30 determine the coefficient on x 12 y 24 x12y24 in ( x 3 + 2 x y 2 + y + 3 ) 18 . (x3+2xy2+y+3)18. (be careful, as x x and y y now appear in multiple terms! )

2 is the corfficient of  2x

Answer is C

16. The price for which supplies equals the demand is 96.236 (see graph)

C) $96.24

17.

 Roots   2, -4, and 1 + 3i

The minimum degree polynomial would be

(x-2)*(x+4)*(x-(1+3i))(x-(1-3i)) = f(x)

f(x) = x4 - 2x2 + 36x - 80

A) f(x) = x4 - 2x2 + 36x - 80

18.
-2i is a zero of f(x) = x4 - 45x2 - 196 

Another zero must be 2i (conjugate) 

f(x) = (x2 +4)(x+7)(x-7) = x4 - 45x2 - 196

2i,7,-7

B) 2i, 7, -7

19. The asymptotes are y = 2 , x = -2, x= 2

(See graph2)

C) x = 2, x = -2, y = 2

20.
           five pi divided by six
360 degrees ………….2pi radians

x……………………..5pi/6 radians

x = 150°

B) 150°

21.

         sin B = 21/75 = 7/25

 

    tan B=21/72 = 7/24

C) sin B = seven divided by twenty five ;

tan B = seven divided by twenty four

22.  X = 17/cos(58°) = 32.080

A) 32.08

23.
    Coterminal angles 202°

202° +360° = 562°

202° -360° = -158°

D) 562°; -158°

24. period of the function.
y = 5 cos (x/2) (see graph3)

A) 4π

25.

y = csc-1(-1) = -pi/2

B) negative pi divided by two

26.
arcos( cosine of pi divided by two)
arcos(cos(pi/2)) = arcos(0) = pi/2

D) pi divided by two

27.

sin45 = 0.7071

cos45 = 0.7071
B) θ = 45°

28.

Pythagoras theorem

c**2 = a**2 + b**2

c = sqrt(17**2 +7**2) = 18.384 ft

C) 18.4 ft

29.
tan (7*pi/8)

 

tan(x/2)  = ±sqrt((1-cosx)/( 1+cosx))
tan(7*pi/8)  = -sqrt((1-cos7*pi/4)/( 1+cos7*pi/4)) = -0.414 = 1-sqrt(2)

B) 1 - square root of two

30. See graph4

 

[0, 2π).
4 sin2 x - 4 sin x + 1 = 0

D) pi divided by six , five pi divided by six

31.

f(x) = 3x**2 - 1 (1 point)
f(-x) = 3(-x)**2 -1 = 3x**2 -1 = f(x)

 

f(x) IS EVEN

B) Even

32. The first polynomial is a factor of the second if the division does not have any remainder.

This can be checked by substituting x = 5 in the second polynomial and verifying if it is a root

 

 3(5)**2 + 5(5) + 50 =  150

 

It is Not a factor

B) No

33.
k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound?

Using synthetic division, the results are (see image 4)

 

2,7,10,24

 

And since they are all positive values, k= 2 is an upper bound.

B) No

34. f(g(x)) = x , g(f(x)) = x.

 

f(x) = (x -7)/(x+3)

g(x) = (-3x - 7)/(x-1)

 

f(g(x)) = [(-3x - 7)/(x-1) -7] / [[(-3x - 7)/(x-1) +3]
f(g(x)) = [-10x/(x-1)] / [-10/(x-1)] = x

 

g(f(x)) = [(-3(x -7)/(x+3) - 7)]/[((x -7)/(x+3)-1)]

g(f(x)) = [-10x/(x+3)] / [-10/(x+3)] = x

35. Verify
cos 4x + cos 2x = 2 - 2 sin2 2x - 2 sin2 x

 

 

If we use the following identity

cos(2a)=1−2.sin2(x)

>> 

cos(4x) = 1-2*sin2(2x)

cos (2x) = 1-2*sin2(x)

If we add them ………..> cos (2x)+ cos (4x) = 2 -2*sin2(x) -2*sin2(2x)

If the demand and supply are equal, then we equate the two functions in p and solve for p.

