what is -2 +5 and why

Answer:

Yes, the graph of y = -2x^2 + 5 is different from the graph of y = -2x^2. Both equations are quadratic functions with a leading coefficient of -2, which means that they have the same shape of a downward-facing parabola.

However, the graph of y = -2x^2 + 5 is shifted upwards by 5 units compared to the graph of y = -2x^2. This means that for any given value of x, the y-value of y = -2x^2 + 5 will be 5 units higher than the y-value of y = -2x^2.

The first-order optimality condition for convex optimization problems can be applied to characterize the optimal point, x* in the given optimization problem.

The first-order optimality condition states that if x* is an optimal point for the given convex optimization problem, then there exists a vector v* such that:

∇f(x*) + v* = 0

Here, ∇f(x*) is the gradient of the objective function f(x) evaluated at x*, and v* is the Lagrange multiplier associated with the constraint x ∈ C.

In the given optimization problem, the objective function is ∥a−x∥², and the constraint set is C.

To apply the first-order optimality condition, we need to find the gradient of the objective function. The gradient of ∥a−x∥² is given by:

∇f(x) = 2(x - a)

Now, let's apply the first-order optimality condition to the given problem:

∇f(x*) + v* = 0

Substituting the gradient expression:

2(x* - a) + v* = 0

Rearranging the equation:

x* = a - (v*/2)

This equation provides a characterization of the optimal point x* in terms of the Lagrange multiplier v*. By solving the equation, we can find the optimal point x*.

It's important to note that the Lagrange multiplier v* depends on the constraint set C. The specific form of v* will vary depending on the nature of the constraint set. In some cases, it may be necessary to further analyze the specific properties of the constraint set C to fully characterize the optimal point x*.

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The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.

The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.

The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.

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The purpose of the by-pass piping in the 3-phase separator is to facilitate maintenance or repair of instruments or equipment in the main process line, increase the process capacity or provide buffer capacity during surge in flow rate, drain away excess feed or product for continuous recycling back into the plant, and allow for sampling of the feed, intermediate, or product along the piping.

The by-pass piping in the 3-phase separator serves multiple purposes. Firstly, it enables maintenance or repair of instruments or equipment in the main process line without disrupting the entire system. By diverting the flow through the by-pass piping, specific components can be isolated and worked on while the rest of the process continues to operate.

Secondly, the by-pass piping allows for the adjustment of process capacity or the provision of buffer capacity during sudden surges in flow rate. By redirecting a portion of the flow through the by-pass piping, the overall capacity of the system can be increased temporarily or excess flow can be safely accommodated without causing disruptions.

Thirdly, the by-pass piping facilitates the drainage of excess feed or product for continuous recycling back into the plant. This prevents any wastage and ensures that resources are efficiently utilized.

Lastly, the by-pass piping enables the sampling of the feed, intermediate, or product along the piping. This is important for quality control, analysis, and monitoring purposes. Samples can be taken at specific points in the piping to ensure that the process is operating within desired parameters and to identify any issues or deviations.

In summary, the by-pass piping in the 3-phase separator serves the purposes of maintenance or repair, increasing process capacity, providing buffer capacity, draining excess feed or product, and allowing for sampling along the piping.

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Answer:

1. 4

2. y = 4x

Step-by-step explanation:

1.

Divide any y value by its corresponding x value to find the constant of proportionality.

8/2 = 4

Constant of proportionality: 4

2.

Equation of proportional relation:

y = kx, where k is the constant of proportionality.

y = 4x

(I) \(-16y = 22 + 6x\)

(II) \(-11y -4x = 15\)

Get x alone in equation (I)

\(-16y = 22 + 6x\\6x = -16y - 22\\x = -\frac{16y}{6} - \frac{22}{6}\\x = - \frac{8y}{3} - \frac{11}{3}\)

Insert in equation (II)

\(-11y - 4(-\frac{8y}{3} - \frac{11}{3}) = 15\\-11y + \frac{32y}{3} + \frac{44}{3} = 15\\-11y \cdot 3 + \frac{32y}{3} \cdot 3 + \frac{44}{3} \cdot 3 = 15 \cdot 3\\-33y + 32y + 44 = 45\\-33y + 32y = 45 - 44\\-y = 1\\y = -1\)

Insert \(y = -1\) in equation (I)

\(x = -\frac{8 \cdot (-1)}{3} - \frac{11}{3}\\x = \frac{8}{3} - \frac{11}{3}\\x = -1\)

Answer:

24

Step-by-step explanation:

5^2-(-3)^0

=25-(-3)^0

=25-3^0

=25-1

24

For the given list, the number of elements will be checked to find the value 89 using binary search is 2.

