Answer:
•cos(s+t) = cos(s)cos(t) - sin(s)sin(t) = (-⅖).(-⅗) - (√21 /5).(⅘) = +6/25 - 4√21 /25 = (6-4√21)/25
•cos(s-t) = cos(s)cos(t) + sin(s)sin(t) = (-⅖).(-⅗) + (√21 /5).(⅘) = +6/25 + 4√21 /25 = (6+4√21)/25
cos(t) = ±√(1 - sin²(t)) → -√(1 - sin²(t)) = -√(1 - (⅘)²) = -⅗
sin(s) = ±√(1 - cos²(s)) → +√(1- cos²(s)) = +√(1 - (-⅖)²) = √21 /5
Answer:
We have the function:
r = -3 + 4*cos(θ)
And we want to find the value of θ where we have the maximum value of r.
For this, we can see that the cosine function has a positive coeficient, so when the cosine function has a maximum, also does the value of r.
We know that the meaximum value of the cosine is 1, and it happens when:
θ = 2n*pi, for any integer value of n.
Then the answer is θ = 2n*pi, in this point we have:
r = -3 + 4*cos (2n*pi) = -3 + 4 = 1
The maximum value of r is 7
(while you may have a biger, in magnitude, value for r if you select the negative solutions for the cosine, you need to remember that the radius must be always a positive number)
#4) 1/6
#5) 1/2
#6) 4/15
#7) 8/15
#8) 11/15
#9) 12
#10) 15
#11) 112
Explanation
#4) There is one section marked 5 out of 6 sections.
#5) There are three odd-numbered sections out of 6 sections.
#6) 2 blue were tossed 4 times out of 15 tosses.
#7) 1 blue and 1 pink were tossed 8 ties out of 15 tosses.
#8) All blue was tossed 4 times out of 15; this means that all blue was not tossed 15-4=11 times out of 15.
#9) There are 4 choices for location and 3 choices for transportation; 4(3) = 12.
#10) There are 3 choices for level and 5 choices for character; 3(5) = 15.
#11) Since 30% are rock, 100%-30% = 70% are not rock. 70% = 70/100 = 0.7; 0.7*160 = 112.
Answer:
⅙ pitcher
Step-by-step explanation:
½ of ⅓ pitcher = ½ × ⅓ pitcher = ⅙ pitcher
Answer:
私は屋根裏部屋に50人の子供がいますが、母は知らないので、入り口の下に机を置いていたので、子供たちは水が不足していて、おそらく死んでいると思います。
Step-by-step explanation:
