Writing in Slope-Intercept Form, 4 Ways

(3, 2) & (-3, -4)

Answer:

1a. 5x+14

1b. 5x+14 < 65

1c. x=51/5

Step-by-step explanation:

Answer:

C. The typical value is greater in set . The spread is greater in set A.

Step-by-step explanation:

Set A data is all over the place meanwhile set b data is clumped in one spot. This means Set A data has its data more spread. Then the value is greater in set B since the arrow is on 8.5 while in set A it is on 4.

The estimated time was 140.3 hours, but Acme took 91.2 hours less than the estimate.

1. The estimated time to assemble all 250 widgets, at an 85% rate, is given by:

250 x 200 / 0.85

= 294,117.65 minutes.

2. The actual time taken to assemble all 250 widgets, at an 80% rate, is given by:

250 x 200 / 0.80

= 312,500 minutes.

3. The difference between the estimated time and actual time is given by:

312,500 - 294,117.65

= 18,382.35 minutes.

4. The time in hours is given by: 18,382.35 / 60

= 306.37 hours.

= 306.37 - 166.07 = 140.3 hours

numeric calculations = 18,382.35 minutes / 60 minutes/hour = 306.37 hours - 294,117.65 minutes / 60 minutes/hour = 166.07 hours = 306.37 - 166.07 = 140.3 hours

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Answer:

12.66 cm

Step-by-step explanation:

Area of the circle = 125.8 Sq cm

\( \therefore \: \pi {r}^{2} = 125.8 \\ \\ \therefore \: 3.14 \times {r}^{2} = 125.8 \\ \\ {r}^{2} = \frac{125.8}{3.14} \\ \\ {r}^{2} = 40.0636943 \\ \\ {r} = \sqrt{40.0636943} \\ \\ r = 6.32958879 \\ \\ r \approx \: 6.33 \: cm \\ \\ d \: = 2r \\ \\ d = 2 \times 6.33 \\ \\ d = 12.66 \: cm \\ \)

Diameter of the circle = 12.66 cm

Since, circumference of the circle touches each of the four sides of the square.

So, length of the sides of the square

= diameter of the circle.

= 12.66 cm

Answer:

7^18

Step-by-step explanation:

When you have an exponent to another exponent, you can multiply the exponents.

(7^3)^6

3*6 = 18

7^18

False, each objective function line is unique and not necessarily parallel to every other objective function line in a problem.

In a multi-objective optimization problem, each objective function represents a different optimization criterion or goal. These objectives can have different slopes and directions, resulting in objective function lines that are not necessarily parallel to each other. The objectives may have conflicting or complementary relationships, leading to different trade-offs and possibilities in the optimization process. Therefore, it is incorrect to assume that all objective function lines are parallel in a problem.

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espero te guste pasó por pasó

Answer:

222

Step-by-step explanation:

Let me know if it is correct!

Answer:

37% of 600 is 222

Step-by-step explanation:

divide 37 by 600 and you'll get 222

the reparameterization of the curve in terms of arc length measured from the point (1, 0) in the direction of increasing t is:

r(s) = (2/|s-1/√2|^2 - 1) i + (2|s-1/√2|/|s-1/√2|^2 + 1)

To reparametrize the curve with respect to arc length measured from the point (1,0) in the direction of increasing t, we need to find the arc length function s(t) and then solve for t in terms of s.

First, we find the derivative of r(t):

r'(t) = [-4t/(t^2+1)^2]i + [2(t^2-1)/(t^2+1)^2]j

Then, we find the magnitude of r'(t):

|r'(t)| = sqrt[(-4t/(t^2+1)^2)^2 + (2(t^2-1)/(t^2+1)^2)^2]
      = sqrt[4t^2/(t^2+1)^4 + 4(t^4-2t^2+1)/(t^2+1)^4]
      = sqrt[(4t^4 + 4t^2 + 4)/(t^2+1)^4]
      = 2sqrt[(t^2+1)/(t^2+1)^4]
      = 2/(t^2+1)^(3/2)

