f(x)=2x^2+x-4

Find f(−10)

The fundamental period of the discrete-time signal x[n] is 10 samples.

N * 0.1 = 1

N = 1 / 0.1

N = 10

The given analog signal is x(t) = 1 + cos(2πt + 4π).

The fundamental frequency (f) of a periodic signal is the inverse of the fundamental period (T), and it represents the frequency at which the signal repeats.

In the given signal x(t), the coefficient of t in the argument of the cosine function is 2π, which corresponds to a frequency of 1 cycle per unit time (1 Hz). Therefore, the fundamental frequency of x(t) is 1 Hz.

The fundamental period (T) is the time it takes for the signal to complete one full cycle. In this case, the argument of the cosine function in x(t) is 2πt + 4π, which completes one full cycle when it increases by 2π. So, the fundamental period of x(t) is 1/1 = 1 second.

To determine the fundamental period of the discrete-time signal x[n], obtained by sampling x(t) with a sampling period T = 0.1 seconds, we need to find the smallest positive integer N for which N * T is equal to the fundamental period of x(t).

Since the fundamental period of x(t) is 1 second, we can calculate:

N * 0.1 = 1

N = 1 / 0.1

N = 10

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Answer:

x =4

Step-by-step explanation:

3x - 2 = 10

Add 2 to each side

3x -2 + 2 = 10+2

3x =12

Divide by 3

3x/3 =12/3

x =4

Answer:

x=4

Step-by-step explanation:

1) First, add 2 to both sides of the equation. This will give you 3x=12.

2) Divide by the 3 on both sides leaving you x=4.

Hope this helps!

Answer:

C

____________

Step-by-step explanation:

4-3

6-5

8-6

10-4

13-3

The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

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The failure mode of a bolt shear connection occurs when the applied shear force exceeds the capacity of the bolt to resist that force. This can lead to the bolt shearing off, causing the connection to fail.

To avoid the occurrence of damage in a bolt shear connection, several measures can be taken:

1. Proper bolt selection: Choosing bolts with the appropriate strength and size is crucial to ensure that they can withstand the shear forces. The bolt material and grade should be selected based on the requirements of the application.

2. Adequate bolt tightening: Properly tightening the bolts ensures that they are securely fastened and can distribute the shear forces evenly. Over-tightening or under-tightening the bolts can compromise the connection's integrity.

3. Use of washers: Washers can be used under the bolt head and nut to provide a larger bearing surface. This helps distribute the load and reduce the risk of the bolt digging into the connected surfaces, which can weaken the connection.

4. Proper joint design: The design of the joint should consider factors such as the number and arrangement of bolts, the thickness and material of the connected plates, and the anticipated loads. A well-designed joint can minimize stress concentrations and ensure a more reliable connection.

5. Regular inspection and maintenance: Periodic inspection of bolted connections is essential to identify any signs of damage, such as loose or corroded bolts. Maintenance procedures should be followed to address any issues and ensure the connection remains secure.

By implementing these measures, the risk of failure in a bolt shear connection can be significantly reduced, ensuring a safer and more reliable structural connection.

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Answer:

they both have right angles

The mortgage loan amount on a home that sells is 207000$.

A down payment is the initial amount a buyer pays to purchase an expensive product or service. The down payment represents a portion of the total purchase price, and the buyer often takes out a loan for the rest.

The formula loan calculators use is I = P * r *T in layman's terms Interest equals the principal amount multiplied by your interest rate times the amount in years.

M = S − D where M is the mortgage loan amount, S is the selling price, and D is the down payment.

M = $230,000 -  $23,000

and  =   207000$

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Answer:

y = 1/2x - 6

Step-by-step explanation:

slope = 1/2 = m

lets find your y-intercept using slope intercept form: y = mx + b using the points they gave us (6, -3)

y = mx + b; plug what we know to find b, which is our y-intercept.

-3 = 1/2(6) + b

-3 = 3 + b

-6 = b

Now you have all you need to write your equation

y = mx + b

y = 1/2x - 6

the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:

x = r cos(θ)

y = r sin(θ)

Substituting the given values, we get:

x = 6 cos(-π/3) = 6 × (1/2) = 3

y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3

Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

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Answer: 20

Step-by-step explanation:

The area of a quadrilateral with given vertices is 20 square units.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

We have to determine the area of a quadrilateral with vertices at (-6,6), (-1,6),(-6,10), and (-1,10).

As per the attached graph, we can see that the dimensions of the rectangle are as follows:

Length (L) = 5 units

Width (W) = 4 units

Area of the rectangle = L × W

Area of the rectangle = 5 × 4 = 20 square units

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The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

If the measures of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:

x + (x + 10) + (2x - 6) = 180

Combine the terms:

4x + 4 = 180

Subtract 4 from both sides:

4x = 176

Divide by 4:

x = 44

Now, we can find the measures of the other two angles:

x + 10 = 44 + 10 = 54
2x - 6 = 2(44) - 6 = 88 - 6 = 82

The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.

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Answer: Find the answer with the largest absolute value.

Step-by-step explanation:

Out of this list:

-25 -> |-25| = 25

-42 -> |-42| = 42

-16 -> |-16| = 16

-3 -> |-3| = 3

Your answer would be -42, as that is farthest from 0.

Out of this list:

40 -> |40| = 40

32 -> |32| = 32

96 -> |96| = 96

101 -> |101| = 101

Your answer would be 101, as that is the farthest from 0.

Answer:

0.5 onces

Step-by-step explanation:

Answer:

0.50 ounce

Step-by-step explanation:

Hope I am right forgive me if I am not

Answer:

6 meters.

Step-by-step explanation:

The scale of a map is 1:10000

The real distance between two banks is 600 meters.

We are to find the distance between the two banks on the map.

This scale means that for every 1 meter on the map there are 10,000 meters on the real world.

So 600 meters on the real world would be represented by;

Cross-multiplying gives:

\(\frac{600}{10000} * 100 = 6\) meters.

Answer:

0.06m or 6cm

Step-by-step explanation:

The scale of the map is 1:10000

Therefore, distance in map/ distance in real = 1/10000

Let the distance between the two banks be x m in the map.

Therefore we get,

                                   x/600 = 1/10000

Therefore,

                                            x = 600/10000 m = 0.06m = 6cm

To change a greater than or equal to type constraint into an equality constraint, a variable is removed from the left side. It also goes by the name "negative slack variable."

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The subject to required sofas ≥ 295x ≤ 140y ≤ 160x > 0, y > 0

Distributor A limitation x ≤ 140

Distributor B limitation y ≤ 160x > 0, y > 0

A Home Furnishing company is contracted to make 295 or more sofas per week. These sofas are to be shipped to two distributors, A and B. In order to minimize the shipping costs, the company is tasked with finding the optimal number of sofas to ship to each distributor.

Let x represent the number of sofas shipped to Distributor A, y the number of sofas shipped to Distributor B, and z the shipping costs in dollars.The objective function:

Minimize Z = 14x + 12y  (Since it costs $14 to ship a sofa to A and $12 to ship to B)

Subject to: required sofas ≥ 295

distributor A limitation: x ≤ 140

distributor B limitation: y ≤ 160x > 0, y > 0  (As negative numbers of sofas are not possible)

Therefore, the objective function and constraints are:

Minimize Z = 14x + 12y

Subject to:required sofas ≥ 295x ≤ 140y ≤ 160x > 0, y > 0

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Renu's present age is 10 years and her mother is 40 years.

Let's take Renu's present age as x years.

And Renu's mother present age as 4x years.

So, after five years,

Renu's age = x+5 years

Renu's mother age = 4x+5 years

According to the question,

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

x = 10

Therefore, Renu's present age is 10 years and Renu's mother present age is 40 years.

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Step-by-step explanation:

the answer to the question is C. 64.

Explanation:

We can use the substitution method to solve this system.

First we clear y from the first equation:

Then we replace this expression into the second equation:

Solve for x:

And with x = 5 we replace it into the first equation and solve for y:

Answer:

The solution is (5, 9)

Answer:

10

Step-by-step explanation:

2+10+18+14+6= 50

then divide by 5 to get mean = 10

Answer:

the answer is 10

Step-by-step explanation:

if you add up all the numbers you get 50

and if you divide it by the number of results, in this case 5, you get 10!

