how to convert rad/s to ft/s?

The board was 519 cm long after the carpenter cut it. To solve the problem, you can use the formula for converting meters to centimeters, which is 1 m = 100 cm. First, convert the length of the board from meters to centimeters. Then, subtract 9 cm from the new length to find the length after the carpenter cut it.

Given that a carpenter had a board that was 5.28 m long.

Using the formula, 1 m = 100 cm, we can convert the length of the board from meters to centimeters.

5.28 m = 5.28 × 100 cm/m

= 528 cm

The length of the board in centimeters is 528 cm.

After cutting 9 cm off the end of the board, the new length is:

= 528 cm - 9 cm

= 519 cm

Therefore, the board was 519 cm long after the carpenter cut it.

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Answer:

62

Step-by-step explanation:

hope this helps have a good day

Answer:

62

Step-by-step explanation:

First add what is inside the parenthesis (8+2)

Then multiply the result of that addition (10) times 6 (10*6=60)

To 60 you add 4  (60+4=64)

To 64 you subtract the 2 (64-2=62)

The solution to the integral is:

∫ (5x^2 + 2x - 5) / (x^3 - x) dx = 4 ln |x| + ln |x-1| - 5 ln |x+1| + C

The solution to the integral is:

∫ (3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2] dx = (1/3) ln |2x + 1| - (64/25) ln |x - 2| - (49/100)/(x - 2) + C

From the question, we are to evaluate the given integral.

To evaluate the integral ∫ (5x^2 + 2x - 5) / (x^3 - x) dx, we can use partial fraction decomposition.

First, we factor the denominator:

x^3 - x = x(x^2 - 1) = x(x-1)(x+1)

So, we can write:

(5x^2 + 2x - 5) / (x^3 - x) = A/x + B/(x-1) + C/(x+1)

where A, B, and C are constants to be determined.

Multiplying both sides by the denominator (x^3 - x), we get:

5x^2 + 2x - 5 = A(x-1)(x+1) + B(x)(x+1) + C(x)(x-1)

Substituting x = 0, we get:

-5 = -A - B - C

Substituting x = 1, we get:

2 = 2B

So, B = 1.

Substituting x = -1, we get:

-8 = -2A

So, A = 4

Substituting these values back into the equation above and simplifying, we get:

(5x^2 + 2x - 5) / (x^3 - x) = 4/x + 1/(x-1) - 5/(x+1)

Hence, the integral becomes:

∫ [(5x^2 + 2x - 5) / (x^3 - x)] dx = 4 ln |x| + ln |x-1| - 5 ln |x+1| + C

where C is the constant of integration.

To evaluate the integral ∫ (3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2] dx

First, we factor the denominator:

(2x + 1)(x - 2)^2 = (2x + 1)(x - 2)(x - 2)

So, we can write:

(3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2] = A/(2x + 1) + B/(x - 2) + C/(x - 2)^2

Where A, B, and C are constants to be determined.

Multiplying both sides by the denominator (2x + 1)(x - 2)^2, we get:

3x^2 - 20x + 33 = A(x - 2)^2 + B(2x + 1)(x - 2) + C(2x + 1)

Substituting x = -1/2, we get:

49/4 = 25C

So, C = 49/100.

Substituting x = 2, we get:

3 = 9A

So, A = 1/3.

Substituting these values back into the equation above and simplifying, we get:

(3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2] = 1/(3(2x + 1)) + B/(x - 2) + (49/100)/(x - 2)^2

To find B, we can take the derivative of both sides with respect to x:

d/dx [(3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2]] = d/dx [1/(3(2x + 1)) + B/(x - 2) + (49/100)/(x - 2)^2]

Simplifying and evaluating at x = 2, we get:

-16/25 = -B/4

So, B = 64/25.

Substituting these values back into the equation above and simplifying, we get:

(3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2] = 1/(3(2x + 1)) + (64/25)/(x - 2) + (49/100)/(x - 2)^2

Hence, the integral becomes:

∫ [(3x^2 - 20x + 33) / [(2x + 1)(x - 2)^2]] dx = ∫ [1/(3(2x + 1)) + (64/25)/(x - 2) + (49/100)/(x - 2)^2] dx

= (1/3) ln |2x + 1| - (64/25) ln |x - 2| - (49/100)/(x - 2) + C

Where C is the constant of integration

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To determine the degree of a polynomial function given in factored form, a good first step is to count the highest power of the variable in the factored expression.

