   ⇒ cot(π + α) = cot(α)

# Fourth quadrant the measure of all angles is between 3π/2 and 2π  

  the measure of any angle is 2π - α  

∴ All the angles are reflex

∴ The value of cos(2π - α) only is positive

  sin(2π - α) = -sin(α)  ⇒ csc(2π - α) = -cscα

  cos(2π - α) = cos(α)   ⇒ sec(2π - α) = sec(α)

  tan(2π - α) = -tan(α)   ⇒ cot(2π - α) = -cot(α)

* Now lets solve the problem

A. The measure of the angle 13π/6 = π/6 + 2π

- The means the terminal of the angle made a complete turn (2π) + π/6

∴ The angle of measure 13π/6 lies in the first quadrant

∴ sec(13π/6) = sec(π/6)

∵ sec(x) = 1/cos(x)

∵ cos(π/6) = √3/2

∴ sec(π/6) = 2/√3 ⇒ multiply up and down by √3

∴ sec(π/6) = 2/√3 × √3/√3 = 2√3/3

* The exact value of sec(13π/6) = 2√3/3

B. The measure of the angle 7π/4 = 2π - π/4

- The means the terminal of the angle lies in the fourth quadrant

∴ The angle of measure 7π/4 lies in the fourth quadrant

- In the fourth quadrant cos only is positive

∴ cot(2π - α) = -cot(α)

∴ cot(7π/4) = -cot(π/4)

∵ cot(x) = 1/tan(x)

∵ tan(π/4) = 1

∴ cot(π/4) = 1

∴ cot(7π/4) = -1

* The exact value of cot(7π/4) = -1

5 0
3 years ago
Two rigid transformations are used to map JKL to MNQ. The first is a translation of vertex L to vertex Q. What is the second tra
harina [27]

The first is a translation of vertex L to vertex Q. What is the

second transformation?

a reflection across the line containing LK

a reflection across the line containing jk

a rotation about point l

a rotation about point k

8 0
3 years ago
Read 2 more answers
Help me out please.i will give brainly
tankabanditka [31]

Answer:

Hello! answer: 17

Step-by-step explanation:

Assuming this is the Pythagorean theorem our formula would be

a^2 + b^2 = c^2

meaning both of those sides multiplied by themselves added together will equal a number which is the result of c multiplied byitself sorry it sounds confused but...

15 × 15 = 225 8 × 8 = 64 225 + 64 = 289

the square root or the (number multiplied byitself that equals 289) is 17 because

17 × 17 = 289 so × = 17 I hope that helps!

7 0
3 years ago
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What is the exact distance from (–1, 4) to (6, –2)? (4 points) units units units units
irina1246 [14]

Answer:

\sqrt{85}

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = \sqrt{(6+1)^2+(-2-4)^2}

  = \sqrt{7^2+(-6)^2}

  = \sqrt{49+36}

  = \sqrt{85} ← exact distance

4 0
3 years ago
(-9m+9) + (8m+8) simplify
lisabon 2012 [21]

Answer:

M+16m

Step-by-step explanation:

-9m+9 cancel eachother out because it is a negative and a postive value, so you would just put the variable. For 8m+8 it would be 16m because the sre both positive so you would add them like normal

7 0
2 years ago
Read 2 more answers
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