Letu = a1i + b1 jv = a2 i + b2 jw = a3 i + b3 j.Prove property by obtaining the vector on each side of the equation (u + v) + w = u + (v + w). Have you proved a distributive, associative, or commutative property of vectors?

Q: Answer the following questions. 1) Determine the following for the function f(x) 4.5x2 + 20x + 6: 3 ...

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Q: Write an equation in slope-intercept form of a linear function f whose graph satisfies the given con...

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Q: Position of a piston The distance between the head of a piston and the end of a cylindrical chamber ...

A: According to the question height of the cylindrical chamber is, h=x(t)=8tt+1 cm And radius is r = 4 ...

Q: Use properties of logarithms to expand the logarithmic expression logM -8 as much as possible. Where...

A: Known fact: log ab=blog alog mn=log m + log n

Q: Use the order of operations to simplify expression. 8 - 3[-2(2 - 5) - 4(8 - 6)]

A: Simplification: 8-3[-2(2-5)-4(8-6)] We need to know the BODMAS rule B-bracket O-of D-division M-mult...

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A: The tangent line of function g at x=a is defined as y-ga=g'ax-a

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A: Given that, f(x)=sin2xlnx2     ...(1)

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Q: Polar curves Graph the following equation. r = 3 sin 4θ

A: Given: r=3sin4θ graph of given polar curve can be draw using graphing utility as below

Q: In Exercises 25-28, calculate the derivative.

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Q: Use the exponential decay model for carbon-14, A = A0e-0.000121t,to solve:Prehistoric cave paintings...

A: Given, the exponential decay model for carbon-14       A=A0e-0.000121tto solve prehistoric cave pain...

Q: Determine whether the sequence converges or diverges.If it converges, find the limit.

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Q: Find the limit (if it exists). If it does not exist, explain why.

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Q: Calculus Question

A: 10)  x=tanyDifferentiating with respect to x on both sides,ddxx=ddxtany1=sec2ydydx1=sec2ydydxdydx=1s...

Q: Use limit methods to determine which of the two given functions grows faster, or state that they hav...

A: fx=x2lnx gx=ln2x⇒gx=lnx2 limx→∞fxgx=limx→∞x2lnxlnx2limx→∞fxgx=limx→∞x2lnx

Q: Evaluate the integrals ∫ ln x/x2 dx

A: Evaluate the integral ∫lnxx2dx.

Q: Give a geometric description of the following sets of points. x2 - 4x + y2 + 6y + z2 + 14 = 0

A: It is given that, x2-4x+y2+6y+z2+14=0We have to give a geometric description of the following sets o...

Q: Evaluate the expression tan 4.7 cot 4.7 without using a calculator.

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Q: Find the domain and the range of f.

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Q: Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1<x < 5

A: Given: hx=kx,0≤x&lt;1x+3,1≤x≤5 given function will be continuous over 0,5, if it will be continuous ...

Q: Locate the critical points and identify which critical points are stationary points: (i)f(x) = 4x^4 ...

A: (i) fx=4x4-16x2+17⇒f'x=16x3-32x Put f'x=0 16x3-32x=0⇒16xx2-2=0⇒x2-2=0⇒x=±2 x=0, ±2

Q: Write each equation in its equivalent exponential form: a. 2 = log5 x  b. 3 = logb 64  c. log3 7 = y...

A: We have to write equation in equivalent exponential form: a. 2=log5xb. 3=logb64c. log37=y We know th...

Q: Using Simpson’s Rule Approximate the following integrals using Simpson’s Rule. Experiment with value...

A: According to Simpson’s rule for integration, ∫abf(x) dx=Δx3f(x0)+4f(x1)+2f(x2) ⋯+4f(xn−1)+f(xn) Here...

Q: Limits Evaluate the following limits using Taylor series.

A: To evaluate: limx→4x2-16lnx-3. Given limit is 00 form. So, using L-hospital rule. limx→4x2-16lnx-3=l...

Q: Is (3, 4, –2) a solution of the following system? 5.x1 - X2 + 2x3 = 7 -2x1 + 6x2 + 9x3 = 0 -7x1 + 5x...

A: The given system of equation is 5x1-x2+2x3=7-2x1+6x2+9x3=0-7x1+5x2-3x3=-7  

Q: f(x) = x2 + 1, g(x) = x2 - 3.Find:a. (f ∘ g)(x)  b. (g ∘ f)(x)  c. (f ∘ g)(2)  d. (g ∘ f)(2).

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Q: Use the graph of g to solve: Find g(2).

A: Given:

Q: Write and find the general solution of the differential equation that models the verbal statement., ...

A: according to given statement dQdt=kt                                      ..1 for finding solution e...

Q: Find the derivative of the function y=excosx.

A: we have to find the derivative of the function y=excosx.

Q: Calculating limits Determine the following limits. x - 5 lim xS-5* x + 5

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Q: Population of a City The population of a certain city was 112,000 in 2014, and the observed doubling...

A: It is given that  In 2014, the population of a city was 112,000 and it double in 18 years.   (A)  Th...

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.