An airline offers tickets on 3 routes from Atlanta: Chicago for $150, Boston for $160, and Dallas for $180, represented by the matrix 150 160 180 . We can find the cost of four of each of the tickets by multiplying this matrix by one of the matrices below. Find it.

Answer-

a. The engine speed that maximizes torque is 3.1 thousand revolutions per minute  and the maximum torque is 74.68 ft-lbs

b. As the engine speed increases, the torque increases until the engine speed reaches  3.1 thousand revolutions per minute and then the torque decreases.

Solution-

The given equation is,

[tex]y=-3.75x^2+23.2x+38.8[/tex]

Where x = the speed of the engine (in thousands of revolutions per minute)

           y = the engine torque y (in foot-pounds)

a.

In order to calculate the max torque and when it is max, we have to take the help of maxima and minima concepts from application of derivatives.

[tex]\Rightarrow y=-3.75x^2+23.2x+38.8[/tex]

[tex]\Rightarrow {y}'=-7.5x+23.2[/tex]

[tex]\Rightarrow {y}''=-7.5[/tex]

Equating the first derivative to 0, in order to find critical points,

[tex]\Rightarrow {y}'=0[/tex]

[tex]\Rightarrow -7.5x+23.2=0[/tex]

[tex]\Rightarrow x=\frac{-23.2}{-7.5} = 3.093 \approx 3.1[/tex]

As the value of second derivative is negative, hence the value of the function at x=3.1 will be maximum.

The value of max torque is,

[tex]y(3.1)=-3.75(3.1)^2+23.2(3.1)+38.8=74.682 \approx 74.68[/tex]

b.

Calculating the roots of the function,

[tex]\Rightarrow y=0[/tex]

[tex]\Rightarrow -3.75x^2+23.2x+38.8=0[/tex]

[tex]x=-1.369,7.556[/tex]

As these are the roots or x-intercept, the value of the function at these points is zero.

As shown in the graph, the function increases from x=0 to x=3.1 (as the speed can not be negative, so neglecting negative values) and after x=3.1 it decreases.

At about 3093 revolutions per minute, the engine torque reaches its maximum of 44.97 ft-lbs. Prior to this, the torque increases with engine speed, but starts to decrease once the speed surpasses this point.

The equation given is that of a downward opening parabola, which means it has a maximum point. The vertex (h, k) of a parabola given by the equation y = a(x-h)^2 + k is at x = -b/2a. For the given equation, a = -3.75 and b = 23.2.

Substituting these values, we get x = -23.2/(2*-3.75) = 3.093 to the nearest thousand, which translates to 3093 revolutions per minute. Substituting this value of x in the equation gives the maximum torque y = -3.75*(3.093)^2 + 23.2*3.093 + 38.8 = 44.97 ft-lbs to the nearest hundredth.

As the engine speed increases, the torque increases until the engine speed reaches about 3093 revolutions per minute. After this, "the torque then starts to decrease".

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Answer:

Step-by-step explanation:

130

Answer is (1, 2, -6)

x + 3y + z = 1   -------> first equation

2x – y – z = 6  -------> second equation

5x + y + z = 1 -------> third equation

Add second and third equation

2x – y – z = 6  -------> second equation

5x + y + z = 1 -------> third equation

-------------------------------------------------

7x = 7 (divide by 7 on both sides)

So x= 1

Now we add first and second equations

x + 3y + z = 1   -------> first equation

2x – y – z = 6  -------> second equation

-------------------------------------

3x +2y = 7

We already got x=1, replace it in the above equation

3(1) + 2y = 7

3 + 2y = 7 (subtract 3)

2y = 4 (divide both sides by 2)

So y =2

Now plug in the values in first equation

x + 3y + z = 1   -------> first equation

1 + 3(2) + z = 1

7 + z = 1 (subtract 7 from both sides)

z = -6

Answer is (1, 2, -6)

Number #2 is D, number #3 i am not sure

The correctly identified hypothesis and conclusion is 'If it is raining, then the humidity level is 100%'. The biconditional form of the statement about complementary angles is 'Angles are complementary if and only if their sum measures to 90°.'

In the given scenarios, the true conditional with a correctly identified hypothesis and conclusion is 'If it is raining, then the humidity level is 100%'. The hypothesis is 'It is raining' and the conclusion is 'The humidity level is 100%'.

In relation to the second question about complementary angles, the definition is indeed reversible. We can write it as a biconditional statement: 'Angles are complementary if and only if their sum measures to 90°.' The biconditional statement holds true in both directions, showing that both conditions are necessary and sufficient for each other.

