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##### 10. (6 pts) Use De Moivre'$ Theorem to derive the following two trig identities:COS 5(30) = cos"(0) _ 3cos(0) sin? (0)sin(30) = 3 cos? (0) sin(0) _ sin? (0)

10. (6 pts) Use De Moivre'$ Theorem to derive the following two trig identities: COS 5(30) = cos"(0) _ 3cos(0) sin? (0) sin(30) = 3 cos? (0) sin(0) _ sin? (0)...

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##### Consider the equation below. (If an answer does not exist, enter DNE:) f(x) = x4 _ 8x2 + 1 (a) Find the interval on which f is increasing: (Enter your answer using interval notation.)Find the interval on which f is decreasing. (Enter your answer using interval notation.)(b) Find the local minimum and maximum values of f.Iocal minimum valuelocal maximum value(c) Find the inflection points.(x, Y) =(smaller X-value)(x, Y) =(larger X-value)Find the interval on which f is concave Up. (Enter your answ

Consider the equation below. (If an answer does not exist, enter DNE:) f(x) = x4 _ 8x2 + 1 (a) Find the interval on which f is increasing: (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum ...

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##### Wote Sighs-hvarhe HL Visubstanc10,000,000X5 1 I? 1 7 1 1L maqr 3chcck d

Wote Sighs-hvarhe HL Vi substanc 10,000,000X 5 1 I? 1 7 1 1 L maqr 3 chcck d...

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##### Of the circle15-If P(a,a' )is any point on y-x (x = 0), let Q be the Point where the normal line intersect the parabola again Show that the line segment PQ has the shortest possible length when a Yi

of the circle 15-If P(a,a' )is any point on y-x (x = 0), let Q be the Point where the normal line intersect the parabola again Show that the line segment PQ has the shortest possible length when a Yi...

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##### 4. (d) f(2) 34 2 1 lim_f(x) ehessi 3 If given it gdoeb 2 2 (e) (b) S> exist, to 7 28 state 2 explain the wakuhy of (c) each 8 2 lim (x)f quantity,NJ2

4. (d) f(2) 34 2 1 lim_f(x) ehessi 3 If given it gdoeb 2 2 (e) (b) S> exist, to 7 28 state 2 explain the wakuhy of (c) each 8 2 lim (x)f quantity, NJ 2...

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##### Multiple Fill in the blank: For the following structure, use a Frost Circle to determine how many electrons are present in each molecular orbital(Type a number between 0-10 for each box):bonding electronsnon-bonding electronsanti-bonding electrons

Multiple Fill in the blank: For the following structure, use a Frost Circle to determine how many electrons are present in each molecular orbital (Type a number between 0-10 for each box): bonding electrons non-bonding electrons anti-bonding electrons...

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##### Use #1 + & / Pant 1 7+1 of the Funndamental Theorem of Calculus find " 9 derivative of de function:

Use #1 + & / Pant 1 7+1 of the Funndamental Theorem of Calculus find " 9 derivative of de function:...

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##### Question 3Total: [45 MarksL() Move Iut '(avoCoeen(b) The triangl ABC , shcwn the dugtam, such tluat Ac Rcm CR = [2 CM An ugle ACB radlans:XcmIimThe area of tinngle ABC 20 cm", Show Lull 0.430 correct lo thrce signilicant liguren. Use the coxitle tule tc caleulute the length ot AB . giving ycur aulswer (o (wO signiticunt figures;The poim D lies on CB such that AD In irc Of 4 circle centre â‚¬ akl radius CM The region |x)utled by the ure' AD JIl the straight lines DB and AB sluuledl

Question 3 Total: [45 MarksL () Move Iut ' (avo Coeen (b) The triangl ABC , shcwn the dugtam, such tluat Ac Rcm CR = [2 CM An ugle ACB radlans: Xcm Iim The area of tinngle ABC 20 cm", Show Lull 0.430 correct lo thrce signilicant liguren. Use the coxitle tule tc caleulute the length ot AB ....

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##### Write the equation in the slope-intercept form, and then find the slope and y-intercept of the corresponding lines.$$2 x-3 y-12=0$$

Write the equation in the slope-intercept form, and then find the slope and y-intercept of the corresponding lines. $$2 x-3 y-12=0$$...

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##### The figure below shows an animal cell after 2 being placed in 3 specific solution: Based on 8 the figure, which of the following describes this solution? L Water Water 6 8?Water molecule Solute

The figure below shows an animal cell after 2 being placed in 3 specific solution: Based on 8 the figure, which of the following describes this solution? L Water Water 6 8? Water molecule Solute...

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##### The flask represents the products of the titration of $25 \mathrm{~mL}$ of sulfuric acid with $25 \mathrm{~mL}$ of sodium hydroxide. (a) Write balanced molecular, total ionic, and net ionic equations for the reaction. (b) If each orange sphere represents 0.010 mol of sulfate ion, how many moles of acid and of base reacted? (c) What are the molarities of the acid and the base?