Binary Search would be a searching algorithm for determining the position of an element in a sorted array.

Its element has always been searched in the center of a component of an array in this approach.

Some key features regarding the binary search are-

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When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer:

13

Step-by-step explanation:

8-15= -7

-7 + 20 = 13

Answer:

x = 45 degrees

Step-by-step explanation:

Using the alternate exterior angle theorem, the angles are equal. You can set the expressions equal to each other:

3x = x + 90
2x = 90
x = 45

The radius of the circle is 38.22.

In geometry, a circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed center point. The distance from the center to any point on the circle is called the radius, and the longest distance across the circle passing through the center is known as the diameter.

Let's r be the radius of the circle.

Given that

The arc length = 40 cm,

Central angle = 60°

                       \(= 60 \times \dfrac{\pi}{180}\\ =\dfrac{\pi}{3}\ radians\)

As it is known that

Arc length = radius × Central angle

\(40 = r \times \dfrac{\pi}{3}\)

\(r = 40\times\dfrac{3}{\pi} \\r = \dfrac{120}{3.14} \\r = 38.22\)

Thus, the radius of the circle is 38.22.

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No, the function y=2sin(2x) is not a solution of the differential equation y'''-8y=0.

To determine whether a function is a solution to the differential equation, we have to first find the derivatives of the function. The derivatives of y=2sin(2x) are y'=4cos(2x), y''=-8sin(2x) and y'''= -16cos(2x).

Next, we have to substitute the derivatives of the given function into the differential equation. When we substitute the derivatives of y=2sin(2x) into the differential equation, we get -16cos(2x) - 8×2sin(2x) = 0. This is not equal to 0, so y=2sin(2x) is not a solution to the differential equation y'''-8y=0.

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Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Answer:

The width of the tank is approximately 7.9 feet.

Step-by-step explanation:

The pool is a rectangular prism with the following dimensions:

length = 2*x feet

width = x feet

height = 4 feet

With volume equal to 500 cubic feet, therefore:

volume = length*width*height = 500

(2*x)*(x)*(4) = 500

8*x² = 500

x = sqrt(500 / 8)

x = sqrt(62.5)

x = 7.90569 feet

The width of the tank is 7.9 feet.

Given:

\(d = 13.3\ in\)

\(w = 11.3\ in\)

\(d=\sqrt{w^2+h^2}\)

To find:

The value of h.

Solution:

We have,

\(d=\sqrt{w^2+h^2}\)

Substituting \(d = 13.3, w = 11.3\), we get

\(13.3=\sqrt{11.3^2+h^2}\)

Taking square on both sides.

\(176.89=127.69+h^2\)

\(176.89-127.69=h^2\)

\(49.2=h^2\)

Taking square root on both sides, we get

\(\pm 7.01427=h\)

\(h\approx \pm 7\)

Height cannot be negative so \(h=7\ in\).

Therefore, the correct option is A.

Answer:

After doing the math, I came up with B and/or C could be the answer

Chess is not a static game of complete information for several reasons. Firstly, the game is dynamic, meaning that the position of the pieces on the board changes constantly throughout the game.

Unlike in games like Tic Tac Toe or Connect Four, the state of the game at any given point is not fixed, and there are a vast number of possible outcomes. This means that players cannot simply memorize the best moves and outcomes for every situation, as they would in a game of complete information.

Secondly, chess is a game of imperfect information, as both players do not know what moves their opponent will make. Even with a complete understanding of the game's rules, players cannot predict with certainty the moves of their opponent, and must instead make strategic decisions based on their best assessment of their opponent's likely choices.

