A DVD costs $18.99 plus 6.5% sales tax. What is the total cost if the DVD?

The equation of motion for the mass attached to the spring

x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2

Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.

In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:

k = F/x = 400 N/2 m = 200 N/m

The equation of motion for a mass on a spring is given by:

F = ma = -kx

where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.

Substituting the values for the spring constant and the mass, we get:

-kx = -(200 N/m)(50 kg)(x'')

Solving for the acceleration, we get:

x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2

This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.

Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:

x = x_0 + v_0t + (1/2)at^2

where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.

Substituting the values for the acceleration and the initial velocity, we get:

x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2

This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.

Read more about velocity

https://brainly.com/question/18084516

#SPJ1

We can tell that the investment results after 4 years will be $761 with the help of compound interest.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

So, we have an initial investment of %600.

And the interest is 6% which will be compounded quarterly for 4 years.

Then the amount we will receive after 4 years is:

(Refer to the table attached below)

So, the amount we will get after 4 years is $761.39.

Rounding off: $761

Therefore, we can tell that the investment results after 4 years will be $761 with the help of compound interest.

Know more about compounding here:

https://brainly.com/question/29523718

#SPJ1

Answer:

f(x) = -2x +7

Step-by-step explanation:

The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

For the given points (0, 7) and (3, 1), the equation is ...

y = (1 -7)/(3 -0)(x -0) +7

y = -6/3x +7 . . . . . . . . simplify.

We can use f(x) for y to get ...

f(x) = -2x +7

1 hot dog cost is $1.20 .

What is costs?

A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

Let's say that each drink costs $x and each hot dog costs $y.

Using the provided information, 3 drinks and 2 hot dogs cost $4.80. In equation form, it reads as follows:

3 x+2 y=4.80

1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:

x+y=2

x=2-y

Using this value of x in first equation, we get:

3(2-y)+2 y=4.80

6-3 y+2 y=4.80

6-y=4.80

y=6-4.80

y=1.20

Thus the cost of one hot dog is  1.20$

To learn more about cost  visit:https://brainly.com/question/15135554

#SPJ1

The natural oil that will be needed to make make 825 liters of Petrolyn oil is 300 liters.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this situation, Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, the natural oil will be:

= 4 / (4+7) × 825

= 4 / 11 × 825

= 300

Learn more about ratio on:

brainly.com/question/2328454

#SPJ

Answer:

1.  y=2x−5

2.  y=-x-4

3. y=-1/2x+1

Step-by-step explanation:

First Question:

We are given (3, 1) and (1, -3)

The slope is the difference of y-values over x-values. From this we get:

(1−−3)/(3−1)=4/2=2

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (3, 1) gives us         1=3∗2+b    ⇒    b=1−6 = −5

We have our slope and y-intercept now, so the equation is y=2x−5.

Second Question:

We are given (-4, 0) and (1, -5)

The slope is

(-5-0)/(1--4)=-5/5=-1

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (-4, 0) gives us         0 = -1∗-4+b    ⇒    b = -4

We have our slope and y-intercept now, so the equation is y=-x-4.

Third Question:

We are given (-6, 4) and (-2, 2)

The slope is

(4-2)/(-6--2)=2/48=-1/2

Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b

Plugging in (-2, 2) gives us         2 = -1/2∗-2+b    ⇒    b = 2-1 = 1

We have our slope and y-intercept now, so the equation is y=-1/2x+1

Answer:As you can see, this line is vertical! It goes directly up. We know that because the equation says that X is equal to -3. It is telling us that no matter what the Y value is, X will be -3.

Step-by-step explanation:

The equation to find slope is to take two points

(A,B) and (C,D) and to do the following equation: D−B

                                                                               ______

                                                                                  C−A

So, let's take two points. Let's say that Y is equal to 3 and 2. In that case, since X is always -3, our points would be (−3,2) and (−3,3).

Now, let's substitute into our formula.

3−2                       1         1

------ =                  ----- =   ---

3 (−3) (subtract)  -3 + 3   0

As you can see, the final slope is 1/0

. If you put that into your calculator, it will come out as undefined, because any number divided by zero is undefined. And so your slope for any vertical line is undefined.

