Simply substitute the given number for all the equations.
17) 5b + 1 = 16 where b is -3
5(-3) + 1 = 16
-15 + 1 = 16
-14 ≠ 16
So, the given number is not a solution.
19) 2 = 10 - 4y where y is 2
2 = 10 - 4(2)
2 = 10 - 8
2 = 2
The given number is a solution.
21) -6b + 5 = 1 where b is 0.5
-6(0.5) + 5 = 1
-3 + 5 = 1
2 ≠ 1
The given number is not a solution.
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!!
I think 10 is the answer, correct me
Increase $110,000 by 20% 3 times.
110,000 x 0.2 = 22000
(0.2 is 20% as a decimal, we needed to convert it to multiply it)
So we must add 22000 to 110,000, then take 20% of the new cost, and repeat.
Add them
110,000 + 22000 = 132000
Take 20% of new value
132000 x 0.2 = 26400
Add that
132000 + 26400 = 158400
Take another 20% of that
31680
Add them
158400 + 31680 = 190080
So the value is now $190,080
A much more efficient way to do this would be multiplying 1.2 instead of 0.2, and skipping the adding part, as you already took 100% of it and are adding 20% more.
Hope this helps!
Rewrite the inequality without the absolute value
-18 < x - 13 < 18
Add 13 to the whole equation
-18 + 13 < x < 18 + 13
Simplify
<u>-5 < x < 31</u>
