The given question seem incomplete
Rewrite the expression as a simplified expression containing one term
cos (α + β)cos(β) + sin( α + β)sin(β)
Answer:
The simplified form of the given expression is cos(α)
Step-by-step explanation:
We are given the expression
cos (alpha + beta)cos(beta) + sin( alpha + beta)sin(beta)
we will proceed by expanding the given expression as
(cos(alpha)cos(beta) - sin(alpha)sin(beta))cos(beta) + (sin(alpha)cos(beta)+cos(alpha)sin(beta))sin(beta)
cos(alpha)cos^2(beta) -sin(alpha)sin(beta)cos(beta) + sin(alpha)cos(beta)sin(beta) + cos(alpha)sin^2(beta)
The two middle terms will cancel each other so we are left with
cos(alpha)cos^2(beta) + cos(alpha)sin^2(beta)
cos(alpha)[cos^2(beta) + sin^2(beta)]
cos(alpha) (1) = cos(alpha) [cos^2(beta) + sin^2(beta) = 1]
Therefore the simplified form of the given expression is cos(α)
Answer:
23.864 ft
Step-by-step explanation:
circumference = pie x diameter
pie= 3.14
diameter= 7.6ft
therefore, circumference =
3.14 x 7.6 ft
=23.864 ft
roundoff to the nearest tens=23.9 ft
Answer:
The time required to finish the work by both candy and Tim working together = 36.83 minute
Step-by-step explanation:
Time taken by the candy to finish the work 
= 85 min
Time taken by the Tim to finish the work 
= 65 min
Thus the time taken by both to finish the work = 
Put the values of and we get ,
= 
= 
= 36.83 minute
Thus the time required to finish the work by both candy and Tim working together = 36.83 minute
Answer:
here you goes hope it helps you
Step-by-step explanation:
1
Common factor
−
3
2
+
7
+
2
0
-3y^{2}+7y+20
−3y2+7y+20
−
1
(
3
2
−
7
−
2
0
)
-1(3y^{2}-7y-20)
−1(3y2−7y−20)
2
Use the sum-product pattern
−
1
(
3
2
−
7
−
2
0
)
-1(3y^{2}{\color{#c92786}{-7y}}-20)
−1(3y2−7y−20)
−
1
(
3
2
+
5
−
1
2
−
2
0
)
-1(3y^{2}+{\color{#c92786}{5y}}{\color{#c92786}{-12y}}-20)
−1(3y2+5y−12y−20)
3
Common factor from the two pairs
−
1
(
3
2
+
5
−
1
2
−
2
0
)
-1(3y^{2}+5y-12y-20)
−1(3y2+5y−12y−20)
−
1
(
(
3
+
5
)
−
4
(
3
+
5
)
)
-1(y(3y+5)-4(3y+5))
−1(y(3y+5)−4(3y+5))
4
Rewrite in factored form
Solution
−
1
(
−
4
)
(
3
+
5
)
The nth term is 2n +1 and the 43rd term is 87
