Answer:
let x be the Robert piece
y Maria's piece
x+y=10
0,5*x ( half of Robert piece)= 2/3 y( 2 thirds)
2 equations then
x+y= 10 then x= 10-y
0,5x= 0,67 y then we replace x by 10-y on the second equation and it gives
0,5(10-y)= 5-0,5y=0,67y
5= 1,17 y so y= 4,27 and then x= 10-y= 5,73
the question asks how much Robert wire is longer than Maria's wire
so we get x-y= 1,46
Answer:
40 × 1/4
Step-by-step explanation:
That is greater because 40 is being multiplied.
Answer:
12-hot dog package is better buy because the per hot dog price is 5 cents cheaper
Step-by-step explanation:
2.40/8 = 0.30 per hot dog
3.00/12 = 0.25 per hot dog (this is the better buy by $.05)
Step-by-step explanation:
<h3><u>Given :-</u></h3>
[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]
<h3>
<u>Required To Prove :-</u></h3>
[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)
<h3><u>Proof :-</u></h3>
On taking LHS
[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]
We know that
Tan θ = 1/ Cot θ
and
Cot θ = 1/Tan θ
=> (1+Cot²θ)(1+Tan²θ)
=> (Cosec² θ) (Sec²θ)
Since Cosec²θ - Cot²θ = 1 and
Sec²θ - Tan²θ = 1
=> (1/Sin² θ)(1/Cos² θ)
Since , Cosec θ = 1/Sinθ
and Sec θ = 1/Cosθ
=> 1/(Sin²θ Cos²θ)
We know that Sin²θ+Cos²θ = 1
=> 1/[(Sin²θ)(1-Sin²θ)]
=> 1/(Sin²θ-Sin²θ Sin²θ)
=> 1/(Sin²θ - Sin⁴θ)
=> RHS
=> LHS = RHS
<u>Hence, Proved.</u>
<h3><u>Answer:-</u></h3>
[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)
<h3><u>Used formulae:-</u></h3>
→ Tan θ = 1/ Cot θ
→ Cot θ = 1/Tan θ
→ Cosec θ = 1/Sinθ
→ Sec θ = 1/Cosθ
<h3><u>Used Identities :-</u></h3>
→ Cosec²θ - Cot²θ = 1
→ Sec²θ - Tan²θ = 1
→ Sin²θ+Cos²θ = 1
Hope this helps!!
If the domian is 1 then range is -5