Next, we integrate |r'(t)| with respect to t to obtain the arc length function:

s(t) = ∫|r'(t)| dt
    = ∫2/(t^2+1)^(3/2) dt
    = -1/(t^2+1)^(1/2) + C

To determine the constant of integration, we use the fact that s(1) = 0 (since we are measuring arc length from the point (1,0)). Therefore,

0 = s(1) = -1/(1^2+1)^(1/2) + C
C = 1/√2

Substituting C into s(t), we get:

s(t) = -1/(t^2+1)^(1/2) + 1/√2

To reparametrize the curve in terms of arc length, we solve for t in terms of s:

s = -1/(t^2+1)^(1/2) + 1/√2
s - 1/√2 = -1/(t^2+1)^(1/2)
(-1/√2 - s)^2 = 1/(t^2+1)
t

We can solve for t by taking the square root of both sides and isolating t:

t^2 + 1 = 1/[(s-1/√2)^2]
t^2 = 1/[(s-1/√2)^2] - 1
t = ±sqrt[1/[(s-1/√2)^2] - 1]

Since we are interested in the direction of increasing t, we take the positive square root:

t = sqrt[1/[(s-1/√2)^2] - 1]

This is the reparameterization of the curve in terms of arc length measured from the point (1, 0) in the direction of increasing t.

To simplify this expression, we can use the identity:

sec^2θ - 1 = tan^2θ

where θ = arctan(s-1/√2). Then,

1/[(s-1/√2)^2] - 1 = sec^2(arctan(s-1/√2)) - 1
                   = tan^2(arctan(s-1/√2))

Substituting this expression into the reparameterization formula, we get:

t = sqrt[tan^2(arctan(s-1/√2))]
 = |tan(arctan(s-1/√2))|
 = |s-1/√2|

Therefore, the reparameterization of the curve in terms of arc length measured from the point (1, 0) in the direction of increasing t is:

r(s) = (2/|s-1/√2|^2 - 1) i + (2|s-1/√2|/|s-1/√2|^2 + 1)

From the expression of the reparameterization, we can see that the curve has a vertical asymptote at t = 0, since the magnitude of the denominator in the expression for r(t) approaches 0 as t approaches 0. Additionally, the curve is symmetric with respect to the y-axis, since r(-t) = r(t) for all values of t.
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The parametric equations for the circle (2)² + (y-8)² = 16 are given by x = 2 + 4cos(t) and y = 8 + 4sin(t), where t is the parameter. These equations trace the circle in a clockwise direction as the parameter increases.

The general equation of a circle centered at (h, k) with radius r is given by (x-h)² + (y-k)² = r². Comparing this with the given equation (2)² + (y-8)² = 16, we can determine that the center of the circle is (2, 8) and the radius is 4.

To obtain the parametric equations for the circle, we can use the angle t as the parameter. By substituting t into the equations x = 2 + 4cos(t) and y = 8 + 4sin(t), we obtain the corresponding x and y coordinates on the circle as t varies.

The term 4cos(t) represents the horizontal displacement from the center, while the term 4sin(t) represents the vertical displacement. As t increases, the angle in the trigonometric functions changes, resulting in a clockwise traversal of the circle.

Therefore, the parametric equations x = 2 + 4cos(t) and y = 8 + 4sin(t) accurately represent the circle (2)² + (y-8)² = 16, with clockwise motion as the parameter t increases.

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Answer:

everytime the x goes up by 3, the y goes down by 3

Step-by-step explanation:

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:

5.35 gallons in 5 days!

Step-by-step explanation:

6 1/2 aka 6.5/7= 1.07 gallons per day!

1.07*5=5.35!

The output of the following code fragment

int x=0;

while( x < 5)

cout << x << endl;

x ++;

cout << x << endl; will be  0, 1, 2, 3, 4, 5.

The code initializes the variable x to 0, and then enters a while loop that will execute as long as x is less than 5. During each iteration of the loop, the value of x is output to the console using the cout statement, followed by a new line character.

After the cout statement, x is incremented by 1 using the x++ statement. This process is repeated until x is equal to 5, at which point the loop terminates. Finally, the value of x is output to the console using the cout statement, followed by a new line character, giving the output of 5.

