Suppose theta= 11pi/12. How do you use the sum identity to find the exact value of sin theta?

Answers

Answer 1

Answer: The better way is, first we have to find the equivalent in degrees

$2\pi=360\º$

$(11\pi)/(12)=345\º$

now we can change this value to $-15\º$

how do we get an angle like this?!

$30\º-45\º=-15\º$

then

$sin(30\º-45\º)=sin(30\º)*cos(45\º)-sin(45\º)*cos(30\º)$

$\begin{Bmatrix}sin(30\º)&=&(1)/(2)\n\nsin(45\º)&=&cos(45\º)&=&(√(2))/(2)}\end{matrix}\n\ncos(30\º)&=&(√(3))/(2)\end{matrix}$

now we replace this values

$sin(-15\º)=(1)/(2)*(√(2))/(2)-(√(2))/(2)*(√(3))/(2)$

$sin(-15\º)=(√(2))/(4)-(√(6))/(4)$

$\boxed{\boxed{sin(-15\º)=sin(345\º)=(√(2)-√(6))/(4)}}$

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A water sprinkler has a range of 5meters. The jet of water from the sprinkler sweeps out at an angle of 85degrees as the nozzle turns. What is the area watered by the sprinkler?

Answers

It's (85/360) of a full circle with a radius of 5meters.

Answer:

I found the image that accompanied this problem.

We need to solve for the area of the sector.

A = n/360 * π * r²

A = 85/360 * 3.14 * 5²

A = 0.2361 * 3.14 * 25

A = 18.5347

Answer is C. 18.5 square meters.

Step-by-step explanation:

10.5 in the form a/b

Answers

10.5 in the form of a/b = 105/10 = 21/2

A gallon of latex paint can cover 300 square feet. Felix has a pentagonal room in which all the sides have the same lenth of 10 feet thr room has a 8 foot celings how many gallon containers of paint does he need to buy to paint two coats on each wall

Answers

area of each wall is 10*8 = 80 square feet
there are 5 walls so total wall area is 5*80=400
he needs two coats on each wall so he needs to cover 2*400=800 square feet

so he needs to buy 3 galon containers

On average, Jenny does five loads of washing per week. She buys a 1.2k box of Kapow! laundry powder. and can only use 60g a loadHow many weeks should the box of powder last for Jenny?

Answers

Given:
5 loads of washing per week
1.2kg box of laundry detergent
60 g per load.

convert 1.2 kg to grams.
1 kg = 1000 grams

1.2 kg * 1,000g/1kg = 1,200 g
1,200 g / 60 g per load = 20 loads
20 loads / 5 loads per week = 4 weeks

It would take 4 weeks for a 1.2 kg box of Kapow! laundry powder to last.

The seventh term of the sequence -2, -6, -10, -14, ... is _____. -26 -24 -22 -20

Answers

We'll it keeps on subtracting by 4 to get each number.

-2,-6,-10,-14,-18,-22,-26.

Negative 26 is your answer. Hope this helped!

Answer:

-26

Step-by-step explanation:

We are counting by 4s

1) 2 - 4 = -2

2) -2 - 4 = -6

3) -6 - 4 = -10

4) -10 - 4 = -14

5) -14 - 4 = -18

6) -18 - 4 = -22

7) -22 - 4 = -26

Hope this helps!!!

Which of the following is an equivalent simplified expression for 2(4x + 7) – 3(2x – 4) ?A. x + 2
B. 2x + 2
C. 2x + 26
D. 3x + 10
E. 3x + 11
Can anyone explain this one for me?

Answers

The expression 2 × (4x + 7) – 3 × (2x – 4) in the equivalent simplified form will be 2x + 26. Then the correct option is C.

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 2 × (4x + 7) – 3 × (2x – 4)

Simplify the expression, then we have

⇒ 2 × (4x + 7) – 3 × (2x – 4)

⇒ 8x + 14 – 6x + 12

⇒ 2x + 26

The expression 2 × (4x + 7) – 3 × (2x – 4) in the equivalent simplified form will be 2x + 26. Then the correct option is C.

More about the equivalent link is given below.

brainly.com/question/889935

#SPJ2

2(4x + 7 ) -3 ( 2x - 4 )
8x + 14 - 6x + 12 combine like terms.
2x + 14 + 12
2x + 26
Answer: C. 2x + 26

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