Finally, chess is a game of hidden information, as players do not know what their opponent is thinking or planning. A player may be able to predict their opponent's next move, but cannot know for sure what their long-term strategy is, making it difficult to make optimal decisions.

Overall, chess is a highly dynamic and complex game that is not static or complete in terms of information. Players must make strategic decisions based on incomplete and uncertain information, making it a challenging and rewarding game for those who play it.

Chess is a strategic board game played between two players, with each player starting with 16 pieces on a 64-square board. The game has been around for centuries and is considered one of the most popular and complex games in the world.

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Answer:

When p = -5 the answer is 45

Step-by-step explanation:

First, since p = -5, you have to plug -5 in as p into the equation

5(-5) + 2(-5)^2 +20          now we do pemdas, so we must fullfill the exponent

5(-5) +2 (25) + 20             now we multiply

-25 + 50 +20                       now we add / subtract

25 + 20                       and we continue adding

45

Answer:

45

Step-by-step explanation:

Substitute p = - 5 into the expression

5(- 5) + 2(- 5)² + 20

= - 25 + 2(25) + 20

= - 25 + 50 + 20

= - 25 + 70

= 45

The work done in stretching the spring 0.5 m beyond its natural length is C, 3 N.m.

Area between the curves is A, 22/3. Area enclosed is A, 64/3.

Third quadrant is D, 37/6.

Region bounded by curves is A, 5/3

Region bounded by the curves is 0.328.

The work done in stretching a spring is given by the formula:

W = (1/2)kx²

where k = spring constant and x = displacement from the natural length.

Use the given information to find the spring constant k:

k = F/x = 2.4 N/0.1 m = 24 N/m  

Now use the formula to find the work done in stretching the spring 0.5 m beyond its natural length:

W = (1/2)(24 N/m)(0.5 m)²

= 3 N.m

Therefore, the work done in stretching the spring 0.5 m beyond its natural length is 3 N.m.

2nd pic:

Part A:

To find the area between two curves, take the integral of the difference of the curves with respect to x over the given interval. In this case:

A = ∫(-1 to 1) [g(x) - f(x)] dx

= ∫(-1 to 1) [7x - 9 - (x³ - 2x² + 3x - 1)] dx

= ∫(-1 to 1) [-x³ + 2x² + 4x - 8] dx

= [-x⁴/4 + 2x³/3 + 2x² - 8x] (-1 to 1)

= [(-1/4 + 2/3 + 2 - 8) - (1/4 - 2/3 + 2 + 8)]

= 22/3

Therefore, the area between the curves from x = -1 to x = 1 is 22/3, A.

Part B:

To find the area enclosed by the curves, find the intersection points between the curves:

f(x) = g(x)

x³ - 2x² + 3x - 1 = 7x - 9

x³ - 2x² - 4x + 8 = 0

(x - 2)(x² - 4x + 4) = 0

(x - 2)(x - 2)² = 0

x = 2 (double root)

So the curves intersect at x = 2.

To find the area enclosed by the curves, take the integral of the difference of the curves over the intervals [-1, 2] and [2, 1]:

A = ∫(-1 to 2) [g(x) - f(x)] dx + ∫(2 to 1) [f(x) - g(x)] dx

= ∫(-1 to 2) [7x - 9 - (x³ - 2x² + 3x - 1)] dx + ∫(2 to 1) [x³ - 2x² + 3x - 1 - 7x] dx

= ∫(-1 to 2) [-x³ + 2x² + 4x - 8] dx + ∫(2 to 1) [x³ - 2x² - 4x + 1] dx

= [-x⁴/4 + 2x³/3 + 2x² - 8x] (-1 to 2) + [x⁴/4 - 2x³/3 - 2x²/2 + x] (2 to 1)

= [(16/3 + 8 - 8 - 16) - (-1/4 + 16/3 + 8 - 32)] + [(1/4 - 8/3 - 2 + 1/4 + 4/3 + 1/2 - 2)]

= 64/3

Therefore, the area enclosed by the curves is 64/3, A.

