Prove the theorem below using the techniques ofbinding the term and splitting thesumorapproximation by integralsto find a tight bound for the sum. Make sure yourproof is complete, concise, clear and precise. Theorem 4.n∑i=1id∈Θ(nd+1)(5 points) 2.Prove the theorem below using the techniques ofbinding the term and splitting thesumorapproximation by integralsto find a tight bound for the sum. Make sure yourproof is complete, concise, clear and precise. Theorem 5.n∑i=1(log2i)c∈Θ(n(log2n)c)(10 points) 3. Consider the recurrenceT(n).T(n)={cifn≤12T(⌊n4⌋) +16ifn>1a)Use the recursion tree or repeated substitution method to come up with a goodguess for a boundf(n) on the recurrenceT(n).b) State and prove by induction two theorems showingT(n)∈Θ(f(n)).GradingYou will be docked points for errors in your math, disorganization, unclarity, orincomplete proofs

answer: f true

step-by-step explanation:

3.76%

step-by-step explanation:

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841