The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The borders of the square and the square shape underneath are something similar.

Perimeter of the square = Perimeter of the rectangle

4a = 2(L +  W)

2a = L + W

If the area of the square is 121 square inches. Then the side length of the square is given as,

a² = 121

a = 11 inches

And the dimension of the rectangle is 3x and x - 2. Then the equation is given as,

3x + x - 2 = 11 (2)

4x - 2 = 22

4x = 24

x = 6

The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

Answer:

1 < x < 8

Step-by-step explanation:

x² - 9x + 8 < 0

(x-8)(x-1) = 0

x = 8

x = 1

these are the points where the parabola intercepts the x axis. We have to find when it is under x axis

1 < x < 8

The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

What is the constant of variation?

The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.

We have,

         x         y

         2         10

         4         24

         6         36

To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.

If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.

If the ratio y/x is not constant for all the data points, then y does not vary directly with x.

so, let's see the k constant of variation,

k =  y/x

k = 2/10 =1/5

k = 4/24 = 1/6

k = 6/36 = 1/6

so,  k = 1/5, k=1/6, k=1/6.

Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

To learn more about the constant of variation visit,

https://brainly.com/question/7764541

#SPJ1

Answer:

182 feet

Step-by-step explanation:

Taking the fact that 112/40 = 2.8, you would need to multiply the miles per hour by 2.8 to get the feet needed.

Why is that, well I cant really explain...its just math and it works out /:

Answer:

A (0, -3) translated to the right 4 units.

Step-by-step explanation:

If you go right 4, you get (4, -3)

To pull values from another worksheet, we need to follow these steps:

Select cell C3 and click on it.

Insert the formula: =VLOOKUP(B3,'Sheet 2'!$ B$3:$C$7,2,0)

Press enter.

Drag the formula down to the other cells in the column by clicking and dragging the little “+” icon at the bottom-right of the cell.

How do I add a LOOKUP field in Excel?

Open Design View on the table. Click a cell in the Field Name column in the first available empty row, and then type a field name for the lookup field. Select Lookup Wizard from the drop-down list by clicking the arrow after clicking in the Data Type column for that row.

To compute values in several columns, the VLOOKUP function may be used in conjunction with other functions like the Sum, Max, or Average. Since this is an array formula, all we need to do to make it function is hit CTRL+SHIFT+ENTER at the conclusion of the formula.

To learn more about pull values visit:https://brainly.com/question/14307039

#SPJ4

The value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

∠C and ​ ∠D ​ are vertical angles.

From the definition of the vertically opposite angles:

5x-7 = 8x-55

After solving we get:

-7 = 3x -55

3x = 48

x = 16

Thus, the value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

The complete question is:

∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?

Learn more about the vertically opposite angles here:

brainly.com/question/24287162

#SPJ1

There are 3 extreme points does the function g(x) = (2 - x) x².

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ g ' (x) = (2 - x) x²

Now,

Since, The function is,

⇒ g ' (x) = (2 - x) x²

We know that;

The extreme points are find as;

⇒ g ' (x) = 0

So, We get;

⇒ g ' (x) = 0

⇒ (x - 2) x² = 0

This gives two values as;

⇒ (x - 2) = 0

⇒ x = 2

And, x² = 0

⇒ x = 0, 0

Thus, The extremes values are;

⇒ x = 2 , 0, 0

Learn more about the function visit:

https://brainly.com/question/13804741

#SPJ1

To find the ordered pair that is the solution to the equation y = (1/3)x - 4, we need to solve the equation for x.

To do this, we can first add 4 to both sides of the equation to get y + 4 = (1/3)x. Then, we can multiply both sides of the equation by 3 to get 3y + 12 = x.

Therefore, the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 3y).

Note that the value of y is unknown in this solution. In order to find the exact solution, we would need to know the value of y. For example, if y = 2, then the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 6).

The solution of the expression will be;

⇒ x = - 88

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Now,

Since, The algebraic expression is,

'' one eighth times quantity x plus 32 end quantity equals negative 7.''