3rd pic:

To find the area of the region in the third quadrant, find the intersection points between these curves as follows:

f(x) = h(x)

x² - 8 = 2x - 5

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = -1 or x = 3

So the curves intersect at x = -1 and x = 3.

Take the integral of each function over its respective interval,

Area 1: y-axis to f(x) = x² - 8, for x from -1 to 0

The area under the curve y = x² - 8 between x = -1 and x = 0 is:

∫(-1 to 0) (x² - 8) dx = [-x³/3 - 8x] (-1 to 0) = 7/3

Area 2: y-axis to h(x) = 2x - 5, for x from 0 to 3

The area under the curve y = 2x - 5 between x = 0 and x = 3 is:

∫(0 to 3) (2x - 5) dx = [x² - 5x] (0 to 3) = 9/2

Total area:

Adding up the two areas:

Area = 7/3 + 9/2 = 37/6

Therefore, the area of the region in the third quadrant bounded by the y-axis and the given functions is 37/6, option D.

4th pic:

To find the area of the region bounded by the curves:

√(x - 3) = (1/2)√x

Squaring both sides gives:

x - 3 = (1/4)x

Multiplying both sides by 4 gives:

4x - 12 = x

Solving for x gives:

x = 4

So the two curves intersect at x = 4.

To find the area of the region, integrate each function.

Area 1: y = 0 to y = √(x - 3), for x from 3 to 4

The area under the curve y = √(x - 3) between x = 3 and x = 4 is:

∫(3 to 4) √(x - 3) dx = [2/3 (x - 3)^(3/2)] (3 to 4) = 2/3

Area 2: y = 0 to y = (1/2)√x, for x from 0 to 3

The area under the curve y = (1/2)√x between x = 0 and x = 3 is:

∫(0 to 3) (1/2)√x dx = [1/3 x^(3/2)] (0 to 3) = 1

Total area:

Adding up the two areas:

Area = 2/3 + 1 = 5/3

Therefore, the area of the region bounded by the curves is 5/3, option A.

5th pic:

To find the area of the region bounded by the curves;

Setting the two functions equal to each other:

sin(πx) = 4x - 1

Using a graphing calculator or a numerical solver, one intersection point is near x = 0.25, and the other intersection point is near x = 1.15.

Area 1: y = 0 to y = sin(πx), for x from 0 to the first intersection point

The first intersection point is approximately x = 0.25. The height of the triangle is:

sin(πx) - 0 = sin(πx)

The base of the triangle is:

x - 0 = x

So the area of the triangle is:

(1/2) base × height = (1/2) x sin(πx)

The integral of this expression over the interval [0, 0.25]:

∫(0 to 0.25) (1/2) x sin(πx) dx ≈ 0.032

Area 2: y = 0 to y = 4x - 1, for x from the first intersection point to the second intersection point

The height of the triangle is:

sin(πx) - (4x - 1)

The base of the triangle is:

x₂ - x₁ = 1.15 - 0.25 = 0.9

So the area of the triangle is:

(1/2) base × height = (1/2) (0.9) (sin(πx) - (4x - 1))

The integral of this expression over the interval [0.25, 1.15]:

∫(0.25 to 1.15) (1/2) (0.9) (sin(πx) - (4x - 1)) dx ≈ 0.296

Total area:

Adding up the two areas:

Area = 0.032 + 0.296 ≈ 0.328

Therefore, the area of the region bounded by the curves is approximately 0.328.

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The greatest number of dabcoins the customer can purchase, rounded to the nearest whole number is 22 dabcoins.

Given the official exchange rate, in U.S. dollars per dabcoin, is $34 and a customer can spend a maximum of $750 on dabcoins and is charged the percentage. Let's find the greatest number of dabcoins the customer can purchase, rounded to the nearest whole number.

As per the given problem,

Official exchange rate, in U.S. dollars per dabcoin, is $34.

So, cost of 1 dabcoin = $34

The customer can spend a maximum of $750 on dabcoins.

So, $750 is the amount available to purchase dabcoin.