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Answer:

75 pages

Step-by-step explanation:

Answer: Option A. |-7| = 7

Solution:

The distance is a positive value, then we must not take in account the sign, and using:

|a| =-a if a<0

with a=-7

|-7| = -(-7)

|-7| = 7

The radical √60 can be expressed as 2√15.

A radical is a mathematical symbol (√) used to represent the square root or other roots of a number. It indicates finding the value that, when squared, equals the given number.

The square root of 60 can be rewritten as the square root of (4 * 15). This allows us to express it as the square root of 4 times the square root of 15.

So, √60 = √(4 * 15)

= √4 * √15

= 2√15.

Therefore, the square root of 60 can be expressed as 2√15.

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The expression 8³ / 8 in the simplified form will be 8².

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Exponentiation is a numerical activity, composed as bⁿ, including two numbers, the base b, and the type of power n, and articulated as "b to the n".

The expression is given below.

⇒ 8³ / 8

We know that 1/aⁿ will be written as a⁻ⁿ. Then the expression is written as,

⇒ 8³ / 8

⇒ 8³ × 8⁻¹

⇒ 8⁽³ ⁻ ¹⁾

⇒ 8²

The expression 8³ / 8 in the simplified form will be 8².

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50 : 45

10 : 9 (10 yellow : 9 red)

50 yellow and 45 red

The ratio of yellow to red = 50/45 = 10/9

Answer

The ratio of yellow to red is 10/9 or 10:9

The answer is 9,850 if you are adding the numbers together.

Answer:

9,000 + 800 + 50 = 9,850

Step-by-step explanation:

Hope it helped!

Let's test each alternative :

2 x - 9 y = 38      ( 7,5 ) :

( 2 * 7 ) -  ( 9 * 5 ) = 38

14 - 45  = 38

-31 ≠ 38   (  wrong )

( 4 , - 1 ) :

( 2 * 4 ) - ( 9 * ( - 1 ) =  38

8 + 9  = 38

17 ≠ 38  ( wrong )

( 3 , - 3 ) :

2 * ( 3 ) - ( 9 * ( - 3 ) = 38

6 + 27 = 38

33 ≠ 38  ( wrong )

( 1 , - 4 ) :

2* ( 1 ) - 9 * ( - 4 ) = 38

2 + 36 = 38

38 = 38    ( Correct alternative )

( 1 , - 4 ) is correct alternative

you would need 7 eggs

Set up the proportion.  Then cross multiply and isolate the variable to solve.

[tex]\frac{2(eggs)}{10 (pancakes)} = \frac{x}{35 (pancakes)}[/tex]

2(35) = 10(x)

70 = 10x

[tex]\frac{70}{10} = \frac{10x}{10}[/tex]

7 = x

Answer: 7 eggs

Answer:

24 feet^2

Step-by-step explanation:

Area = 1/2 × base × height

Base = 8 feet

Height = 6 feet

Area = 1/2 × 8 feet × 6 feet = 24 feet²

Answer:

Area = 24 square feet.

Step-by-step explanation:

Given  : A  triangular window has a base of 8 feet and a height of 6 feet.

To find :What is its area?

Solution :  We have given

Base of triangular window = 8 feet.

Height of triangular window = 6 feet.

Area = [tex]\frac{1}{2} * base*height[/tex].

Plugging the values.

Area = [tex]\frac{1}{2} *8* 6[/tex].

Area = 24 square feet.

Therefore, Area = 24 square feet.

The equivalent of 10095 m/s is 6.2728 mi/s.

Further Explanation

To get the answer to this problem we use the conversion factor for meters to miles: 1609.34 m = 1 mi.

Setting up the dimensional analysis:

[tex]speed \ = 10095 \frac{m}{s} \times \frac{1 \ mi}{1609.34 \ m}\\[/tex]

We put the number of meters in the numerator so that the unit (meter) may be cancelled.

By multiplying the given by the number of meters in mile, we arrive at the answer:

[tex]\boxed {\boxed {speed = 6.2728 \ \frac{mi}{s}}}[/tex]

Since the given has 5 significant figures, the final answer must also have five significant figures.

Additional Example:

Sometimes the problem requires the conversion of both numerator and denominator. Below is a worked example for these kinds of question.

The conversion factor relating miles to meters is 1mile=1610m. The speed of light is 3.00×108 m/s. How fast is this in miles per hour (miles/h)?

