1. ____× 9,000=63,000? 2. 7×_____=56,000 3. 8×____

Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1. cos 41π 12.

PtichkaEL [24]

Answer: $\frac{\sqrt{6}-\sqrt{2}}{2}$

Step-by-step explanation:

We apply the formula $\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)$ .

Note that $\cos(\frac{41}{12}\pi)=\cos((\frac{36}{12}+\frac{7}{12})\pi)=\cos(3\pi + \frac{7}{12})\pi)$ . Take $x=3\pi$ and $y=\frac{7}{12}\pi$ in the formula above to get

$\cos(\frac{41}{12}\pi)=\cos(3\pi)\cos(\frac{7}{12}\pi)-\sin(3\pi)\sin(\frac{7}{12}\pi)=(-1)\cdot \cos(\frac{7}{12}\pi)-0\cdot\sin(\frac{7}{12}\pi)=-\cos(\frac{7}{12}\pi)$

Then the value of this expression is $-\cos(\frac{7}{12}\pi)$

We can use the cosine addition formula again to simplify further. Decompose the fraction in the argument as:

$\cos(\frac{7}{12}\pi)=\cos((\frac{3}{12}+\frac{4}{12})\pi)=\cos((\frac{1}{4}\pi + \frac{1}{3})\pi)$

Applying the formula with $x=\frac{1}{4}\pi$ and $y=\frac{1}{3}\pi$ we obtain

$\cos(\frac{7}{12}\pi)=\cos(\frac{1}{4}\pi)\cos(\frac{1}{3}\pi)-\sin(\frac{1}{4}\pi)\sin(\frac{1}{3}\pi)=\frac{\sqrt{2}}{2}\cdot\frac{1}{2} -\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2}=\frac{\sqrt{2}-\sqrt{6}}{2}$

We conclude that this expression has the value $-\frac{\sqrt{2}-\sqrt{6}}{2}=\frac{\sqrt{6}-\sqrt{2}}{2}$

8 0

3 years ago

Solve each equation with the quadratic formula

sp2606 [1]

First step, list your A,B,C’s.
A=5
B=-9
C=-116

The quadratic formula is:
y= -b +/- the square root of b^2-4(a)(c)
———————————————————-
2a

^ all of that is divided by 2(a)

now you wanna fill in your a,b,c’s.

(im gonna use sr to shorten (s)quare (r)oot)

y= -(5)

7 0

3 years ago

A regular polygon has its interior angles all equal to 174°

Vika [28.1K]

The shape has sixty sides

working out:
180 - 174 = 6
360 / 6 = 60

5 0

3 years ago

Tina Thompson scored 34 points in a recent basketball game without making any 3-point shots. She scored 23 times, making several

zheka24 [161]

F + g = 23
f+g-g=23-g
f = 23-g
f + 2g =34
23-g+2g=34
23+g=34
23-23+g=34-23
g = 11

f + g = 23
f + 11 = 23
f +11-11 =23-11
f = 12

Check
f + 2g =34
12 + 2(11) =34
12 + 22 = 34
34=34

She made 11 free throws and 12 field goals

6 0

4 years ago

Read 2 more answers

HELPP ASAP! WILL GIVE BRILLIANT! PLUS 20 POINTS

iragen [17]

Answer:

A. Yes the table represents a proportional relationship

B. The constant of proportionality is 1.2

Step-by-step explanation:

Two quantities are proportional if:

One of them is equal to the constant times the other one

If x and y are proportion, then y = k x, where k is constant

∵ Total wight in pounds ⇒ 12 , 18 , 30 , 60

∵ Number of books ⇒ 10 , 15 , 25 , 50

- Divide each two corresponding data to check if all they give

the same constant or not

∵ 12 ÷ 10 = 1.2

∵ 18 ÷ 15 = 1.2

∵ 30 ÷ 25 = 1.2

∵ 60 ÷ 50 = 1.2

- That means the total wight is equal to constant times the

number of books

∴ Total wight = 1.2 Number of books

∴ The total wight and the number of books are in a proportional

relationship

A. Yes the table represents a proportional relationship

∵ Total wight = 1.2 Number of books

∴ The constant of proportionality = 1.2

B. The constant of proportionality is 1.2

Learn more:

You can learn more about the proportionality in brainly.com/question/10708697

#LearnwithBrainly

Can I be Brainliest? TYSMMMMMMMMMMMMMMMMM

6 0

3 years ago

1. ____× 9,000=63,000? 2. 7×_____=56,000 3. 8×_____=3,200

1. __× 9,000=63,000? 2. 7×_=56,000 3. 8×___=3,200