Please I need help!!

Find the exact value of Cos 240 degrees without a calculator. Show your work!

VMariaS [17]

it equals (−12) because cos(60∘)=12

Explanation:

The reference angle for 240∘ is 60∘ (since 240∘=180∘+60∘)

60∘ is an angle of one of the standard triangles with
cos(60∘)=12

240∘ is in the 3rd quadrant so (either by CAST or noting that the "x-side" of the associate triangle is negative)
cos(240∘)=−cos(60∘)

cos(240∘)=−12

6 0

3 years ago

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the oppor

stepan [7]

Answer:

Step-by-step explanation:

Answer:

a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢

b. The amount of interest is $2,769.20¢

Step-by-step explanation:

Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.

We will first state the formula for calculating the future value of annuity:-

Future value of annuity =

$P[\frac{(1 + r)^{t}-1 }{r}]$

Where P is the amount deposited per year.

r is the rate of interest

t is the time or period

and in this case, the actual value of P = $4,000

rate of interest, r is 6.5% = 0.065

time, t is 5 years.

Substituting e, we have:

Fv of annuity =

$4,000[\frac{(1 + 0.065)^{5}-1 }{0.065 }]$

= 4,000 × [((1.065)^5)- 1/0.065]

= 4,000 × [(1.37 - 1)/0.065]

= 4,000 × (0.37/0.065)

= 4,000 × 5.6923

= $22,769.20¢

a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢

b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).

Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =

4,000 × 5 = $20,000

The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢

3 0

3 years ago

Use the hundreds try to find a mystery number The number has 2 even digits the number in the tens place is greater than the numb

AlladinOne [14]

Answer:

84

Step-by-step explanation:

2 even numbers and its sum is 12: 4, 8 and 6, 6

tenth place > ones place 84