That is

We can rearrange to obtain,

The real roots of this polynomial equation are:

Since price can not be negative, we discard the negative value ,

The correct answer for question 16 is C.

We were given the solution to this polynomial as

We need to recognize the presence of the complex root and treat it nicely.

There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if

is a solution to

then the complex conjugate

is also a root.

Since

is a solution then,

is also a solution.

Therefore we have

We expand to obtain,

Note that:

We now expand to obtain,

We simplify further to obtain,

The correct answer for question 17 is A.

If

is a zero of the polynomial,

then the complex conjugate

is also a zero,

This means that ,

are factors of the polynomial.

The product of these two factors,

is also a factor , so we use it to divide and get the remaining factors.

see diagram for long division.

The above polynomial can therefore factored completely as,

Applying our knowledge from difference of two squares, we obtain,

Hence all the zeroes of these polynomial can be found by setting

This implies,

The correct answer for question 18 is B

We were asked to find the horizontal and vertical asymptote of

To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,

For vertical asymptote, equate the denominator to zero and solve for x.

None of the options is correct, so the correct answer for question 19 is A.

We are converting,

to degrees .

To convert from radians to degrees, multiply by,

That is,

We simplify to obtain,

The correct answer is B.

Recall the mnemonics, SOH CAH TOA

The sine ratio is given by,

From the diagram,

The correct answer is C.

From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.

Using the cosine ratio, we obtain,

We can simply switch positions to make x the subject.

Hence the correct answer is A.

Coterminal angles have the same terminal sides.

To find coterminal angles, we keep adding or subtracting 360 degrees.

See diagram.

is coterminal with

or

The correct answer is D.

See the attached file for continuation.

Coefficient of x, in this case, is '2'

coefficient of x³y²=80

Step-by-step explanation:

using pascal triangle to expand we get

(2x+y)⁵=32x⁵+80x⁴y+{80x³y²}+40x²y³+10xy⁴+y⁵

the one in bracket is the answer so the coefficient of x³y²=80

If it's x²y³ then we know it's the second term of the expansion, that known we can use the combination

C(5, 2) = 5!/(2!.3!) = 10

Then if we had something like

(a + b)^5 our second term would be 10a²b³ but as we can see it's "a²"

And in our case we have 2x as a

So we must do 2² too

2² = 4

10 . 4 = 40

Then our second term of the expansion would be

40x²y³

The solution of this system is x=9/4, y=5/2, and z=-13/8

Step-by-step explanation:

1. Writing the equations in matrix form

The system of linear equations given can be written in matrix form as

Writing

A =

X =

B =

we have

AX=B

This is the matrix form of the simultaneous equations.

2. Solving the simultaneous equations

Given

AX=B

we can multiply both sides by the inverse of A

We know that , the identity matrix, so

All we need to do is calculate the inverse of the matrix of coefficients, and finally perform matrix multiplication.

3. Calculate the inverse of the matrix of coefficients

A =

To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be inverse matrix.

Make zeros in column 1 except the entry at row 1, column 1. Subtract row 1 multiplied by 2 from row 2

Make zeros in column 2 except the entry at row 2, column 2. Add row 2 multiplied by 3 to row 3

Multiply row 2 by −1

Make zeros in column 3 except the entry at row 3, column 3. Divide row 3 by −8

Subtract row 3 multiplied by 2 from row 1

Subtract row 3 multiplied by 4 from row 2

As can be seen, we have obtained the identity matrix to the left. So, we are done.

4. Find the solution

C

Hello, there!

A coefficient is a number that comes before a variable and is used to multiply the variable. 

A variable can never be a coefficient, so we already know that the answer cannot be B or D.

Now we are left with A and C. 4 is the exponent, not the coefficient, so the answer can't be A.

So, we are left with C. 2 multiplies x and comes before x. Therefore, our answer is C.

I hope I helped!

Let me know if you need anything else!

~ Zoe

The coefficient of x in Y^2x+y is 2