Evaluate the exact value: tan(pi/6)

Answers

Answer 1

Answer: pi/6 = 180°/6 = 30°

This produces a triangle that has 30-60-90 angles.

Its short leg will measure = y = sinΘ
Its long leg will measure = x = √1-y² = sin(2Θ)
Its hypotenuse will measure = 1

Tangent Θ = opposite / adjacent or short leg / long leg
Tan(pi/6) = 1/3 √3

Answer 2

Answer:

The exact value of tan (π/6) is 1/√3.

Given a trigonometric function,

tan (π/6)

We have to find the exact value of the given function.

We know that, the value of π/6 in degrees is 30 degrees.

So here, we have to find the value of tangent function of 30 degrees.

We know that,

Tan (x) = sin (x) / cos (x)

Here x = π/6

Tan (π/6) = sin (π/6) / cos (π/6)

= (1/2) / (√3 / 2)

= 1/√3

Hence the tan (π/6) is 1/√3.

Learn more about Tangent Functions here :

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Fifteen tickets cost $193.75. what is the average cost of each ticket

Answers

15 tickets cost = 193.75
So, 1 ticket costs = 193.75 / 15 = 12.92

In short, Your Answer would be $12.92

Hope this helps!

Answer:

$12.92

Step-by-step explanation:

PLEASE HELP!!!!!!!! A cardboard box is 32 centimeters long, 15 centimeters wide, and 6 centimeters tall. The box does not have a top. How much cardboard was used to make the box?

Answers

Answer:

1044 cm²

Step-by-step explanation:

Since the box doesn't have the top, the total surface area includes 4 sides and the bottom.

S = 32(15) + 2(32 + 15)(6) = 1044 cm²

Cardboard used is 1044 cm²

Evaluate the following expression: 7.0 x 10⁴ + 6.0 x 10³

A) 13 x 10⁷
B) 42 x 10⁷
C) 67 x 10³
D) 76 x 10³

Answers

$7.0 \cdot 10^4 + 6.0 \cdot 10^3=10^3\cdot (7.0 \cdot 10+6.0)= (70.0 +6.0)\cdot10^3= 76 \cdot10^3\n \n Answer: \ D) \ \ 76 \cdot 10^3$

There are 4 fewer shovels than rakes. There are 6 shovels . How many rakes are there? Show your work.Can someone help me thank you

Answers

Answer:

Step-by-step explanation:

s= shovels=6

r= rakes= 6 + 4

Because 10 - 6= 4

(i hope this helped)

A small box weighs 1 25 pounds. A large box weighs 3 1/3 time as much as the small box. how much does the large box weigh?

Answers

Answer:

416.7pounds

Step-by-step explanation:

Given parameters:

Weight of the small box = 125pounds

Unknown:

Weight of the larger box = ?

Solution:

The large box weighs $3(1)/(3)$ times as the small box:

So;

= 125pounds x $(10)/(3)$

= 416.7pounds

A similarity transformation maps polygon ABCD to polygon PQRS. If the length of is 6 and the length of the corresponding side, , is 12, what is the scale factor of dilation

Answers

For this case, what we must do is find the scale factor.
We have then that the scale factor is given by:
$k = (L1)/(L2)$
Where,
L1: side length of polygon ABCD
L2: side length of polygon PQRS
Note: both sides belong to the same side of each polygon
Substituting the values we have:
$k = (6)/(12)$
Rewriting we have:
$k = (1)/(2)$
Answer:
The scale factor of dilation is given by:
$k = (1)/(2)$

$(6)/(12)$ = $(1)/(2)$ from the larger polygon to smaller one

$(12)/(6)$ = 2, from the smaller polygon to the larger one.

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