The flask represents the products of the titration of $25 \mathrm{~mL}$ of sulfuric acid with $25 \mathrm{~mL}$ of sodium hydroxide. (a) Write balanced molecular, total ionic, and net ionic equations for the reaction. (b) If each orange sphere represents 0.010 mol of sulfate ion, how many moles of a...

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##### What is represented by the orange shape in the membrane?Complex Complex Il Coenzyme Coenzyme A

What is represented by the orange shape in the membrane? Complex Complex Il Coenzyme Coenzyme A...

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##### Consider tWo masses (m1 and mz) are in motion On the frictionless inclined surfaces having angles 01 and 02 as shown in the figure: (frictionless pulley with negligible mass)a) Draw the free body diagram for cach mass b) Write down the equations of motion for cach mass Calculate the acceleration of masses in term of m; mz , 01 ,02 and g: ~h)

Consider tWo masses (m1 and mz) are in motion On the frictionless inclined surfaces having angles 01 and 02 as shown in the figure: (frictionless pulley with negligible mass) a) Draw the free body diagram for cach mass b) Write down the equations of motion for cach mass Calculate the acceleration of...

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##### M MreibutaraIk 0 Qutermno Aetal Hemaneonnc inunc] LIttleEeerataianlicaniStbriEmcer KanttIncorrect; Iny Aqaln , atantdle (om-iningFun â‚¬Dulunrunu Iiogolo ulhameaued teucton weanfaAinnincMmncoPtr&

M MreibutaraIk 0 Qutermno Aetal Hemaneonnc inunc] L Ittle Eeerat aianlicani Stbri Emcer Kantt Incorrect; Iny Aqaln , atantdle (om-ining Fun â‚¬ Dulunrunu Iiogolo ulha meaued teucton w eanfa Ainninc Mmnco Ptr&...

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##### Theorem 85 (Squeeze theorer) nutrber L â‚¬R such thal haveSuppose we have two sequencesN +R and g : N +R andlirn(9) aned N we have If(n) _ Ll < g(n) Then lim(f ) = L_ 2. If we have sequence :N+R und nluinber L â‚¬ R such thalVn â‚¬ N, If(n) - Ll <thene linn(f ) = L.Definition 56 We will define FZ (N,N) to be the set of all funclions $ : N = N such thal $ is increasing:Vin, n â‚¬ N we have (Im < np(rn) < P(n)) _TheoremGicen function $ Ny2, il is increasing if aned only &Vin â‚¬ N_

Theorem 85 (Squeeze theorer) nutrber L â‚¬R such thal have Suppose we have two sequences N +R and g : N +R and lirn(9) aned N we have If(n) _ Ll < g(n) Then lim(f ) = L_ 2. If we have sequence :N+R und nluinber L â‚¬ R such thal Vn â‚¬ N, If(n) - Ll < thene linn(f ) = L. Definition...

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##### Solve the differential equation 1 dy csc - +xy = xdxSelect one;e 3 y =-rcsc-lx 2 Vrz+iq =e 3 y =Xsec FIx+ QC 2vx? + 1e 3y = xsec-lx + { Vre+i-q3y = xcsc-lx JQ 2vrz +1

Solve the differential equation 1 dy csc - +xy = xdx Select one; e 3 y =-rcsc-lx 2 Vrz+iq = e 3 y =Xsec FIx+ QC 2vx? + 1 e 3y = xsec-lx + { Vre+i-q 3y = xcsc-lx JQ 2vrz +1...

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##### Table LapH efproducts throughout_thefermentation Drucess- Starter Culture hours aomra 16 hours 24 hours 6,32 535 5449 4 486 Current in use New Startcr 6.07 545 463 501 New Starter 6.35 6.36 5.82 5.69 524 5.57 49 5.28 465 468 "Hint: The facility would like= kecp the fermentation process, indicated by pH over time, as close to what thcy have now &S possible So acceptable starter cultures would have similar behavior ovcr time the startcr currentlyTable Z: Physicochemical properties of the

Table LapH efproducts throughout_thefermentation Drucess- Starter Culture hours aomra 16 hours 24 hours 6,32 535 5449 4 486 Current in use New Startcr 6.07 545 463 501 New Starter 6.35 6.36 5.82 5.69 524 5.57 49 5.28 465 468 "Hint: The facility would like= kecp the fermentation process, indica...

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##### Solve the implicit differentiation and related rates_ 1.) 3x2 y +y2 = 4at (-1,3), find y'

Solve the implicit differentiation and related rates_ 1.) 3x2 y +y2 = 4at (-1,3), find y'...

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##### Use the method of separation of variables to solve0lu 02u =0 in (0,1)x(O,+o); Ot2 Ox u(0,t) = u(1,t) = 0,t > 0, Ou u(x,0) = sin Tnx, (x,0) =1,0 < x <1. Ot

Use the method of separation of variables to solve 0lu 02u =0 in (0,1)x(O,+o); Ot2 Ox u(0,t) = u(1,t) = 0,t > 0, Ou u(x,0) = sin Tnx, (x,0) =1,0 < x <1. Ot...