Answer:
²
Step-by-step explanation:
Given,
f ( θ ) = tan θ + sec θ
g ( θ ) = cosθ/1-sinθ
To prove : -
f ( θ ) = g ( θ )
Proof : -
LHS = f ( θ )
RHS = g ( θ )
LHS
= f ( θ )
= tan θ + sec θ
{ Identities : -
tan θ = sin θ/cos θ
sec θ = 1/cos θ }
= sin θ/cos θ + 1/cos θ
= ( sin θ + 1 )/cos θ
= ( 1 + sin θ )/cos θ
Multiply ( 1 - sin θ ) to both numerator and denominator,
= ( 1 + sin θ ) ( 1 - sin θ ) / ( cos θ ) ( 1 - sin θ )
{ ( 1 + sin θ ) ( 1 - sin θ ) is in the form a² - b² Identity,
so,
( 1 + sin θ ) ( 1 - sin θ ) = 1² - sin²θ = 1 - sin²θ
Formula : -
sin²θ + cos²θ = 1
cos²θ = 1 - sin²θ
So,
1 - sin²θ = cos²θ }
= cos²θ / ( cos θ ) ( 1 - sin θ )
{ cos²θ = cos θ . cos θ }
= cos θ . cos θ / ( cos θ ) ( 1 - sin θ )
= cos θ / 1 - sin θ
= RHS
= g ( θ )
Hence proved.
If it’s 16 for base length and 16 for base width and 17 for height then this is the answer
Answer:
Quarters: 7
Dimes: 9
Nickels: 14
Step-by-step explanation:
Bank --> 30 coins
Base Equations:
N+D+Q=30
5N+10D+25Q=335
Equation 1: 2Q=N
Equation 2: D=30-(N+Q)
Substitute Equation1 : D=30-(2Q+Q)
D=30-3Q
0.05(2Q)+0.10(30-3Q)+0.25Q=3.35
0.10Q+3-0.3Q+0.25Q=3.35
0.5Q+3=3.35
0.5Q=0.35
Q=7
if Q=7, N= 2*Q
N=14
D=9
Check Step:
7*25=175
14*5=70
9*10=90
175+70+90=335
Correct
Answer:
3/8 pounds of compost
Step-by-step explanation:
Find how much compost she'll put in each garden bed by dividing the number of pounds of compost by the number of garden beds:
3/8
This fraction cannot be simplified further, so the answer is 3/8.
She will put 3/8 pounds of compost into each garden bed