In factored form, a polynomial function is expressed as the product of linear factors or irreducible quadratic factors.

Each factor represents a root or zero of the function.

The degree of a polynomial is determined by the highest power of the variable in the expression.

To find the degree of the function, examine each factor in the factored form.

For linear factors, the degree is 1 since the highest power of the variable is 1.

For irreducible quadratic factors, the degree is 2 since the highest power of the variable is 2.

By observing the highest power in the factored expression, you can determine the degree of the polynomial function.

If the highest power is 1, the polynomial has a degree of 1 (linear function). If the highest power is 2, the polynomial has a degree of 2 (quadratic function). And so on.

It's important to note that the degree of a polynomial corresponds to the highest power of the variable in the expression and not the number of factors.

The number of factors indicates the number of roots or zeros of the polynomial, but it doesn't determine the degree.

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Answer:

All of the above

Step-by-step explanation:

Answer:

28 points per game

42 miles per gallon

$2.99 per bag

Step-by-step explanation:

140 points in 5 games. To find the amount of points in one game, we divide the total points by the total games: 140/5=28

504 miles with 12 gallons. To find the amount of miles with one gallon, we divide the total miles by the total gallons: 504/12=42

$8.97 for 3 bags. To find the amount of dollars for one bag, we divide the total amount of dollars by the total bags: 8.97/3=2.99

Step-by-step explanation:

1 ) 402

402 - 2 = 400 which is a perfect sqrt ( 20)^2

so u must subtract 2

2) 1989

1989 - 53 = 1936 which is a perfect sqrt (44)^2

3) 3250

3250 -1 = 3249 which is a prefect sqrt (57)^2

4) 4000

4000 - 31 = 3969 which is a perfect sqrt (63)^2

We are required to factorize the given expression `x⁴ - 5x³ + 4x²`.Factorization of `x⁴ - 5x³ + 4x²`We notice that each term in the expression contains `x²`.

We can factorize by taking out `x²` as a common factor. `x⁴ - 5x³ + 4x²

= x²(x² - 5x + 4)`Now we need to factorize the expression inside the bracket `(x² - 5x + 4)`.We observe that the expression inside the bracket is a quadratic equation. We will solve this equation by using the splitting the middle term method. For this we need to find two numbers whose product is `4` and sum is `-5`.

Let's check different possibilities: 4 × 1 = 4 and

4 + 1 = 5 which is not equal to

-5 2 × 2 = 4 and

2 + 2 = 4 which is not equal to -5. So, there is no pair of numbers whose product is 4 and sum is -5. Therefore, the given expression cannot be factorized further.Therefore, the complete factorization of `x⁴ - 5x³ + 4x²` is `x²(x² - 5x + 4)`.

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The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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The speed of River's mom drove for 10 miles distance is 0.234 mph

The speed of  River's mom drove for 25 miles is 10.234 mph  

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Given as :

The first distance cover by River's mom = 10 miles

The rate of speed = x mph

The second distance cover by river's mom = 25 miles

The rate of speed = x + 10 mph

The total driving time = 45 min

Now, According to question

Time = speed/distance

So, 45 =10/x  +  25/(x+10)

Or, 9 =2/x  + 5/(x+10)

Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x

Or, 9 x² + 90 x = 2 x + 20 + 5 x

Or, 9 x² + 90 x = 7 x + 20

Or, 9 x² + 90 x - 7 x - 20 = 0

Or, 9 x² + 83 x - 20 = 0

Solving this quadratic equation

x = 0.234 , - 9.4567

so, the value is,

I.e x = 0.234 , - 9.4567

now,

We consider x = 0.234

So, The speed for 10 miles distance = x = 0.234 mph

and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph

Hence The speed of River's mom drove for 10 miles distance is 0.234 mph

and The speed of  River's mom drove for 25 miles is 10.234 mph

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Answer:

a

Step-by-step explanation:

it has a negative number which causes the parabola to be a maximum as opposed to a minimum

Using parabola concepts, it is found that the graph that represents \(f(x) = -2x^2\) is given by option A.

In this problem, we have \(f(x) = -2x^2\), which has a negative leading coefficient, thus it is a concave down parabola, which is represented by option A.

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Answer:

-5/4

Step-by-step explanation:

(-2,5) (2,0)

0 - 5 / 2 - (-2)

-5 / 2- (-2)

-5 / 2 + (+2)

-5/4

To determine the required mass flow rate of diesel fuel to supply a heat rate of 2400 kJ/s, we need to consider the energy balance in the combustion chamber. Assuming complete combustion and given the initial and final conditions, we can calculate the mass flow rate using the energy equation and the heating value of diesel fuel.

