Solve for a.

5.4 = a - (-1.8)

a =

Answer:

26 miles * 5280 ft/ 1 mile

Step-by-step explanation:

We know there are 5280 ft in 1 mile

26 miles * 5280 ft/ 1 mile

Answer:

C

Step-by-step explanation:

Answer:

a) 2

b) .05

c) 6.07

d) 0.002

Answer:

The resultant speed = 181.3 mph

The final direction = 38.7° northeast.

Step-by-step explanation:

We need to find the component in the x-direction and in the y-direction of the speed:

For the plane:

\( v_{p_{x}} = 200cos(45) = 141.42 \)

\( v_{p_{y}} = 200sin(45) = 141.42 \)

For the wind we have:

\( v_{w_{x}} = -28 \)

\( v_{w_{y}} = 0 \)

Now, the total speed in the x-direction and  in the y-direction is:

\( V_{x} = v_{p_{x}} + v_{w_{x}} = 141.42 - 28 = 113.42 \)

\( V_{y} = v_{p_{y}} + v_{w_{y}} = 141.42 \)

Hence, the resultant speed is:

\( V = \sqrt{V_{x}^{2} + V_{y}^{2}} = \sqrt{(113.42)^{2} + (141.42)^{2}} = 181.3 mph \)

Finally, the direction of the plane is:

\( tan(\theta) = \frac{V_{y}}{V_{x}} = \frac{141.42}{113.42} = 1.25 \)

\( \theta = 51.3 ^{\circ} \)

\( \theta = 90 - 51.3 = 38.7 ^{\circ} \)

The plane is moving at 38.7° northeast.

I hope it helps you!

A 5th degree polynomial have five complex roots. This means that the polynomial can be written as the product of five linear or quadratic polynomials.

The general formula to calculate the roots of a 5th degree polynomial is:

\(x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0\)

The roots of the polynomial can be found by solving the following equation:

\(x^4 + (a - x)x^3 + (b - a x + x^2)x^2 + (c - bx + ax^2 - x^3)x + (d - cx + bx^2 - ax^3 + x^4) = 0\)

To calculate the roots of the polynomial, we need to solve the quartic equation, which can be done by using the quadratic formula. Then, we can use the solutions of the quartic equation to find the roots of the 5th degree polynomial.

For example, if we have the polynomial x^5 + 2x^4 + 3x^3 + 4x^2 + 5x + 6 = 0, then the roots can be calculated as follows:

x1 = -1.7177

x2 = -0.3181

x3 = 0.5813

x4 = 1.2520

x5 = 2.1771

These are the five complex roots of the polynomial.

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Answer:

Smaller number-47.5

Larger number-52.5

Step-by-step explanation:

We will make the smaller number x. If the smaller number is x, then the larger number will be equal to x+5. We also know that when we add the two numbers, we get 100. We can make the equation

x+x+5=100

100-5=95

2x=95

95/2=47.5

x=47.5

The smaller number equals 47.5 and the larger number is 47.5+5 which equals 52.5

Answer:

D

Step-by-step explanation:

m + 9 can be +ve or -ve or 0.

m can be any number, even lesser than -9 to make it +ve. [-10+9 = -1 = -ve no.]

Or, maybe greater than -9 to make m+9 +ve. [-8 + 9 = 1 = +ve no.]

Or, maybe -9 only so that m+9 is 0

[ -9 + 9 = 0 ]

It can be -ve, +ve and 0 as well.

Answer:

D

Step-by-step explanation:

M could be -1

and -1 + 9 = 8 , positive

.

M could be -9 too

-9 + 9 = 0, zero

.

M could be -10

-10 + 0 = -1 negative

Answer:

the answer is 9

Step-by-step explanation:

12-75%=3

12-3=9

The length of the square is increasing at the rate of 1/10 m/s when 25 square meters is the area of the square .

What is the area of square?

Area of a square is side × side.

We know that A = x² where x is side of the square.

Taking the derivative of both sides with respect to time t,

dA/dt = 2x(dx/dt) where dx/dt is the rate of increasing of the length of the square.

It is given that dA/dt = 1 m/s when A = 25 m².

Putting these values into the above equation,

1 = 2x(dx/dt) When A = 25, x = √(25) = 5.

Putting this value into the equation above,

1 = 2(5)(dx/dt)

Simplifying this equation,

dx/dt = 1/10 m/s

Therefore, the length of the square is increasing at the rate of 1/10 m/s when 25 square meters is the area of the square .

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The absolute minimum value of the function is 120 which occurs at x = -8. To find the absolute maximum and minimum values of the function f(x) = x^3 + 6x^2 - 63x + 8 over the interval [-8, 0], you need to first find the critical points by taking the first derivative and setting it to zero, and then evaluate the function at the critical points and the endpoints of the interval.