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Answer:

 1,616.60

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above  

Step-by-step explanation:

Problem 1

r = radius

A(r) = circular area function in terms of radius

A(r) = pi*r^2

=================================================

Problem 2

t = number of minutes that have elapsed

r(t) = radius function at time t

r(t) = 0.1t

=================================================

Optional Section:

Apply function composition to find the area in terms of elapsed time.

A(r) = pi*r^2

A( r(t) ) = pi * ( r(t) )^2

A(t) = pi*(0.1t)^2

A(t) = pi*0.01t^2

A(t) = 0.01pi*t^2

This gives the area of the circular puddle at any time t

The required equations are =

a) y = 3x + 2

b) 2y = -4x + 1

c) y = -2x + 2

a) System of Equations with One Solution:

To create a system of equations with one solution, we can introduce a second linear equation that intersects the first equation at a single point.

Let's consider the equation y = -2x + 0.5 and add another equation that doesn't have the same slope or intercept.

Let's say the second equation is y = 3x + 2. To create a system of equations with one solution, we can combine these two equations:

y = -2x + 0.5 (Equation 1)

y = 3x + 2 (Equation 2)

This system of equations will have one unique solution since the two lines intersect at a single point.

b) System of Equations with Infinitely Many Solutions:

To create a system of equations with infinitely many solutions, we can create two equations that represent the same line.

Let's consider the equation y = -2x + 0.5 and multiply it by a constant to create a second equation.

Multiplying the equation by 2, we get 2y = -4x + 1.

The system of equations will be:

y = -2x + 0.5 (Equation 1)

2y = -4x + 1 (Equation 2)

Both equations represent the same line, so any point on the line will satisfy both equations. This system will have infinitely many solutions.

c) System of Equations with No Solution:

To create a system of equations with no solution, we can create two parallel lines.

Let's consider the equation y = -2x + 0.5 and add a second equation with the same slope but a different intercept.

Let's say the second equation is y = -2x + 2. To create a system of equations with no solution, we can combine these two equations:

y = -2x + 0.5 (Equation 1)

y = -2x + 2 (Equation 2)

Since both equations have the same slope but different y-intercepts, the lines will never intersect.

Therefore, this system of equations will have no solution.

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On solving for [v], we get v = p/m.

Momentum is defined as the product of mass and velocity of a body. Mathematically, we can write vector as -

p = mv

It is a vector quantity. In a three dimensional coordinate, the momentum vector can be resolved as -

[p] = p[x] a[x] + p[y] a[y] + p[z] a[z]

[p] = m {v[x] a[x] + v[y] a[y] + v[z] a[z]}

Given is the momentum of an object whose formula is p=mv.

We have the formula for momentum as -

p = mv

We can solve for [v] as -

p = mv

Divide by [m] on both sides, we get -

p/m = mv/m

v = p/m

Therefore, on solving for [v], we get v = p/m.

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Answer:

1887.6 ft³

Step-by-step explanation:

What is the volume of a cylinder with a height of 6.8 ft and a base with a radius of 9.4 ft, to the nearest tenth of a cubic foot?

The formula for the volume of a cylinder is given as:

πr²h

From the above question,

r = 9.4 ft

h = 6.8 ft

The volume of the cylinder =

π × 9.4² × 6.8

= 1887.61966 ft³

Approximately = 1887.6 ft³

If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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When x = 0 and y = 6, the partial derivatives ∂P/∂x and ∂P/∂y are ∂P/∂x = 12 and ∂P/∂y = 0, respectively.

To find the partial derivatives ∂P/∂x and ∂P/∂y using the Chain Rule, we start by computing the partial derivatives of P with respect to each variable u, v, and w, and then differentiate u, v, and w with respect to x and y.

