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3 years ago

Prove the identity. sin(−θ) cot(−θ) = cos θ

1 answer:

6 0

Hello :
sin(−θ) = - sin(θ)
cot(−θ) = - cot(θ)
cot(θ) = cos(θ)/sin(θ)
sin(−θ) cot(θ) = (- sin(θ))×(-cos(θ)/sin(θ)) = cos(θ)

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. A regular hexagon is composed of 12 congruent 30 o -60 o -90 o triangles. If the length of the hypotenuse of one of those tria

sergey [27]

see the attached figure to better understand the problem

Let

2L---------> lenght side of hexagon

we know that

in one of those triangles

sin 30=1/2

sin 30=L/hypotenuse

solve for L

L=hypotenuse*sin 30-------->L=( 1 8 √ 3 )*(1 /2)------> L=9√3 units

Find the perimeter

perimeter=(2L)*6--------> L*12-------> Perimeter=9√3*12--------->108√3 units

therefore

the answer is

the perimeter of the regular hexagon is 108√3 units

5 0

4 years ago

Last year, an orange tree produced 36 oranges. This year, it produced fewer than 10. What are the possible values for how many f

weeeeeb [17]

Answer:

d : [ 0 , 26 ]

Step-by-step explanation:

Given:-

- The oranges produced last year, x = 36

- The oranges produced this year, y < 10

Find:-

What are the possible values for how many fewer oranges were produced from the tree this year

Solution:-

- The possible values for how many fewer oranges were produced this year relative to last can be determined by solving an inequality that signifies a difference (d) between last year and this year production as follows:

d = x - y

d = 36 - (<10)

- To remove the inequality from Right hand side we we can shift it to left hand side by inverting the inequality sig, since last production is exactly known we have:

d≥36 - 10

d≥ 26

- So the number of oranges produced are at least 26 less than last year and lower bound would be if there is no orange produced this year. Hence, the range is:

d : [ 0 , 26 ]

4 0

3 years ago

3 to the 2 power times 5 to the 3 times 8 divided by 3 times 5 to the 3 times 8

IceJOKER [234]

Answer:

Step-by-step explanation:

First condense all the numbers with exponents:

3² x 5³x 8 divided by 3 x 5³ x 8

27 x 125 x 8 divided by 3 x 27 x 8

Then multiply 27 , 125 ,and 8

27 x 125 x 8 =27000

Then multiply 3, 27 ,and 8

3 x 27 x 8 = 648

Then divide 27000 by 648

27000 / 648 = 41.6666666667

Which rounds to about: 42

3 0

4 years ago

The high school soccer team can have no more than 26 players. Write and solve an inequality to determine how many more players c

Mariana [72]

Answer:

The inequality to determine how many more players can make the team is:

$x+17\leq 26$

On solving it we get : $x\leq 9$

Thus, the number of players that can still make in the team must be no more than 9.

Step-by-step explanation:

Given:

Maximum number of players the soccer team can have = 26

Number of players already chosen by coach = 17

To find how many players can still make the team.

Solution:

Let the players that can still make the team be = $x$

Players already chosen = 17

Total number of players in the team can be given as = $x+17$

Total numbers must not exceed 26.

So, the inequality can be written as:

$x+17\leq 26$

Solving for $x$

Subtracting both sides by 17.

$x+17-17\leq 26-17$

∴ $x\leq 9$

Therefore, no more than 9 players can still make in the soccer team.

3 0

3 years ago

A small tree was planted at a height of 5 feet. The tree has been planted for 14 months, and is now 41.4 feet tall. Which equati

zlopas [31]

5 times 14 divided by 41-4

5 0

4 years ago