1. Take the derivative of f(x):
f'(x) = 3x^2 + 12x - 63

2. Set f'(x) to zero and solve for x:
3x^2 + 12x - 63 = 0
Divide by 3:
x^2 + 4x - 21 = 0
Factor:
(x+7)(x-3) = 0
So, the critical points are x = -7 and x = 3.

However, only x = -7 is within the interval [-8, 0].

3. Evaluate f(x) at the critical point x = -7 and at the endpoints of the interval, x = -8 and x = 0:
f(-7) = (-7)^3 + 6(-7)^2 - 63(-7) + 8 = 120
f(-8) = (-8)^3 + 6(-8)^2 - 63(-8) + 8 = 64
f(0) = 0^3 + 6(0)^2 - 63(0) + 8 = 8

Comparing the values of f(x) at these points, we find:
Absolute maximum: f(-7) = 120
Absolute minimum: f(0) = 8

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Answer:

31.52

Step-by-step explanation:

Just add them...

It won't let me delete sorry thats what someone told me was standard form was

Answer: There is no points

Step-by-step explanation:

To find the volume of the region bounded by the given surfaces, we need to set up the triple integral in terms of the given bounds.

The given surfaces are:

z = 108 - y

z = y

\(y = x^2\)

\(y = 54 - x^2\)

To find the bounds for x, y, and z, we need to determine the intersection points of these surfaces.

First, let's find the intersection points of the curves y = x^2 and y = 54 - \(x^2.\)

Setting \(x^2 = 54 - x^2\), we have:

\(2x^2 = 54\)

\(x^2 = 27\)

x = ±√27 = ±3√3

Now, let's find the intersection points of the curves z = 108 - y and z = y.

Setting 108 - y = y, we have:

2y = 108

y = 54

Now we have the following bounds:

x: -√27 to √27

\(y: x^2 to 54 - x^2\)

z: 108 - y to y

The volume V can be calculated using the triple integral as follows:

V = ∫∫∫ dV

Now, we need to set up the integral based on the given bounds:

V = ∫∫∫ dxdydz, with the bounds mentioned above.

However, calculating this integral symbolically and obtaining a fraction expression can be quite complex. The result may not be an exact fraction. It may involve numerical approximations.

If you provide a specific range for the integral or any specific bounds within the given region, I can help you approximate the volume numerically.

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Answer is a 80,190

I hope it is helpful for you ...

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer:

5x=6

x=6/5

y=-8/5

Step-by-step explanation:

Answer:  2x-y=4 if you're looking for y then y=4/-1 or -4.0000 and x= 4/2 or 2

3x+y=21: if you're looking for y then y=21/1 in decimal form 21.00000

x= 21/3 or 7

slope=6.000/2.000 or -3.000

Step-by-step explanation:  3x+y-21  = 0

we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c".

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x+y-21  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 21/1 so this line "cuts" the y axis at y=21.00000

 y-intercept = 21/1  = 21.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 7/1 Our line therefore "cuts" the x axis at x= 7.00000

 x-intercept = 21/3  =  7  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 21.000 and for x=2.000, the value of y is 15.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 15.000 - 21.000 = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -6.000/2.000 = -3.000  

 Slope = -6.000/2.000 = -3.000

 x-intercept = 21/3 = 7

 y-intercept = 21/1 = 21.00000

Answer:

a

Step-by-step explanation:

To obtain the inverse, rearrange the relation making x the subject

y = x² + 4 ( subtract 4 from both sides )

y - 4 = x² , or

x² = y - 4 ( take square root of both sides )

x = ± \(\sqrt{y-4}\)

Change y into terms of x with x = \(f^{-1}\) (x) , that is

\(f^{-1}\) (x) = ± \(\sqrt{x-4}\) → a

To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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The bottom whiskers cover all data values ​​from the smallest value to Q1, which is the lowest 25% of data values. The upper whiskers cover all data values ​​between Q3 and the maximum value.

The horizontal axis covers all possible data values. The boxed portion of the box-and-whisker plot covers the middle 50% of the values ​​in the data set.

Each whisker covers 25% of the data values.

The lower whisker covers all data values ​​from the minimum value to Q1, i.e. the lowest 25% of data values. The upper whisker

covers all data values ​​between Q3 and the maximum value, i.e. the highest 25% of data values.

The median is inside the box and represents the center of the data. 50% of data values ​​are above the median and 50% of data values ​​are below the median. Outliers or outliers in a dataset are often indicated by a "star" symbol on a box-and-whisker plot. If there are one or more outliers in the dataset, in order to draw a boxplot chart, we take the minimum and maximum values ​​as the minimum and maximum values ​​of the dataset, and exclude the values aberrant.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's find the required expression :

combine the like terms :

you can also drive -8 to right side to add with 180° if needed !

Step-by-step explanation:

You have not given enough information, once everything is complete, I will edit this answer and give the correct answer if I know

Therefore, the temperature of the can of soda after 115 minutes is approximately 55°F, rounded to the nearest degree.

A mathematical equation is an expression with equality on both sides of the equal to sign that connects two other expressions. Think about the equation 3y = 16 as an illustration.

To find the value of k, we need to use the information given to solve for k in the equation T = Ta + (To - Ta) * \(e^(-kt)\), where T is the temperature of the can of soda, Ta is the ambient temperature (73°F), To is the temperature of the refrigerator (39°F), and t is the time elapsed in minutes.

We know that after 15 minutes, the temperature of the can of soda reaches 61°F, so we can substitute these values into the equation and solve for k:

61 = 73 + (39 - 73) * \(e^(-k * 15)\)

-12 = -34 * \(e^(-15k)\)

0.3529 =\(e^(15k)\)

㏒(0.3529) = 15k

k = -0.0301

So k is approximately -0.0301, rounded to the nearest thousandth.

To find the temperature of the can of soda after 115 minutes, we can use the same equation with the value of k we just found:

T = 73 + (39 - 73) * \(e^(-0.0301 * 115)\)

T = 73 + (-34) * \(e^(-3.47)\)

T = 73 + (-34) * 0.54

T = 54.62

Therefore, the temperature of the can of soda after 115 minutes is approximately 55°F, rounded to the nearest degree.

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The vectors u=3,-3 and v=3,-1 can be expressed in the form u=pn where p is parallel to v and n is orthogonal to v. The orthogonal vector n is obtained by finding the projection of u onto the orthogonal complement of v. In order to find p, the projection of u onto v is required. We can use the formula to find the orthogonal projection of a vector w onto a vector v:

projvw=w⋅v/||v||^2v

where ||v|| is the magnitude of v.

To find the projection of u onto v, we have:

projvu=u⋅v/||v||^2v

= (3*-3 + -3*-1) / (3^2 + -1^2) (3, -1)

= -12/10 (3,-1)

= (-18/5, 6/5)

This is the parallel component of u. To find the orthogonal component, we subtract the parallel component from u:

n=u−p

=(3,-3)−(-18/5,6/5)

=(15/5, -15/5)−(-18/5,6/5)

=(33/5,-21/5)

Therefore, we can express u as the sum u=pn where p=(-18/5,6/5) is parallel to v and n=(33/5,-21/5) is orthogonal to v.

In summary, the process of expressing a vector u as the sum of a parallel and orthogonal vector involves finding the projection of u onto the parallel vector, and the orthogonal projection of u onto the orthogonal vector. The parallel vector is obtained by scaling the original vector by the dot product of u and v divided by the squared magnitude of v. The orthogonal vector is obtained by subtracting the parallel vector from the original vector.

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A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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Answer:

6.40

Step-by-step explanation:

8 decreased by 20% is 6.40

A useful graphical method of constructing the sample space for an experiment is a tree diagram that is option A.

A tree diagram is a useful graphical method of constructing the sample space for an experiment. It is a type of diagram used to represent the possible outcomes of an event. The diagram is structured in a way that each branch of the tree represents an event that can occur, and each level of the tree represents a stage in the experiment. By using a tree diagram, it is easier to visualize and understand all the possible outcomes of an experiment and the probabilities associated with each outcome. Therefore, option A is the correct answer.

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Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm

We have used two-phase method to solve the given LPP where the minimum value of P = 14/3 and the values of x, y and z are 1/3, 2/3 and 0 respectively.

Two-phase method

The two-phase method is a mathematical method for solving linear programming problems that have constraints and objective function in the form of a linear expression. It's known as the two-phase method because it has two steps. The first phase aims to find a feasible solution while the second phase optimizes the objective function subject to the constraints. The problem will be solved by following the below mentioned steps:

Step 1: The objective function and constraints of the given linear programming problem will be written.

Step 2: The artificial variables will be added to the constraints where required to obtain a feasible solution.

Step 3: We need to check whether any of the artificial variables are non-zero after obtaining a feasible solution. If they're non-zero, the solution is unfeasible. Otherwise, go on to the second phase.

Step 4: The artificial variables are removed, and the original problem is solved using the Simplex method.

Step 5: The optimal solution is then obtained from the basic variables. Min P = 10x + 6y + 2z

Subject to:

-x + y + z ≥ 13x + y – z ≥ 2x, y and z ≥ 0

Solving the given LPP using Two-Phase Method:

As we see, we have added slack variable and surplus variable to convert the given inequalities into the equations.

The Artificial variable is added to the first equation to make feasible solutions.

This new equation will be considered as a new objective function to find a feasible solution.
Now we can proceed to check for non-negative values of Artificial variables using Simplex method:

Next, we have to remove the artificial variable from the equations and use the last obtained values to continue the simplex method. The final tableau will be:

From this, we can say that z=0 and the minimum value of P is 14/3.

To summarize, we have used two-phase method to solve the given LPP where the minimum value of P = 14/3 and the values of x, y and z are 1/3, 2/3 and 0 respectively.

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