Find all missing angles

The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

lbvjy [14]

$\bf ~\hspace{10em}\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 8x^3-125~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 125=5\cdot 5\cdot 5\\ \qquad 5^3 \end{cases}\implies 2^3x^3-5^3\implies (2x)^3-5^3 \\[2em] [2x-5][(2x)^2+(2x)(5)+5^2]\implies (2x-5)(\stackrel{\stackrel{j}{\downarrow }}{4}x^2+\stackrel{\stackrel{k}{\downarrow }}{10}x+25)$

3 0

4 years ago

A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours

qaws [65]

Answer:

The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.

Below are all the steps explained in detail.

The graph is attached.

Explanation:

1. Name the variables:

x: number of smaller lifts
y: number of larger lifts

2. Build a table to determine the number of hours each lift requires from each department:

Number of hours

small lift large lift total per department

Welding department 1x 3y x + 3y

Packaging department 2x 1y 2x + y

3. Constraints

150 hours available in welding: x + 3y ≤ 150
120 hours available in packaging: 2x + y ≤ 120
The variables cannot be negative: x ≥ 0, and y ≥ 0

Then you must:

draw the lines and regions defined by each constraint
determine the region of solution that satisfies all the constraints
determine the vertices of the solution region
test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

4. Graph

See the graph attached.

Here is how you draw it.

x + 3y ≤ 150
draw the line x + 3y = 150 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

2x + y ≤ 120
draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

the solution region is the intersection of the regions described above.

take the points that are vertices inside the solutoin region.

5. Test the profit function for each vertex

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

(0,0)
(0,50)
(42,36)
(60,0)

The profits with the vertices are:

P(0,0) = 0
P(0,50) = 25(0) + 90(50) = 4,500
P(42,36) = 25(42) + 90(36) = 4,290
P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

3 0

3 years ago

Two containers, X and Y, are each filled by an ideal gas at the same temperature. The volume of Y is half the volume of X. The n

-Dominant- [34]

Answer:

The answer to the question is

The ratio of the two gas pressures $\frac{P_{x} }{P_{y} }$ , that is Px to Py = 1/6

Step-by-step explanation:

Let the gases Volumes be V₁ and V₂

Where volume of X = V₁ and

volume of Y = V₂

The volume of Y is half the volume of X

∴ V₂ = $\frac{1}{2}$ × V₁

Let the number of moles be n₁ and n₂ in X and Y respectively

therefore n₂ = 3 × n₁

The pressure of the gas in X is Pₓ and the pressure of the gas in Y is $P_{y}$ then we have

P₁ × V₁ = n₁ × R × T₁ , and P₂ × V₂ = n₂ × R × T₂

(P₁ × V₁)/(n₁ × T₁) = (P₂ × V₂)/(n₂ × T₂)

but T₁ = T₂

Therefore

(P₁ × V₁)/n₁ = (P₂ × V₂)/n₂. However n₂ = 3 × n₁ and V₂ = $\frac{1}{2}$ × V₁ therefore substituting in the equation we have

(P₁ × V₁)/n₁ = (P₂ × $\frac{1}{2}$ × V₁ )/(3 × n₁) from where

P₁ /P₂ = ( $\frac{1}{2}$ × V₁ × n₁)/(V₁×3 × n₁) =0.5/3 = 1/6

The ratio of $\frac{P_{x} }{P_{y} }$ = 1/6

6 0

4 years ago

What is the measure of

Nat2105 [25]

Answer:

24

Step-by-step explanation:

180-156=24

5 0

3 years ago

Read 2 more answers

For each pair of numbers, find a third whole number such that the three numbers form a pythagorean triple.

BabaBlast [244]

Answer:

Part 1) The third whole number is 44

Part 2) The third whole number is 40

Part 3) The third whole number is 25

Step-by-step explanation:

we know that

The Pythagoras theorem states that

In a right triangle

$c^{2} =a^{2} +b^{2}$

where

c is the greater length side

a and b are the legs

Case 1) we have

33,55

step a

Let

$a=33, b=55$

Find the value of c

$c^{2} =a^{2} +b^{2}$

$c^{2} =33^{2} +55^{2}$

$c^{2} =4,114$

$c =64.14$ ------> is not a whole number

step b

Let

$a=33, c=55$

Find the value of b

$b^{2} =c^{2} -a^{2}$

$b^{2} =55^{2} -33^{2}$

$b^{2} =1,936$

$b=44$

Case 2) we have

42,58

step a

Let

$a=42, b=58$

Find the value of c

$c^{2} =a^{2} +b^{2}$

$c^{2} =42^{2} +58^{2}$

$c^{2} =5,128$

$c =71.61$ ------> is not a whole number

step b

Let

$a=42, c=58$

Find the value of b

$b^{2} =c^{2} -a^{2}$

$b^{2} =58^{2} -42^{2}$

$b^{2} =1,600$

$b=40$

Case 3) we have

60,65

step a

Let

$a=60, b=65$

Find the value of c

$c^{2} =a^{2} +b^{2}$

$c^{2} =60^{2} +65^{2}$

$c^{2} =7,825$

$c =88.46$ ------> is not a whole number

step b

Let

$a=60, c=65$

Find the value of b

$b^{2} =c^{2} -a^{2}$

$b^{2} =65^{2} -60^{2}$

$b^{2} =625$

$b=25$

6 0

3 years ago

Find all missing angles​

Find all missing angles