The energy balance equation for the combustion chamber can be written as:

Q_dot = m_dot_fuel * HHV_fuel + m_dot_air * Cp_air * (T_out - T_in)

where:

Q_dot is the heat rate (2400 kJ/s),

m_dot_fuel is the mass flow rate of diesel fuel,

HHV_fuel is the higher heating value of diesel fuel,

m_dot_air is the mass flow rate of air,

Cp_air is the specific heat capacity of air,

T_out is the temperature of the products leaving the combustion chamber (440 K),

and T_in is the temperature of the air entering the combustion chamber (298 K).

Since the combustion is complete, the air-to-fuel ratio can be determined using the stoichiometry of the reaction:

C12H26 + (37/2)O2 -> 12CO2 + 13H2O

For every 1 mole of diesel fuel, we need (37/2) moles of oxygen. The molar mass of diesel fuel is 170.34 g/mol, and the molar mass of oxygen is 32 g/mol. The excess air is given as 40%.

Using these values, we can calculate the mass flow rate of air and the mass flow rate of fuel. The mass flow rate of air can be determined as:

m_dot_air = m_dot_fuel * (37/2) * (32/170.34) * (1 + 0.4)

Substituting this value and the given parameters into the energy balance equation, we can solve for the mass flow rate of fuel (m_dot_fuel).

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The results of the expressions are as follows: num1 + num2 = 17; num3 - num4 = 7; num1 * num4 - num2 = 31; num3 / num2 = 2; num1 % num4 = 0.

To determine the results of the expressions, we can evaluate them using the given assignments:

num1 + num2:

Result: 12 + 5 = 17

num3 - num4:

Result: 10 - 3 = 7

num1 * num4 - num2:

Result: 12 * 3 - 5 = 31

num3 / num2:

Result: 10 / 5 = 2

num1 % num4:

Result: 12 % 3 = 0

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Answer:

(-2,-3)

Step-by-step explanation:

a. The average acceleration in the time interval t = 0 to t = 2.0 s is -10 m/s². b. The acceleration at t = 2.0 s is -20 m/s².

a. To find the average acceleration in the time interval t = 0 to t = 2.0 seconds, we need to first find the initial and final velocities:

Initial velocity (t = 0 s):
v0x = (40 - 5(0)²) m/s = 40 m/s

Final velocity (t = 2.0 s):
v2x = (40 - 5(2)²) m/s = (40 - 5(4)) m/s = 20 m/s

Average acceleration is defined as the change in velocity divided by the change in time:
a_avg = (v2x - v0x) / (t2 - t0) = (20 m/s - 40 m/s) / (2.0 s - 0 s) = -20 m/s² / 2.0 s = -10 m/s²

b. To determine the acceleration at t = 2.0 s, we need to find the derivative of the velocity expression with respect to time (t):

v_x(t) = 40 - 5t²

Taking the derivative with respect to time:
a_x(t) = dv_x(t)/dt = -10t

Now, we can find the acceleration at t = 2.0 s:
a_x(2.0) = -10(2.0) = -20 m/s²

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Answer:

x ∈ ( - ∞ , - 8 ) ∪ ( - 8 , 0 ) ∪ ( 0 , 8 ) ∪ ( 8 , ∞ )

Step-by-step explanation:

x³ - 64x = x( x² - 64 ) ≠ 0 ⇒ x ≠ 0 and x ≠ ± 8

x ∈ ( - ∞ , - 8 ) ∪ ( - 8 , 0 ) ∪ ( 0 , 8 ) ∪ ( 8 , ∞ )

There are 60 possible outcomes for this experiment.

The problem asks to determine the total number of outcomes for an experiment consisting of three steps with different numbers of possible outcomes at each step.

To solve this problem, we need to apply the multiplication principle, which states that the total number of outcomes for a sequence of events is equal to the product of the number of outcomes at each event.

In this case, there are two possible outcomes for the first step, six possible outcomes for the second step, and five possible outcomes for the third step.

Therefore, the total number of outcomes possible is:

2 * 6 * 5 = 60

Therefore, there are 60 possible sequences of events that can occur in this experiment.

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Answer:

  2

Step-by-step explanation:

If the number must be even, the units digit must be 8. That leaves 2 choices for the tens digit. The possible numbers are ...

  78

  98

There are 2 of them.

Answer: Only two: 78 and 98

Step-by-step explanation: 8 is the only even number available to put in the units place where even or odd is determined. With no repetition allowed, the only possibilities left are to switch positions of the 7 and 9 in the tens place.

to answer the question, we would need to perform a statistical analysis and report the correlation coefficient between log(income) and prppov as well as the two-sided p-values for each variable. If the p-value for each variable is less than 0.05, we can conclude that each variable is statistically significant in some way.

To determine the correlation between log(income) and prppov, we can use a statistical analysis tool such as a Pearson's correlation coefficient. The resulting correlation coefficient will be between -1 and 1, with a value of 0 indicating no correlation, a value of -1 indicating a negative correlation, and a value of 1 indicating a positive correlation.

To determine if each variable is statistically significant, we can calculate the two-sided p-values. A p-value is a measure of the probability of obtaining a result as extreme as the one observed, assuming that there is no true association between the variables. A p-value less than 0.05 is typically considered statistically significant, meaning that the probability of obtaining the observed result if there is no true association is less than 5%.

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Problem Solving and Data Analysis, Heart of Algebra, and Passport to Advanced Mathematics are three additional topics in math that are part of the SAT Math section. These topics cover various concepts and skills that are essential for solving complex mathematical problems and analyzing data effectively.

Problem Solving and Data Analysis: This topic focuses on the ability to interpret and analyze real-world scenarios, solve problems using quantitative reasoning, and apply mathematical models to data. It includes concepts such as ratios, proportions, percentages, statistics, data interpretation, and data representation.

Heart of Algebra: This topic emphasizes algebraic concepts and skills, particularly those related to linear equations, linear inequalities, and systems of linear equations. It involves understanding and solving equations, manipulating algebraic expressions, graphing linear functions, and solving word problems using algebraic methods.

Passport to Advanced Mathematics: This topic builds upon the foundational algebraic skills and extends into more advanced mathematical concepts. It covers topics such as quadratic equations, exponential and logarithmic functions, radicals and rational exponents, polynomial operations, and complex numbers. It also involves solving higher-order equations, understanding function transformations, and applying algebraic concepts in various contexts.

These topics are important for SAT Math because they assess a student's ability to apply mathematical knowledge and problem-solving strategies to real-world situations. Familiarity with these topics enables students to analyze data, reason quantitatively, solve complex algebraic problems, and make connections between different mathematical concepts.

In conclusion, Problem Solving and Data Analysis, Heart of Algebra, and Passport to Advanced Mathematics are key topics in the SAT Math section. Mastering these topics is essential for achieving a high score on the SAT and for developing strong problem-solving and data analysis skills in mathematics.

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The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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Answer:

Step-by-step explanation:

The statement "x = y² - 9" is not a function because for some values of y, there are multiple corresponding values of x.

A relation between a set of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Now in the given question ,

In particular, when y = 3, there are two possible values of x (x = 0 and x = 6), so (3, 0) and (3, 6) are two points on the graph of this equation. This violates the definition of a function, which states that for each input (in this case, y), there can only be one output (x). The other statements are not relevant to determining whether the equation is a function.

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\( \sqrt{180} \)

\( \sqrt{ {6}^{2} \times 5 } \)

\( \sqrt{ {6}^{2} } \sqrt{5} \)

\(6 \sqrt{5} \)

Answer:

\(m=12\,,n=7\)

Step-by-step explanation:

The magnitude of vector \((x,y)\) is given by \(\sqrt{x^2+y^2}\)

The magnitude of vector \(a=(5,m)\) is \(13\).

\(\sqrt{5^2+m^2}=13\\5^2+m^2=13^2\\25+m^2=169\\m^2=169-25\\m^2=144\\m=12\)

The magnitude of vector \(b=(n,24)\) is \(25\).

\(\sqrt{n^2+24^2}=25\\n^2+24^2=25^2\\n^2+576=625\\n^2=625-576\\n^2=49\\n=7\)

Therefore,

\(m=12\,,n=7\)

Answer; hint

Step-by-step explanation:

Answer:

Part A: the dependant variable is how many hours he works mowing lawns.

the independent variable is that she earns $7 per hour.

Part B:(1,7) 1 hour working for $7

(2,14) 2 hours working for $14

(3,21) 3 hours working for $21

Part C: Y=7h (h represents the number of hours she works)

Step-by-step explanation:

I'm not 100% sure about part A I have not done this in a while but here you go

hope this helps