A vértical plane passes through a oyramid that has a horizontal base

The given function is f(x) = −2cos(x) − 2x, on the interval [0,2π]. The required triangles to complete the choices are as follows: Box 1: (−4π, 5π/2) Box 2: (0, 0) Box 3: (−4π, 0)

We need to determine the critical values of the function in order to find the absolute maximum and minimum values. So, we will differentiate the given function to find the critical values. Let us differentiate the given function to get the main answer and explanation of the given problem: Differentiating the given function f(x) = −2cos(x) − 2x, we get:f′(x) = 2sin(x) − 2The critical values of the given function occur where f′(x) = 0. So, we need to solve the following equation:2sin(x) − 2 = 0⇒ 2sin(x) = 2⇒ sin(x) = 1On the interval [0,2π], the solutions of sin(x) = 1 are x = π/2 and x = 5π/2.

Therefore, the critical values of the given function f(x) are π/2 and 5π/2. Now, we will determine the values of f(x) at the critical points and the endpoints of the interval [0,2π]. We get:f(0) = −2cos(0) − 2(0) = −2f(π/2) = −2cos(π/2) − 2(π/2) = −π − 2f(2π) = −2cos(2π) − 2(2π) = −4πf(5π/2) = −2cos(5π/2) − 2(5π/2) = 3π − 2 Hence, the absolute maximum value of the function f(x) on the interval [0,2π] is 0 and the absolute minimum value is −4π. The required triangles to complete the choices are as follows: Box 1: (−4π, 5π/2) Box 2: (0, 0) Box 3: (−4π, 0).

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The equation representing visual models is z+1/5=3/5.

Since it is given in the question that the hanger image represents a balanced equation therefore equating LHS with RHS it can be written as follows.

LHS = 1/5 + z

RHS = 3/5+ z

Equating both the equations it can be written as

LHS = RHS

1/5+z=3/5

or z=3/5-1/5

Therefore, z=2/5

Hence, for z=2/5 the hanger will represent a balanced equation.

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The function with the smallest slope is g(x), since it has a slope of 0.

The correct answer to the given question is option B.

To determine which function has the smallest slope, we need to first understand the concept of slope. Slope is the measure of the steepness of a line. It can be defined as the ratio of the vertical change to the horizontal change between two points on a line.

The slope of a line can be positive, negative, zero or undefined. A positive slope means that the line is increasing from left to right, while a negative slope means that the line is decreasing from left to right. A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.

To calculate the slope of a line given its equation, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Once we have the equation in this form, we can easily read off the slope.

Now let's look at the given functions:

f(x) = 5x - 4
g(x) = 0
h(x) = 1

The slope of f(x) is 5, since the equation is already in slope-intercept form and the coefficient of x is 5.

The slope of g(x) is 0, since the equation is just a constant and does not involve x. The slope of h(x) is 0, since the equation is just a constant and does not involve x.

Therefore, the function with the smallest slope is g(x), since it has a slope of 0.

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The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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Answer:

14 or 0.14

Step-by-step explanation:

3 1/2 ÷ 1/4

1/4 = 25

3 1/2 ÷ 25 = 0.14 or 14

This is correct answer can you mark me brainliest

Using multiplication, Correct option is B, Justin earned $144 in 4 weeks.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product. Let's examine a few various forms of multiplication sentences and discover how to finish them.

As per the question,

Each week they make a total of $72.00,

Money earned in 4 weeks = 72 × 4 = $288

They split in equal halves,

⇒ $288 / 2 = $144

∴ Justin earned $144 in 4 weeks.

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Therefore, the phasor representation of v is: v = (10cos(-T/3) + 12cos(30°)) + j(10sin(-T/3) + 12sin(30°)) V.

To transform the given sinusoids to phasors, we can use Euler's formula, which states that e^(jθ) = cos(θ) + j sin(θ), where j is the imaginary unit.

(a) -20 cos(4t + 135°):

Using Euler's formula, we can rewrite this as:

-20 cos(4t + 135°) = -20 Re[e^(j(4t + 135°))]

The phasor representation of this sinusoid is -20e^(j135°).

(b) 8 sin(20t + 30°):

Using Euler's formula, we can rewrite this as:

8 sin(20t + 30°) = 8 Im[e^(j(20t + 30°))]

The phasor representation of this sinusoid is 8e^(j30°).

