Examine the series in consecutive pairs.
-101 + 102 = 1
-103 + 104 = 1
-199 + 200 = 1
The second number of the pairs go from 102 to 200 so there are (200 -102) / 2 + 1 = 49 + 1 = 50 pairs
Answer = the value is 1 * 50 = 50
Answer:
Step-by-step explanation:
According to the problem, calculation of given data are as follows,
Volume of cylindrical vase = 
As, Cone has same height and radius as cylinder, than we can calculate volume of cone by using following formula,
Volume of cone = 
× Volume of cylindrical vase
By putting the value, we get
Volume of cone = × 63
Volume of cone =
We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
<h3>How to solve Trigonometric Identities?</h3>
We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
Read more about Trigonometric Identities at; brainly.com/question/7331447
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Answer:
61
Step-by-step explanation:
1. let the unknown be x
2. using theorem of Pythagoras that states the hypotenuse will be equal to the sum of the other two sides we can determine that 75=14+X
3. this implies that X=75-14
4. therefore X= 61
For 300 more square feet the rent is $150 more.
Rent per additional square foot is 150/300 or 0.50.
For an additional 400 square feet the rent is an additional 400(0.50) or $200.
The rent for 1500 feet squared office is $1325.