Given expressions are:

\(P = u^2 + v^2 + w^2\)

\(u = xe^y\\ v = ye^x\\ w = e^{xy}\\\)

x = 0

y = 6

Let's begin with ∂P/∂x:

Using the Chain Rule, we have:

∂P/∂x = ∂P/∂u × ∂u/∂x + ∂P/∂v × ∂v/∂x + ∂P/∂w × ∂w/∂x

Differentiating each component:

∂P/∂u = 2u

∂u/∂x = \(e^y\)

∂P/∂v = 2v

∂v/∂x = \(ye^x\)

∂P/∂w = 2w

∂w/∂x = \(e^{xy}\)

Substituting the given values:

x = 0

y = 6

∂P/∂x = 2(0 × e^6) × e^0 + 2(6 × e^0) × 0 + 2(e^0 × 6) = 12

Next, let's find ∂P/∂y:

Using the Chain Rule, we have:

∂P/∂y = ∂P/∂u × ∂u/∂y + ∂P/∂v × ∂v/∂y + ∂P/∂w × ∂w/∂y

Differentiating each component:

∂u/∂y = x × \(e^y\)

∂v/∂y = x × \(e^y\)

∂w/∂y = \(e^x\) × y

Substituting the given values:

x = 0

y = 6

∂P/∂y = 2u × (0 × e^6) + 2v × (0 × e^6) + 2w × (e^0 × 6) = 0

Therefore, when x = 0 and y = 6, the partial derivatives are ∂P/∂x = 12 and ∂P/∂y = 0.

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Answer:

Step-by-step explanation:

Say what now

Answer:

thank you kanye, very cool!

Step-by-step explanation:

The number that will complete the square to solve equation is 1/36.

What is completing the square?

For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form

ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.

Consider, the given polynomial

3w^2 - w - 24 = 0

Rewrite the polynomial in the form ax^2 + bx = c

Add 24 on both sides,

3w^2 - w - 24 + 24 = 24

⇒ 3w^2 - w = 24

Divide both sides by 3,

\(w^2-\frac{1}{3}w = 8\)

To complete the square x^2 + bx, we add \((\frac{b}{2} )^2\)

Here, b = -1/3

So, \((\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}\)

Adding to both sides of the equation, we have

\(w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}\)

Hence, the number that will complete the square to solve an equation is 1/36.

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Step-by-step explanation:

The period of f(x) is π.

To calculate the period using the formula derived from the basic sine and cosine equations. The period for function y = A sin (B a – c) and y = A cos ( B a – c ) is equal to 2πB radians. The reciprocal of the period of a function is equal to its frequency.

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

The simplificatiοn fοrm οf the prοvided expressiοn is (7/3)²(2/3)³ after using the cοncept οf the integer expοnent οptiοn (A) seven-thirds squared times twο-thirds cubed is cοrrect.

In mathematics, integer expοnents are expοnents that shοuld be integers. It may be a pοsitive οr negative number. In this situatiοn, the pοsitive integer expοnents determine the number οf times the base number shοuld be multiplied by itself.

It is given that:

The number expressiοn is:

\($ \mathrm { =\left[\left(\frac{3}{7}\right)^2 \left(\frac{2}{3}\right)^{-3} \right] ^{-1} }\)

As we knοw, frοm the definitiοn οf the integer expοnent, the pοsitive integer expοnents determine the number οf times the base number shοuld be multiplied by itself.

Using the integer expοnent prοperties:

\($ \mathrm {= \dfrac{1}{ \left(\dfrac{3}{7}\right)^2 \left(\dfrac{2}{3}\right)^{-3} } }\)

(7/3)²(2/3)³

Thus, the simplificatiοn fοrm οf the prοvided expressiοn is (7/3)²(2/3)³ after using the cοncept οf the integer expοnent οptiοn (A) seven-thirds squared times twο-thirds cubed is cοrrect.

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Complete correct question:

Which is an equivalent expressiοn fοr three sevenths squared times twο thirds raised tο the pοwer οf negative three all raised tο the pοwer οf negative οne?

Answer:

Hi uddin

Step-by-step explanation:

Do u remember me

I am the ghost of the uchiha i searched ur this question and found ur brainly thing

The difference of 12. 4 and 3 times a number.

Which of the following is not a translation of the algebraic expression 12. 4 – 3b into words?

According to the question

The given expression is;

\( =12.4 - 36 \)

The minus sign between the terms shows the difference between the first term and the second term.

And the dot sign in the expression shows the product of the 12 and 4.

Hence, The difference of 12. 4 and 3 times a number.

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Answer: The difference of 12. 4 and 3 times a number.

Step-by-step explanation:

hope this helps