(c) 20 cos(2t) + 15 sin(2t):

Using Euler's formula, we can rewrite this as:

20 cos(2t) + 15 sin(2t) = 20 Re[e^(j2t)] + 15 Im[e^(j2t)]

The phasor representation of this sinusoid is 20e^(j0°) + 15e^(j90°).

For the second part of the question, to find v = v1 + v2, we can simply add the phasors representing v1 and v2.

v1 = 10 cos(50t - T/3) V = 10 Re[e^(j(50t - T/3))]

The phasor representation of v1 is 10e^(-jT/3).

v2 = 12 cos(50t + 30°) V = 12 Re[e^(j(50t + 30°))]

The phasor representation of v2 is 12e^(j30°).

Now, we can add the phasors:

v = v1 + v2 = 10e^(-jT/3) + 12e^(j30°)

To simplify further, we can combine the phasors using Euler's formula:

v = 10e^(-jT/3) + 12e^(j30°)

= 10(cos(-T/3) + j sin(-T/3)) + 12(cos(30°) + j sin(30°))

Expanding and combining the real and imaginary parts, we get:

v = (10cos(-T/3) + 12cos(30°)) + j(10sin(-T/3) + 12sin(30°))

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The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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The length of a leg of an isosceles right triangle can be found using the concept of Pythagoras' theorem by the formula sqrt (hypotenuse ^ 2 / 2) = x.

Since, two sides of an isosceles triangle are equal, let us consider the two equal sides as 'x' and let the hypotenuse of the triangle be 'h'.

Being a right triangle, by Pythagoras' theorem,

h ^ 2 = x ^ 2 + x ^ 2

h ^ 2 = 2x ^ 2

Hence, we can find the length of a leg of an isosceles triangle by:

sqrt (h ^ 2 / 2) = x

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio. A ratio is a comparison of two numbers or measurements, and it can be written in different ways.

For example, if we have two quantities A and B, the ratio of A to B can be written as

A/B

A:B

"A is to B"

The ratio of A to B tells us how many times A is contained within B, or how many units of A we would need to have to match the amount of B.

Ratios are useful in many fields, such as finance, engineering, and science, where they are used to compare and analyze different quantities and their relationships.

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Answer:

Left up x=34

Left down x=87

Right x=17

Step-by-step explanation:

The picture is the working out.

Answer:

could you snap the question in full like the whole page so that I can get a better look and snap an example of the question either on the textbook or the one to you've answered

The distance of the swing of a pendulum decreases by a constant amount each swing. To find the distance of the swing at the tenth swing, you can use the formula:

distance at nth swing = distance at first swing * (1 - decay factor)^(n-1)

Where decay factor is the fractional decrease in distance per swing. In this case, the decay factor is (80 - 76) / 80 = 0.05. Plugging this into the formula above, we get:

distance at 10th swing = 80 * (1 - 0.05)^9 = 53.78 cm

So the distance of the swing at the tenth swing is approximately 53.78 cm.

Power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x=1.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

The given equation: \(\left(x^2-2 x+26\right) y^{\prime \prime}+x y^{\prime}-4 y=0\)

It is necessary to determine the power series solutions' minimal radius of convergence R around the typical points x = 0 and x = 1.

The separation between the ordinary point and the differential equation's singularity is now the minimal radius of convergence.

The polynomial's root, which is connected to the second derivative, is the singularity point.

The singularity points will be determined as follows:

\(\begin{aligned}& x^2-2 x+26=0 \\& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\& x=\frac{2 \pm \sqrt{(-2)^2-4 \times 1 \times 26}}{2} \\& x=1 \pm \sqrt{-100} \\& x=1 \pm 10 i\end{aligned}\)

In this case, x1 = 1+10i and x2 = 1-10i are the singularity sites.

The ordinary points at this time are z1 = 0+01 and z2 = 1+0i.

One can compute the minimum radius of convergence using the formula:

\(\begin{aligned}& r_1=\left|z_1-x_1\right| \\& =|0+0 i-1-10 i| \\& =\sqrt{101} \\& =10.0498 \\& r_2=\left|z_2-x_1\right| \\& =\sqrt{100} \\& =10\end{aligned}\)

Therefore, power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x = 1.

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Answer:

The area of the space that will be covered bricks is 4/15 ft^2

Step-by-step explanation:

Here, we are interested in calculating the area of the space that will be covered by bricks.

