What is sink?<br> HELP ASAP 20 POINTS

What is the exact value of cos(7pi/8)

Damm [24]

Answer:

cos ( $\frac{7\pi}{8}$ ) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos $\frac{7\pi}{8}$ = cos $(\pi-\frac{\pi}{8})$ = −cos $\frac{\pi }{8}$

Now using half angle formula, cos(x) = 2 cos²( $\frac{\pi }{2}$ ) − 1, we can write cos $\frac{\pi }{4}$ = 2

cos²( $\frac{\pi }{8}$ ) − 1

This means $\frac{1}{\sqrt{2}}$ + 1 = 2 cos²( $\frac{\pi }{8}$ )

2 cos²( $\frac{\pi }{8}$ ) = $\frac{\sqrt{2}+1}{\sqrt{2}}$

cos²( $\frac{\pi }{8}$ ) = $\frac{\sqrt{2}+1}{2\sqrt{2}}$

cos( $\frac{\pi }{8}$ ) = $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$

Simplify,

$\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$ = $\sqrt{\frac{2+\sqrt{2}}{4}$ = $\frac{\sqrt{2+\sqrt{2}}}{2}$

Hence,

cos ( $\frac{7\pi}{8}$ ) = −cos ( $\frac{\pi }{8}$ ) = $-\frac{\sqrt{2+\sqrt{2}}}{2}$

3 0

3 years ago

Read 2 more answers

A stock trading company charges a commission of $10 per trade plus $0.025 per dollar value of stock traded. If your commission i

pickupchik [31]

Answer:

Value of the stock traded was $5200.

Step-by-step explanation:

In this question it is given that trading company charges commission of $10 per trade or transaction plus $.025 per dollar value of stock.We have to calculate the value of stock we traded if total commission (commission on trade value + commission on trade) is $140.

Let the value of stock traded was $x.

Then commission on value of the stock = x×.025

Commission on transaction = $10

Total commission = 140 = ( .025x + 10)

⇒.025x = 140-10 = 130

x = 130÷.025 = $5200

So the value of the stock = $5200

4 0

3 years ago

Read 2 more answers

Chris can be paid in one of two ways. Plan A is a salary of $490 per month, plus a commission of 9% of sales. Plan B is a sal

Tanya [424]

Step-by-step explanation:

Explanation:

First, when dealing with percents, "Percent" or "%" means "out of 100" or "per 100", Therefore x% can be written as

x/100.

The expression for Plan A can be written as:

490+(9/100)s where s is the sales for the month.

The expression for Plan B can be written as:

826+(3/100)s

The question we are being asked is when is Plan A > Plan B. So, we can write and solve this inequality:

490+(9/100)s>826+(3/100)s

490+(9/100)s−490−(3/100)s>826+(3/100)s−490−(3/100)s

490−490+(9/100)s−(3/100)s>826−490+(3/100)s−(3/100)s

0+(9/100)s−(3/100)s>826−490+0

(9/100)s−(3/100)s>826−490

(9/100−3/100)s>336

(6/100)s>336

(100/6)×(6/100)s>(100/6)×336

s> 33600/6

s>5,600

Plan A is better when sales for the month are greater than $5,600.

8 0

4 years ago

What are the odds against selecting a red marble

kodGreya [7K]

Answer: it’s the first one.

Step-by-step explanation:

6 0

3 years ago

Billy has already knit 23 centimeters of scarf, and can knit 1 centimeter each night. How many nights will Carey have to spend k

Kruka [31]

Answer:

13 nights

Step-by-step explanation:

To figure this out you first need to find out how many more centimeters to get to 36

36cm-23cm= 13 cm

If he needs to knit 13 more centimeters and he can knit 1 centimeter each night it would take him a total of 13 nights in order to knit a total of 36 centimeter scarf

4 0

3 years ago

What is sink? HELP ASAP 20 POINTS