Hence, We can formulate;

⇒ 1/8 (x + 32) = - 7

⇒ x + 32 = - 56

⇒ x = - 56 - 32

⇒ x = - 88

Thus, The solution of the expression will be;

⇒ x = - 88

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The system of inequalities shown by the graph are

There are some points that help in interpreting inequality graphs.

The first part is to arrange the equation in the form so that y is the subject of the formula and to the left

Then watch out for dashed lines or solid lines

Another part is the shaded portion

Equipped with tis information, it is clear that the two lines of the graph are both dashed and shaded above the line,

Hence we look out for equations having no equality sign in the inequality and due to the shading must be greater than.

This makes the first option the best choice

Learn more about linear functions at:

https://brainly.com/question/29323505

#SPJ1

x[tex]x\geq 6[/tex].

[tex]\frac{1}{2}x \geq 3[/tex]

[tex]\frac{\frac{1}{2}}{\frac{1}{2} } x\geq \frac{3}{\frac{1}{2} }[/tex]

Dividing by a fraction of the same as multiplying by its multiplicative inverse. Since the multiplicative inverse of 1/2 is 2/1, we may rewrite as:

[tex]\frac{2}{1} *\frac{1}{2} x\geq \frac{2}{1} *3[/tex]

[tex](1)x\geq(6)\\ \\x\geq6[/tex]

[tex]\frac{1}{2}(6) \geq 3\\ \\3\geq 3[/tex]

Correct!

x[tex]x\geq 6[/tex].

Thank you so much, I have a test tomorrow so I really appreciate it. Answering again so I can give you brainliest.

Answer:

Below

Step-by-step explanation:

In three years the interest will be

50 000 *  .1  * 3  = 15 000

He pays this and 25 000   so his remaining loan is 25 000

  we want to know how long will it be before this remaining loan

      incurs 5 000 interest ( for a total of 20 000)

25000 * . 1 * n = 5000     shows n = 2 years   more

              ( 5 years from original loan date)

Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.

Hope it helps!

Brainliest pls!

Follow me <3

The expression -16x^(-3/2) represents a term that has a coefficient of -16 and a variable x raised to the power of -3/2.

Generally, The expression -16x^(-3/2) represents a term that consists of a coefficient of -16 and the variable x raised to the power of -3/2.

In general, the exponentiation operator (^) represents the idea of raising a number (called the base) to a certain power (called the exponent). For example, x^2 means "x raised to the power of 2" and can be calculated as x * x = x^2.

Similarly, x^3 means "x raised to the power of 3" and can be calculated as x * x * x = x^3.

The exponent -3/2 means that the base (in this case, x) is raised to the power of -3/2. This can be simplified as follows:

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

The expression -16x^(-3/2) can then be simplified as follows:

-16x^(-3/2) = -16 * 1 / x^(3/2) = -16 / x^(3/2)

Read more about expression

https://brainly.com/question/14083225

#SPJ1

The complete Question was not found

The flow chart to prove m∠3≅m∠4 is given below.

What is the vertical angle theorem?

The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.

Given, m∠1≅m∠2

Then, m∠1≅m∠3 ( vertical angles theorem)

m∠2≅m∠3 (Given)

Then, m∠2≅m∠4 (vertical angle theorem)

Hence, m∠3≅m∠4 (transitive property of congruence) proved

To learn more about the vertical angle theorem

https://brainly.com/question/1673457

#SPJ4

The equation that relates F and s for the spring on the jumper will be F=4x.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, Todd increases the weights by 8 and observes a 2 cm spring extension. According to Hook's Law, the force exerted on a spring by the weights directly affects how much it is stretched, or s.

The equation that relates F and s for the spring on the jumper is obtained as,

F=ks

8=k×2

k=8/2

F=4 x

Thus, the equation that relates F and s for the spring on the jumper will be F=4x.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ1

Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.

Inflection points for the given equation x^2e^{-2x} are

f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]

f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]

x= -b±√(b^2 - 4ac)/2a

x=4±√(16+16)4

x=4±4√2/4

x=[tex]\sqrt{2+2/2}[/tex]

x=[tex]\sqrt{2-2/2}[/tex]

We get,

x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]

so, inflection points are,

To learn more about inflection refer to:

https://brainly.com/question/29530328

#SPJ4