This can be obtained directly by finding the area of the rectangular shape;

Mathematically;

area of a rectangle = L * B

Since we have both measurements already;

Then the area of the space will be 3/5 * 4/9 = 12/45 = 4/15 ft^2

\( \large \mathfrak{Answer : }\)

The given series are :

6.) 7, 14, 28, 54 - Geometric series

7.) 1000, 200, 40, 8, 5 - Geometric series

8.) 7, 14, 21, 28 - Arithmetic series

Answer:

The last choice

Step-by-step explanation:

So, - 5 1/2 is negative so it's on the left side of 0. 2 is a positive number so it's on the right side of the 0.

The last choice shows one blue dot on -5 1/2 and the other on 2, so it is correct

Answer:

a)

Step-by-step explanation:

2(6x)=12x

2(5x)=10x

=22x

2(-4)=-8

22x-8

True, The range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.


The range of a linear transformation defined by the matrix transformation t(x) = ax is equal to the column space of matrix A (col A).

The range of a linear transformation is the set of all possible output values. In this case, the matrix A represents the transformation, and the column space of matrix A represents the span of the columns of A. The column space of matrix A is the set of all possible linear combinations of the columns of A.

To prove that the range of the linear transformation t(x) = Ax is equal to the column space of matrix A, we can show that every vector in the column space of A can be obtained as an output of the transformation t(x) = Ax. Additionally, we can show that every output of the transformation t(x) = Ax belongs to the column space of A.


Therefore, it is true that the range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.

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we find that x = 2 satisfies both conditions. Therefore, the largest of the eight consecutive integers is 2 + 4 = 6.

Explanation:

Let's assume that the first of the five consecutive integers is x. Then, the sum of the five consecutive integers can be written as x + (x + 1) + (x + 2) + (x + 3) + (x + 4), which simplifies to 5x + 10.

Similarly, let's assume that the first of the next three consecutive integers is y. Then, the sum of the three consecutive integers can be written as y + (y + 1) + (y + 2), which simplifies to 3y + 3.

Now, we are given that the sum of the five consecutive integers is equal to the sum of the next three consecutive integers. Therefore, we can set the two expressions equal to each other and solve for y:

5x + 10 = 3y + 3

5x + 7 = 3y

y = (5x + 7) / 3

Since y represents the first of the next three consecutive integers, we know that y must be an integer. Therefore, (5x + 7) must be divisible by 3.

The largest of the eight consecutive integers will be the last of the five consecutive integers. Since we know that the first of the five consecutive integers is x, we can express the largest integer as x + 4.

We can now try different values of x to find which one satisfies the condition that (5x + 7) is divisible by 3. For example, if x = 1, then (5x + 7) / 3 = 4, which is an integer. Therefore, the largest of the eight consecutive integers is 1 + 4 = 5.

However, we need to check if this value satisfies the condition that the sum of the five consecutive integers is equal to the sum of the next three consecutive integers. We can plug in x = 1 and y = 5 into the expressions we derived earlier:

5x + 10 = 5(1) + 10 = 15

3y + 3 = 3(5) + 3 = 18

Since 15 is not equal to 18, the value x = 1 does not work. We can try different values of x until we find one that satisfies both conditions. After trying a few values, we find that x = 2 satisfies both conditions. Therefore, the largest of the eight consecutive integers is 2 + 4 = 6.

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Answer:

Down

Step-by-step explanation:

The negative before the x^2 makes it Down.

\(\\ \sf\longmapsto \dfrac{6x^2y^3}{(-4x^4y)(-3x^3y^2)}\)

\(\\ \sf\longmapsto \dfrac{6x^2y^3}{12x^{4+3}y^{2+1}}\)

\(\\ \sf\longmapsto \dfrac{6x^2y^3}{12x^7y^3}\)

\(\\ \sf\longmapsto \dfrac{1}{2}x^{2-7}y^{3-3}\)

\(\\ \sf\longmapsto \dfrac{1}{2}x^{-5}y^0\)

\(\\ \sf\longmapsto \dfrac{1}{2x^5}\)

Answer:

The area is 36 square units.

Step-by-step explanation:

Answer: 38

Step-by-step explanation:

The correct answer is not given in the options.

To find the values of c and d, we can use the formula for the inverse of a 3x3 matrix:

A^-1 = 1/det(A) x [adj(A)],

where det(A) is the determinant of matrix A and adj(A) is the adjugate matrix of A.

