Answer:
60, 75
150 165
240 255
330 345
Step-by-step explanation:
csc 4 theta = -2 sqrt(3)/3
Write in terms of sin
1/ sin (4 theta) = -2 sqrt(3)/3
Using cross products
-2 sqrt(3) = 3 sin (4 theta)
Divide each side by 3
-2 sqrt(3)/3 = sin (4 theta)
Take the inverse sin on each side
sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))
240 +360n = 4 theta
and 300 +360n = 4 theta where n is an integer
Dividing each side by 4
240/4 +360n/4 = 4/4 theta and 300/4 +360n/4 = 4/4 theta
60 + 90n = theta and 75 +90n = theta
We want all the values between 0 and 360
Let n=0
60, 75
n=1
60+90=150 and 75+90 =165
n=2
60+180= 240 75+180=255
n=3
60+270 = 330 75+ 270 =345
Answer:
Step-by-step explanation:
If Quan had 15 and Kaden had 3 times as much, then Kaden had 15(3) = 45. If he spent 10 then he had 35 left. The amount of money Quan had after his mom gave him some was 4/5 the amount of Kaden's 35 (let x = the amount of money Quan has after his mom gives him some):
35 divides by the 5 in the denominator 7 times, and 7 times 4 is 28. That's how you get your 28 in part a.
For part b., he started with 15 and ended with 28, so his mom gave him 28-15=13. That's how you get the 13.
If you're multiplying by 10, you're moving the decimal point to the right, the same with any multiplication in the 10's, so 100, 1,000, etc. This is because you are making the number 10 times larger, so if you had 3.4, the 4 is in the 1/10 column so multiplying by 10 would put it in the units column, making the number 34.
On the other hand, dividing by the 10's makes the decimal point move to the left because you are making the number 10 times smaller, so if the units column is worth 1, then 10 times less than that is 1/10, which is the first decimal place.
I hope this helps! I tried to explain it well but let me know if you still don't understand or if I've confused you in any way :)
Answer:
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Step-by-step explanation:
