Find the orthogonal trajectory of the family of curves for:
y=k/x

Answer:

18 yards in 3 feet

Step-by-step explanation:

54 / 3 = 18

The company has $41,463.52 in cash on hand and is prepared to purchase the equipment.

The formula is

Principal * (1 + r)^t =  Amount

12000 * (1 +0.055)⁵ = Amount

The 12,000 capitalize for 5 years

$15,638,52

15000 * (1+0.055)¹ = Amount

Capitalize for 1 year

$15,825

$10,000 This deposit is only used to finish and buy the equipment; it has no capitalizing effect.

$15,638.52 + $15,825 + $10,000 =  $41,463.52

Hence, The company named Howell corporation has $41,463.52 in cash on hand and is prepared to purchase the equipment.

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(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8  .

(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .

What is Scientific Notation ?

The general form of writing a number in scientific notation is ⇒ \(a\times 10^{k}\) ;

Part (a) ;

the number is given to be : 299790000 ;

For writing it in scientific notation, decimal point will be placed after 2 ;

So , the scientific notation of the number is ⇒ \(2.9979 \times 10^{8}\) ,

On comparing it with the general form of scientific notation,

we get , a = 2.9979 and k = 8 .

Part (b) ;

the number is given to be : 0.51 ;

For writing it in scientific notation, decimal point will be placed after 5 ;

So , the scientific notation of the number is ⇒ \(5.1 \times 10^{-1}\) ,

On comparing it with general form of scientific notation,

we get , a = 5.1 and k = -1 .

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Answer:

\( y = - \frac{1}{2} x - 9\)

Step-by-step explanation:

\(y + 7 = - \frac{1}{2} (x + 4) \\ \\ y + 7 = - \frac{1}{2} x + (- \frac{1}{2}) \times 4 \\ \\ y = - \frac{1}{2} x - 2 - 7 \\ \\ y = - \frac{1}{2} x - 9\)

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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This is an example of a c)confounding variable. A confounding variable is a type of bias that occurs when the researcher is unable to accurately determine the cause of the results.

In this case, the researchers cannot tell if the difference in yield between soybean type 1 and soybean type 2 is a result of the superiority of type 1 soybeans or the drought, so the drought is the confounding variable.

To accurately determine the cause of the difference in yield, a bias-matched pairs design should be used. This involves replicating the experiment by planting both soybean types in the same location with and without the drought, and then comparing the results.

This would reveal whether the difference in yield was actually caused by the superiority of type 1 soybeans or the drought.

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Answer:

confounding variable

Step-by-step explanation:

I got it right on the test :)

Answer:

Hello there I would love to assist but could you give me a little more info I think I know the answer but I want to make sure I got it 100% correct unless you cant give me more info ill just tell you what I think it is but if u can give me more info before I give u the answer to make sure its correct would be appreciated

Step-by-step explanation:

Answer:

-3/4

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -4 - -7)/(-2-2)

   ( -4+7)/(-4)

    3/-4

   -3/4

here is your answer.hope it helps you

y =\((x/2)^2 + 1 or y = (x/2)^2 + 1\)

The curve represents a parabola opening upwards. It is symmetric about the y-axis.

Let's eliminate the parameter t and sketch the curves for each exercise:

1. x = t^2 + 2t, y = t + 1

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 + 2t = x

t = -1 ± √(x + 1)

Substituting the expression for t into the equation y = t + 1, we get:

y = (-1 ± √(x + 1)) + 1

y = -√(x + 1) or y = √(x + 1)

The curve represents two branches of a parabola opening upwards. It is symmetric about the y-axis.

2. x = cos(t), y = sin(t), (0, 2π]

Eliminating the parameter t, we obtain:

\(x^2 + y^2 = cos^2(t) + sin^2(t) \\= 1\)

The curve represents a circle centered at the origin with a radius of 1. It covers a full revolution (360 degrees or 2π) in the counterclockwise direction.

3. x = 2t + 4, y = t - 1

By eliminating the parameter t, we have:

t = (x - 4) / 2

Substituting this expression into the equation for y, we get:

y = ((x - 4) / 2) - 1

y = (x - 6) / 2

The curve represents a line with a slope of 1/2 and a y-intercept of -3. It is inclined upwards from left to right.

4. x = 3 - t, y = 2t - 3, 1.5 ≤ t ≤ 3

Eliminating the parameter t, we have:

t = 3 - x

Substituting this expression into the equation for y, we get:

y = 2(3 - x) - 3

y = 6 - 2x - 3

y = -2x + 3

The curve represents a line with a slope of -2 and a y-intercept of 3. It is inclined downwards from left to right.

\(5. x = 2t^2, y = t^4 + 1\)

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 = x/2

t = ±√(x/2)

Substituting the expressions for t into the equation y = t^4 + 1, we get:

y = (√(\(x/2))^4\) + 1 or y = (-√\((x/2))^4\) + 1

\(y = (x/2)^2 + 1 or y = (x/2)^2 + 1\)

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Answer: Median

Step-by-step explanation: The median is the middle number.

(also i'll give the definitions of mean, mode, and range in case you need it)

Mean - average

Mode - the value that appears the most

Range - The largest value subtracted by the smallest value

Answer:

Median is the answer

Step-by-step explanation: 100%

Answer:

0.31

Step-by-step explanation:

1 1/4 - 1/3 - 3/5 = 19/60

≅ 0.3166667

Answer:

x² - 64

Step-by-step explanation:

Difference of squares: (x - a)²(x +a )²

With that, you have to have (x - 8) as a factor as well. Simply just multiply (x - 8) to (x + 8) and you get x² - 64 as your answer!

Answer:

C

Step-by-step explanation:

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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Answer:

8/x^3

Step-by-step explanation:

(2x^-1)^3

First, we must use the power-to-power rule to eliminate the double exponents. When a power is raised to a power, we must multiply them. This makes the exponent of x-3 and makes two into 8.

8x^-3

We can eliminate negative exponents by bringing their subject to the opposite side of the fraction line, so in this case, we bring down the x^-3 to the bottom, making it x^3. The final answer is:

8/x^3

Answer:

heyyyyyyyyyyyyyyyyyyyhyhhhh

Answer:

$2431.01

Step-by-step explanation:

2000×(1 + 0.05)^4 = 2431.0125

The 3 × 3 matrix that translates a point in r 2 by (3, 1) then rotates the result 45 degrees about the origin is

M = | 1/√2    -1/√2    3/√2- 1/√2 |

      | 1/√2    1/√2     1/√2 + 1/√2 |

       | 0           0                1 |

To find the 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates, we can follow these steps:

Translation Matrix:

The translation matrix for a 2D translation by (3, 1) is:

T = | 1 0 3 |

| 0 1 1 |

| 0 0 1 |

This matrix translates a point (x, y) by adding the translation vector (3, 1) to it.

Rotation Matrix:

The rotation matrix for a 2D rotation by 45 degrees counterclockwise is:

R = | cos(theta) -sin(theta) 0 |

| sin(theta) cos(theta) 0 |

| 0 0 1 |

Since we want to rotate by 45 degrees, theta = 45 degrees = π/4 radians. Therefore, the rotation matrix becomes:

R = | cos(π/4) -sin(π/4) 0 |

| sin(π/4) cos(π/4) 0 |

| 0 0 1 |

Simplifying, we have:

R = | 1/√2 -1/√2 0 |

| 1/√2 1/√2 0 |

| 0 0 1 |

Combine Translation and Rotation:

To obtain the combined transformation matrix, we multiply the translation matrix T by the rotation matrix R:

M = T * R

Performing the matrix multiplication:

M = | 1 0 3 | | 1/√2 -1/√2 0 |

| 0 1 1 | * | 1/√2 1/√2 0 |

| 0 0 1 | | 0 0 1 |

Simplifying, we have:

M = | 1/√2 -1/√2 3/√2 - 1/√2 |

| 1/√2 1/√2 1/√2 + 1/√2 |

| 0 0 1 |

This is the desired 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates.

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Answer:

I'm pretty sure it is A

Step-by-step explanation:

Answer:

Any graph that looks like the graph on the picture is the answer.

Step-by-step explanation:

Graph the absolute value using the vertex and a few selected points.

a. The domain of the function is [-2.5, 3]

b. The range of the function is  (-∞, ∞)

The domain of a function is the number of valid inputs to the function.

The range of a function is the number of valid outputs to the function.

To find the domain of the function, we need to find the range of input of x in which the function is valid.

We see that the function tends to infinity as x tends to 3 and also, the function tends to minus infinity as x tends to -2.5

We see that there are vertical asymptotes at x = -2.5 and x = 3.

So, the x values are bounded within this region and does not include both vaues.

So, the domain is [-2.5, 3]

To find the range of the function, we need to find the range of output of y in which the function is valid.

We see that the function tends to infinity as x tends to 3 and also, the function tends to minus infinity as x tends to -2.5

So, the y values are within (-∞, ∞)

So, the range is  (-∞, ∞)

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Answer:

\(18.03\)

Step-by-step explanation:

Formula: \(a^{2}+b^{2}=c^{2}\)

\(15^{2}+10^{2}=x^{2}\)

\(225+100=x^{2}\)

\(x^{2}=325\)

\(x = 5\sqrt{13}=18.03\)

Theresa and Raul have approximately $264,875.60 in equity in their house after making 120 monthly payments. Emon’s balloon payment at the end of 7 years is approximately $190,347.68.