First, we need to find the determinant of matrix A:

det(A) = 1(1 x 4 - (-2)(0)) - 0(1 x 4 - 0(-2)) + 0(1 x 1 - 0(0)) = 4.

Next, we need to find the adjugate matrix of A, which is the transpose of the matrix of cofactors of A:

adj(A) = [{begin{array}{cc} 4&0&2 \ 0&4&0 \-2&0&1 \end{array}\right].

Therefore, we have:

A^-1 = 1/4 x [{begin{array}{cc} 4&0&2 \ 0&4&0 \-2&0&1 \end{array}\right)]

Multiplying out, we get:

A^-1 = [{begin{array}{cc} 1&0&1/2 \ 0&1&0 \-1/2&0&1/4 \end{array}\right)]

Comparing this with the given formula for A^-1:

A^-1 = 1/6(a^2 + cA + dI)

We can see that the diagonal elements of A^-1 correspond to the values of dI, so d = 1/4.

Also, the (1,3) entry of A^-1 corresponds to the value c in cA, so c = 2 x 6 = 12.

Therefore, the correct answer is not given in the options.

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Using the long division method, it is proved that (x + 2) is a factor of (x³ + 8), because the result of the remainder is 0.

To show that (x + 2) is a factor of (x³ + 8) using long division, we can divide (x³ + 8) by (x + 2) and see if the remainder is 0. If the remainder is 0, then (x + 2) is a factor of (x³ + 8). Here's how the long division would look:

        x² - 2x + 4

x+2 | x³ + 0x² + 0x + 8

      - (x³ + 2x²)

    --------------------

         -2x² + 0x + 8

       - (-2x² - 4x)

         ---------------

              4x + 8

            - (4x + 8)

              --------

                 0

Since the remainder is 0, we can conclude that (x + 2) is a factor of (x³ + 8).

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Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

The enhanced entity-relationship (EER) diagram for AutoPlanet's information system includes entities such as Dealership, City, Employee, Dependent, Category, Training Program, Mechanic, Car, Customer, and more. The diagram also includes attributes for each entity, capturing relevant information like addresses, phone numbers, employee numbers, and sales commission percentages.

The enhanced entity-relationship (EER) diagram for AutoPlanet's information system captures the entities and relationships involved in the system. The main entities in the diagram are Dealership, City, Employee, Dependent, Category, Training Program, Mechanic, Car, Customer, and Salesperson.

The Dealership entity is identified by a unique dealership number and stores information such as address, phone number, and the name of the general manager. The City entity is identified by state and city names and stores data about the mayor, city hall address, and telephone number.

The Employee entity has attributes like employee number, name, home address, and cell phone number. Employees can have dependents, represented by the Dependent entity, which stores their names, ages, and gender. The Category entity represents the different employee categories, such as salesperson and mechanic.

The relationships between entities include Employee-Dependent (one-to-many), Employee-Category (many-to-many), Salesperson-Car (many-to-many), Mechanic-Training Program (many-to-many), and more.

The Car entity is identified by its vehicle identification number (VIN) and includes attributes for model and year of manufacture. The Customer entity is identified by a unique customer number and stores information like name, address, and telephone number. The Salesperson entity is linked to the Car and Customer entities, capturing data about which salesperson sold a car to a customer, along with the sale date and selling price.

The EER diagram provides a visual representation of the entities, relationships, and attributes in AutoPlanet's information system, allowing for a better understanding of the system's structure and data flow.

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In ℝ4, a set of three vectors cannot span all of ℝ4. However, if we consider n vectors in ℝm, where n is less than m, it is possible for the set to span all of ℝm.

The dimension of ℝ4 is four, meaning that any set of vectors that spans all of ℝ4 must have at least four linearly independent vectors. If we have only three vectors in ℝ4, they cannot form a spanning set for ℝ4 because they do not provide enough dimensions to cover the entire space. Therefore, a set of three vectors in ℝ4 cannot span all of ℝ4.

On the other hand, if we have n vectors in ℝm, where n is less than m, it is possible for the set to span all of ℝm. As long as the n vectors are linearly independent, they can cover all dimensions up to n, effectively spanning the subspace of ℝm that they span. However, they cannot span the entire ℝm since there will be dimensions beyond n that are not covered by the set.

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