And, charged the percentage is not given so, let's consider it x%

Now, the amount spent on dabcoin can be represented by the product of the cost of 1 dabcoin and the number of dabcoins purchased plus the percentage charged.

Amount spent = (Cost of 1 dabcoin × Number of dabcoins purchased) + (Percentage charged)

According to the problem, the amount spent on dabcoin is limited to $750.

Therefore, (Cost of 1 dabcoin × Number of dabcoins purchased) + (Percentage charged) = $750... (1)

Also, cost of 1 dabcoin = $34.

Now substitute the value of cost of 1 dabcoin in equation (1).

$34 × Number of dabcoins purchased + (Percentage charged) = $750

Now solve for Number of dabcoins purchased.

Number of dabcoins purchased = $750/$34 - Percentage charged / $34

Number of dabcoins purchased = $22.0588235294 - Percentage charged / $34

To find the greatest number of dabcoins the customer can purchase, rounded to the nearest whole number, we need to round off Number of dabcoins purchased.

So, Number of dabcoins purchased = 22 - Percentage charged / $34

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Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

Answer:

yes because its not how much you walk if it is the same distance to the park, then yes. You walked the same distance to the park, however the dog ran more around, you were possibly following the dog so... yea.

Answer:

Last option,

is correct (☑️)

The given expression cos(s + t) = (3/5)(√21/5) - (2/5)(2√6/5),

cos(s - t) = (3/5)(√21/5) + (2/5)(2√6/5)

To find cos(s + t) and cos(s - t), we can utilize the cosine of a sum and cosine of a difference identities. The cosine of a sum identity states that cos(s + t) = cos(s)cos(t) - sin(s)sin(t), while the cosine of a difference identity states that cos(s - t) = cos(s)cos(t) + sin(s)sin(t).

Given that cos(s) = 3/5 and sin(t) = -2/5, we can substitute these values into the identities. For cos(s + t), we have cos(s + t) = (3/5)(cos(t)) - (sin(s))(sin(t)). Substituting the values, we get cos(s + t) = (3/5)(√21/5) - (2/5)(2√6/5), which simplifies to the given expression.

Similarly, for cos(s - t), we have cos(s - t) = (3/5)(cos(t)) + (sin(s))(sin(t)). Substituting the values, we get cos(s - t) = (3/5)(√21/5) + (2/5)(2√6/5), which simplifies to the given expression.

In summary, cos(s + t) = (3/5)(√21/5) - (2/5)(2√6/5) and cos(s - t) = (3/5)(√21/5) + (2/5)(2√6/5).

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Answer:

-17

Step-by-step explanation:

\(2^3\) - 5 * (6 + 4) ÷ 2

Following PEMDAS, we must focus on the parenthesis first.

\(2^3\) - 5 * (6 + 4) ÷ 2

\(2^3\) - 5 * (10) ÷ 2

Now we will focus on the exponent:

\(2^3\) - 5 * 10 ÷ 2

8 - 5 * 10 ÷ 2

Now Multiplication/Division.

This is where you must follow the order in the equation where you see the multiplication sign first, so you multiply first.

8 - 5 * 10 ÷ 2

8 - 50 ÷ 2

Next, Divide:

8 - 50 ÷ 2

8 - 25

Subtract:

8 - 25

-17

\(2^3\) - 5 * (6 + 4) ÷ 2 = -17.

2^3 - 5*(6+4) / 2

= 2^3 - 5*10 / 2    [PEMDAS says to perform functions inside the brackets first.]

= 8 - 5*10/2          [We solve the exponent]

= 8 - 50/2             [Perform the multiplication before the division]

= 8 - 25                 [Perform division before subtraction]

= -17

Answer:

Step-by-step explanation:

(-5/3)(-5/3)= 25/9= 2 7/9

Answer:

Do a quick conversion: 1 dimes = 0.1 dollars using the online calculator for metric conversions. Check the chart for more details. ... Convert dime to dollar - Conversion of Measurement Units ... 30 dime to dollar = 3 dollar. 40 dime to ... You can do the reverse unit conversion from dollar to dime, or enter any two units below: ...

Step-by-step explanation:

Not an answer but an explanation. Hope this helped :)