Let’s calculate the equity that Theresa and Raul have in their house now:

1. Initial purchase price: $200,000

Down payment: 20% of $200,000 = $40,000

Loan amount: $200,000 - $40,000 = $160,000

2. Monthly interest rate: 6% / 12 months = 0.06 / 12 = 0.005

Number of monthly payments: 30 years * 12 months = 360 months

To calculate the monthly payment, we can use the formula for a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n – 1)

Where:

P = Loan amount = $160,000

R = Monthly interest rate = 0.005

N = Number of monthly payments = 360

Using this formula, we can calculate the monthly payment:

Monthly payment = $160,000 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 – 1)

             ≈ $959.37

Now, let’s calculate the total amount paid over the 120 monthly payments:

Total amount paid = Monthly payment * Number of monthly payments

                = $959.37 * 120

                = $115,124.40

Finally, to calculate the equity, we subtract the total amount paid from the current house value:

Equity = Current house value – Total amount paid

      = $380,000 - $115,124.40

      = $264,875.60

Therefore, Theresa and Raul have approximately $264,875.60 in equity in their house now.

Now let’s calculate Emon’s balloon payment at the end of 7 years:

1. Loan amount: $280,000

2. Monthly interest rate: 2.9% / 12 months = 0.029 / 12 = 0.00242

Number of monthly payments: 7 years * 12 months = 84 months

To calculate the monthly payment, we can use the same formula as before:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n – 1)

Where:

P = Loan amount = $280,000

R = Monthly interest rate = 0.00242

N = Number of monthly payments = 360

Using this formula, we can calculate the monthly payment:

Monthly payment = $280,000 * 0.00242 * (1 + 0.00242)^84 / ((1 + 0.00242)^84 – 1)

             ≈ $1,125.32

Since the monthly payments are based on a 30-year amortization, at the end of 7 years, there will still be a remaining balance on the loan.

Remaining balance = Loan amount – (Monthly payment * Number of monthly payments)

                = $280,000 – ($1,125.32 * 84)

                ≈ $190,347.68

Therefore, Emon’s balloon payment at the end of 7 years would be approximately $190,347.68.

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Answer:350

Step-by-step explanation:you multiply the amount of points which is 70 times the amount of targets which is 5 so it’s 70x5=350

Answer:

Consider the form

x

2

+

b

x

+

c

. Find a pair of integers whose product is

c

and whose sum is

b

. In this case, whose product is

−

72

and whose sum is

−

1

.

−

9

,

8

Write the factored form using these integers.

(

n

−

9

)

(

n

+

8

)

Step-by-step explanation:

The solution to the linear ordinary differential equation (ODE) y' + xy = 2x, obtained using the method of integrating factor, is

\(\[ y = 2 - 2xe^{-\frac{x^2}{2}} + Ce^{-\frac{x^2}{2}} \]\), where C is an arbitrary constant.

To solve the linear ODE y' + xy = 2x using the integrating factor method, we first rewrite the equation in the standard form, which is

y' + p(x)y = q(x), where p(x) = x and q(x) = 2x. The integrating factor is given by μ(x) = \(e^{\int p(x)\) dx). In this case, μ(x) = \(e^{\int x dx\) = \(e^{(x^2/2)\).

Multiplying the given equation by the integrating factor μ(x), we obtain  \(e^{(x^2/2)\).y' + x \(e^{(x^2/2)\).y = 2x \(e^{(x^2/2)\). Recognizing the left-hand side as the product rule of ( \(e^{(x^2/2)\).y), we can rewrite the equation as

d/dx ( \(e^{(x^2/2)\).y) = 2x \(e^{(x^2/2)\).

Integrating both sides with respect to x gives us

\(e^{(x^2/2)\).y = ∫(2x \(e^{(x^2/2)\).) dx. Evaluating the integral yields

\(e^{(x^2/2)\).y = \(x^2\) \(e^{(x^2/2)\). + C, where C is an arbitrary constant.

Finally, we solve for y by dividing both sides of the equation by  \(e^{(x^2/2)\) resulting in y = \(x^2\) + C \(e^{(x^2/2)\).Simplifying further, we obtain

y = 2 - 2x \(e^{(x^2/2)\). + C \(e^{(x^2/2)\)., where C is the arbitrary constant. This is the general solution to the given ODE. To verify the solution, you can substitute it back into the original equation and see if it satisfies the equation for all x.

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The given graph that is in pictorial form is a function. Hence, Option A is correct.

Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function fulfils the function equation.

See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.

An ordered set of pairs or a continuous line can both be used to represent a function on a graph.

Therefore,  given graph that is in pictorial form is a function. Option C is correct.

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Answer: Choice B)   sin (33) = x/14

This is because the sine of an angle is equal to the opposite side over the hypotenuse

sin(angle) = opposite/hypotenuse

sin(33) = x/14

We can't use cosine because we don't have a variable for the adjacent side.