Answer:

w = \(\frac{ut}{vs}\)

Step-by-step explanation:

ut = wvs ( isolate w by dividing both sides by vs )

\(\frac{ut}{vs}\) = w

Answer:

here

ut= wvs

w=ut/vs

the value of w is ut/vs

Answer:

<6 = 68

Step-by-step explanation:

<5 + <6 + 90 = 180  since the 3 angles form a straight line

22 + <6 + 90 =180

Combine like terms

112+ <6 = 180

Subtract 112 from each side

<6 = 180-112

<6 =68

Answer:

\frac{30}{104}

Step-by-step explanation:

9 is the number of boys who play football AND wrestle. 18 is the mumber of footballers, and 12 is the number of wrestlers.

18 + 12, or 30, is the number of boys who EITHER play football or wrestle.

The total number of boys playing sports is 104, so 30 out of 104 boys either play football or wrestle.

You can write this in fraction form as \(\frac{30}{104}\).

Answer:

39/143 (B)

Step-by-step explanation:

All the boys who play football, wrestle, or both equals 18 + 12 + 9 = 39

All of the boys are the boys who play football, wretle, or both (39) + the number of outlier boys, (104) = 143 boys in total.

There is a probability of 39/143 that a boy will wrestle or football.

Thus, the dimensions that will give the maximum enclosed area are:  x = (320 - 3w)/4 and y = 80 - 3w/2.

To find the dimensions that will give the maximum enclosed area, we need to use the formula for the area of a rectangle, which is A = lw (where A is the area, l is the length, and w is the width).

Let's call the length of one corral x and the length of the other corral y. Since the corrals are adjacent, they share a common side, which we'll call w.

So we have two equations:

2x + y + 3w = 320 (the total amount of fencing)

A = xy (the area we want to maximize)

We can solve the first equation for y:

y = 320 - 2x - 3w

Then substitute that into the equation for the area:

A = x(320 - 2x - 3w)

Now we need to find the value of x that will give us the maximum area. To do this, we'll take the derivative of A with respect to x, set it equal to zero, and solve for x:

dA/dx = 320 - 4x - 3w = 0

4x = 320 - 3w

x = (320 - 3w)/4

Now we can substitute that value of x back into our equation for y:

y = 320 - 2(320 - 3w)/4 - 3w

y = 80 - 3w/2

We know that w must be positive, so we can find the maximum value of the area by taking the second derivative of A with respect to x:

d^2A/dx^2 = -4

Since this is negative, we know that we have a maximum.

So the dimensions that will give the maximum enclosed area are:

x = (320 - 3w)/4

y = 80 - 3w/2

w > 0

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The general solution to the given second-order linear homogeneous differential equation, y′′ ―4y′ ―12y= 0, is y_c = c_1e^(6t) + c_2e^(-2t), where c_1 and c_2 are arbitrary constants.

To find the particular solution, we can use the Method of Undetermined Coefficients.

For the particular solution, we consider the right-hand side of the equation, 23 ―+ 3, as a forcing term. Since the equation is linear and the forcing term is a polynomial, we can assume a particular solution of the form y_p = At + B, where A and B are constants to be determined.

Differentiating y_p, we have y_p' = A, and y_p'' = 0. Substituting these values into the differential equation, we get -4(A) - 12(At + B) = 23 ―+ 3. Simplifying the equation, we have -12At - 4A - 12B = 26.

From this equation, we can equate the coefficients of the terms on both sides. The coefficient of t on the left side is -12A, and the constant term on the left side is -4A - 12B. Equating these coefficients with the corresponding terms on the right side, we have -12A = 0 and -4A - 12B = 26.

Solving these equations, we find that A = 0 and B = -13/6. Therefore, the particular solution is y_p = -13/6.

Combining the complementary solution and particular solution, the general solution to the given differential equation is y = y_c + y_p = c_1e^(6t) + c_2e^(-2t) - 13/6.

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To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.

To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.

After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.

Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.

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