The problem gives the conversion factor for miles to meter:

1 mi =1610 m

To convert the speed of light into the desired unit the following steps must be carried out:

These conversion may be done individually or simultaneously in a single dimensional analysis equation. The equation below shows the simultaneous conversion in one equation:

[tex]speed \ of \ light = 3.00 \times 10^8 \ \frac{m}{s} \times \frac{1 \ mi}{1610 \ m} \times \frac{60 \ s}{1 \ min} \times \frac{60 \ min}{1 \ h}\\\\\boxed {speed \ of \ light = 6.71 \times 10^8 \ \frac{mi}{h}}[/tex]

Since the answer must be expressed with only 3 significant figures, the final answer is:

Learn More

Keywords: miles, meters, conversion

How to get answer:

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3x^4-8x^3+9x+5+x-2\\Group\:like\:terms\\=3x^4-8x^3+9x+x+5-2\\\mathrm{Add\:similar\:elements:}\:9x+x=10x\\=3x^4-8x^3+10x+5-2\\\mathrm{Add/Subtract\:the\:numbers:}\:5-2=3\\=3x^4-8x^3+10x+3[/tex]

For this case we have a polynomial division.

A term of the quotient must be found step by step to eliminate the terms of the dividend.

The final result must comply with:

[tex]P (x) = Q (x) * D (x) + R (x)\\[/tex]

Where:

P (x) is the dividend

Q (x) is the quotient

D (x) is the divisor

R (x) is the remainder

Answer:

See attached image

Given

He earns a commission of 5 percent on the first 10 suits.

he sells more than 10, he earns an additional 3 percent on the additional suits

Last weekend Juan sold 13 suits at a price of $250 each.

Find out Juan Ramirez commission

To proof

As given in the question

Juan sold 13 suits at a price of $250 each

13 suit selling price = 13 × 250

                               = $ 3250

As given

He earns a commission of 5 percent on the first 10 suits.

and for more than 10, he earns an additional 3 percent on the additional suits

Juan Ramirez sells 13 suit which are more than the 10 suits

Hence  

commission percent for the 13 suits = 8 %

First write 8% in the decimal form

[tex]= \frac{8}{100}[/tex]

=0.08

Than commission on the 13 suits = 0.08 × 3250  

                                                       = $260.

Therefore option ( D) is correct.

Hence proved

Answer:

It IS balanced.  There are 4 Hydrogen atoms on the left and the right and 2 Oxygen atoms on the left and the right.  

Step-by-step explanation:

The given reaction follows the law of conservation of mass and is balanced. Thus, the correct option is C.

The balanced chemical equation for the reaction has been:

[tex]\rm 2\;H_2\;+\;O_2\;\rightarrow\;2\;H_2O[/tex]

The law of conservation of mass states that the mass of each element on the product and the reactant side has been equal. The mass has been proportional to the number of atoms, thus the atoms have been equal on both sides of the reaction.

In the given reaction:

Reactant = 4

Product = 4

Reactant = 2

Product = 2

Since there has been the same number of atoms of each element on both sides of the reaction, the reaction has been termed a balanced reaction. The law of conservation of mass has been followed in the equation.

Thus, option C is correct.

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First we can calculate how many seconds there are in an hour:​

Since 1 hour has 60 minutes and each minute has 60 seconds.​

Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.​

Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.​

In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds​

Answer : 144,000 seconds there are in a 40-hour work week​

​Hope this helps!

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

The correct formula to calculate the number of seconds in a 40-hour work week is 40 hours * 60 minutes/hour * 60 seconds/minute (option a). This method accurately converts hours to minutes and then minutes to seconds.

The correct formula for calculating the number of seconds in a 40-hour work week is as follows:

a. 40 hours * 60 minutes/hour * 60 seconds/minute

Here's the breakdown:

1. Start with the number of hours, which is 40 hours.

2. Convert hours to minutes using the conversion factor of 60 minutes per hour.

3. Convert minutes to seconds using the conversion factor of 60 seconds per minute.

By multiplying these three factors together, you obtain the total number of seconds in a 40-hour work week.

The other options (b, c, d) do not correctly set up the conversion factors and units, leading to incorrect results.

So, the correct answer is (a), as it correctly converts 40 hours into seconds using the appropriate conversion factors.

