1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timurjin [86]
3 years ago
6

17) Solve the system as matrix equations using inverses. 17) A company produces three models of MP3 players, models A, B, and C.

Each model A machine requires 3.2 hours of electronics work, 2.8 hours of assembly time, and 4.4 hours of quality assurance time. Each model B machine requires 5.4 hours of electronics work, 2.4 hours of assembly time, and 3.4 hours of quality assurance time. Each model C machine requires 2.2 hours of electronics work, 5.8 hours of assembly time, and 4.8 hours of quality assurance time. There are 303 hours available each week for electronics, 393 hours for assembly, and 416 hours for quality assurance. How many of each model should be produced each week if all available time must be used? A) Model A: 28 B) Model A: 30 C) Model A: 30 D) Model A: 31 Model B: 22 Model B: 15 Model B: 20 Model B: 20 Model C: 45 Model C: 50 Model C: 45 Model C: 44
Mathematics
1 answer:
Vinvika [58]3 years ago
8 0

Answer:

Model A=30, Model B: 20, Model C: 45

Step-by-step explanation:

Let x be the amount of type A mp3 produced, and the amount of model B mp3's produced and z the amount of model C mp3 produced.

Since in total there are 303 hours for electronics work, then:

3.2x+5.4y+2.2z=303

Since in total there are 393 hours for assembly, then:

2.8x+2.4y+5.8z=393

Since in total there are 416 hours for quality assurance, then:

4.4x+3.4y+4.8z=416

Then, the linear system associated to the problem is

3.2x+5.4y+2.2z=303\\2.8x+2.4y+5.8z=393\\4.4x+3.4y+4.8z=416

with coefficient matrix A=\left[\begin{array}{ccc}3.2&5.4&2.2\\2.8&2.4&5.8\\4.4&3.4&4.8\end{array}\right] and vector of constant terms b=\left[\begin{array}{ccc}303\\393\\416\end{array}\right]

Since the determinant of A is equal to 36.704 then A is invertible.

Then for solve the system Ax=b, is enough find the inverse of A and operate

Ax=b\\A^{-1}Ax=A^{-1}b\\x=A^{-1}b

Using Octave we obtain that

A^{-1}=\left[\begin{array}{ccc}-0.22&-0.50 &0.71\\0.33&0.15&-0.34\\-0.028& 0.35&-0.20\end{array}\right]

Then

x=A^{-1}b=\left[\begin{array}{ccc}30\\20\\45\end{array}\right]

This means that 30 mp3's of model A, 20 of model B and 45 of model C must be produced

You might be interested in
Helllllppp please asap
BartSMP [9]

Answer:

1). a = 9.42 m

2). b = 6.37 m

3). c = 4.48 m

Step-by-step explanation:

In the figure attached,

By applying tangent rule in triangle ADE,

tan47 = \frac{h}{c}

c = \frac{h}{\text{tan}47}

c = \frac{4.8}{\text{tan}47}

c = 4.476

c ≈ 4.48 m

Now we apply the same rule in triangle ACE,

tan37° = \frac{h}{b}

b = \frac{h}{\text{tan}37}

b = \frac{4.8}{1.0724}

b = 6.37 m

Now apply the tangent in triangle ABE,

tan27° = \frac{h}{a}

a = \frac{h}{\text{tan}27}

a = \frac{4.8}{0.5095}

a = 9.42 m

5 0
3 years ago
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What i
ahrayia [7]

Answer:

42.25 feet

Step-by-step explanation:

The height function is a parabola.  The maximum value of a negative parabola is at the vertex, which can be found with:

x = -b/2a

where a and b are the coefficients in y = ax² + bx + c.

Here, we have y = -16t² + 52t.  So a = -16 and b = 52.  The vertex is at:

t = -52 / (2×-16)

t = 13/8

Evaluating the function:

h(13/8) = -16(13/8)² + 52(13/8)

h(13/8) = -169/4 + 169/2

h(13/8) = 169/4

h(13/8) = 42.25

7 0
3 years ago
Read 2 more answers
Find the measures of
ki77a [65]

3y+15=4y-3

Subtract 3y from both sides

15=y-3

Add 3 to both sides

Y=18

4(18)-3

72-3

69 both angles are 69

8 0
3 years ago
Can someone help me please???​
Karolina [17]

Answer:

Altitude of Equilateral Triangle h = (1/2) * √3 * a. Angles of Equilateral Triangle: A = B = C = 60° Sides of Equilateral Triangle: a = b = c.

Hope this helped!

If you would like me to simplify it a little let me know.

8 0
3 years ago
Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims tha
GalinKa [24]

Answer:

\theta_1 \ n\ \theta_2 = 120, 240

Step-by-step explanation:

The question is incomplete, as the angles of rotation are not stated.

However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself

We have:

Nonagon = 9\ sides

Hexagon = 6\ sides

Divide 360 degrees by the number of sides in each angle, then find the multiples.

<u>Nonagon</u>

\theta = \frac{360}{9} =40

List the multiples of 40

\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320

<u>Hexagon</u>

\theta = \frac{360}{6} =60

List the multiples of 60

\theta_2 = 60, 120, 180, 240, 300

List out the common angles

\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320

\theta_2 = 60, 120, 180, 240, 300

\theta_1 \ n\ \theta_2 = 120, 240

This means that, only a rotation of 120, 240 will lift both shapes onto themselves, when applied to both shapes.

The other angles will only work on one of the shapes, but not both at the same time.

7 0
3 years ago
Other questions:
  • How to simplify 3×m×m??
    13·2 answers
  • The height of a triangle is 3cm less than the length of its base and is area is 27m,find the height
    10·1 answer
  • How many 4 minutes and 30 seconds in 2 hours
    7·2 answers
  • Choose the equation of the horizontal line that passes through the point (-2,-1)and has a slope of 5
    8·1 answer
  • out of the total 20000 people, it was found that 30% like to listen to hindi flim songs 20% like to listen to english music 15%
    12·1 answer
  • Select all the expressions that all have the following quotient 2m+3
    6·1 answer
  • Composite shapes find the total volume of the 3D shapes round to the nearest hundredth
    8·1 answer
  • Find the x-and y -intercepts.<br> y=20<br> The x-intercept is <br> The y-intercept is
    6·1 answer
  • 3. There were 567 whos in Whoville. Each who ate 814 bowls of
    5·1 answer
  • Select ALL the terms that are like 5b2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!