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We have the following function:

[tex]f(x)=x^2+3x-10[/tex]

So, we need to find the x- and y-intercepts of the graph of that function, therefore:

1. x-intercepts

x-intercepts can be found when [tex]y=0[/tex], so:

[tex]0=x^2+3x-10 \\ \\ Using \ Quadratic \ Formula \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ Where: \\ \\ a=1, b=3, c=-10 \\ \\ x=\frac{-3 \pm \sqrt{3^2-4(1)(-10)}}{2(1)} \\ \\ Two \ values: \\ \\ x=2 \ and \ x=-5[/tex]

So, the x-intercepts are:

[tex]\boxed{(2,0) \ and \ (-5, 0)}[/tex]

2. y-intercepts

x-intercepts can be found when [tex]x=0[/tex], so:

[tex]y=(0)^2+3(0)-10 \\ \\ \therefore y=-10[/tex]

So, the y-intercept is:

[tex]\boxed{(0,-10)}[/tex]

_______________________________________

Therefore the right answer is:

x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)

This is indicated in the Figure bellow.

Answer:

2, 0) and (−5, 0)

Step-by-step explanation:

Since the greatest common factor for 48 and 80 is 16 then we conclude the largest number of stack is 16

The largest number of coins that the child can place in each stack is 16, which is the greatest common divisor of the number of quarters (48) and dimes (80) they have.

In this problem, we're looking for the greatest number of coins that can evenly divide both the total number of quarters and the total number of dimes the child has. This can be solved by finding the greatest common divisor (GCD) of the numbers, 48 and 80.

The GCD of 48 and 80 is 16. Therefore, the child can create stacks of 16 coins each (either quarters or dimes), ensuring that each stack has the same number of coins and that all coins are used.

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The y-intercept of the equation 6x + 12y = 60 is 5, and the slope of the line through points (1, -1) and (-2, 8) is -3. Therefore the correct option is A.

Finding the Y-Intercept of a Linear Equation

To find the y-intercept of the linear equation 6x + 12y = 60, we need to set x to 0. If x=0, the equation simplifies to 12y = 60. Dividing both sides by 12 gives us the y-intercept: y = 5. Therefore, the correct answer is A: 5.

Calculating the Slope between Two Points

The slope of a line containing the points (1, -1) and (-2, 8) can be found by using the formula (y2 - y1) / (x2 - x1). Substituting the given points into the formula results in: (8 - (-1)) / (-2 - 1) = 9 / -3 = -3.

[tex]\vec{u}=[5,\ 2],\ \vec{v}=[4,\ -3]\\\\2\vec{u}=2[5,\ 2]=[(2)(5),\ (2)(2)]=[10,\ 4]\\\\3\vec{v}=3[4,\ -3]=[(3)(4),\ (3)(-3)]=[12,\ -9]\\\\2\vec{u}+3\vec{v}=[10,\ 4]+[12,\ -9]=[10+12,\ 4+(-9)]=[22,\ -5][/tex]

[tex]70 = -5(-2 + x)\\\\70=10-5x\\\\5x=-60\\\\x=-12[/tex]

Answer:

Phase angle is 50.527°

Step-by-step explanation:

Given that in a parallel circuit [tex]E_{T}=277V[/tex], R=56kΩ and [tex]X_{L} =[/tex]68kΩ.

And we are asked to find phase angle.

In any circuit, phase angle[tex]\theta=tan^{-1}(\frac{X_L-X_C} {R})[/tex]

Since we don't have any capacitor,[tex]X_{C}=0[/tex]

Hence phase angle,[tex]\theta=tan^{-1}(\frac{68000}{56000})[/tex]

                                                  [tex]=tan^{-1}(1.2143)[/tex]=50.527°≈50.53°

2y - 3 > -1    |add 3 to both sides

2y > 2     |divide both sides by 2

y > 1

-----------------------------

5 - y > 4      |subtract 5 from both sides

-y > -1      |change the signs

y < 1

y > 1 or y < 1

The furniture company decreases its chair production by 66%, resulting in a reduction of 5214 chairs. The new production level is 2686 chairs per month.

A furniture company reduces its chair production by 66%. To find the amount of the decrease and the new number of chairs produced, we first calculate the decrease: 7900 chairs × 0.66 = 5214 chairs. Therefore, the reduction in the number of chairs produced is 5214. To find the new production amount, subtract the decrease from the original production: 7900 - 5214 = 2686 chairs.

The new number of chairs produced each month is then 2686 chairs. This calculation helps both the company and stakeholders understand the adjustment in production capacity and potentially adjust business strategies or resource allocation accordingly.