Which expression is equivalent to 8 - (6r + 2)?
A) -6r + 6
B) 2r + 2
C) 6r + 10
D) -6r + 10

Answer:

x = \(\sqrt{116}\)  feet

Step-by-step explanation:

Pythagorean Theorem: \(a^2=b^2+c^2\)

where a = hypotenuse, and b and c are legs of the right triangle.

We plug in our variables into the equation and solve for x:

\(10^2=4^2+x^2\)

which would isolate to:

\(116=x^2\)

so x = \(\sqrt{116}\)

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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The given data are:N = 600; G = 24; S = 4 m/s; Up-peak interval = 32 s; Expected up-peak demand = 20%; h = 8 m; Door opening time = 2 s; Door closing time = 2 s; Passenger loading time = 0.8 s;

Passenger unloading time = 0.8 s; Single floor flight time = 5 s; Hence, the minimum up-peak handling capacity (UPPHC) is 20% of 600 persons as per the question. Thus, UPPHC = (20/100) × 600=120 persons.

(a) Minimum up-peak handling capacity (UPPHC): UPPHC = 120 persons.

(b) Minimum contract capacity (CC): The formula for CC is given byCC = [(UPPHC × 3600)/Up-peak hours] = [(120 × 3600)/4] = 10800 persons/hr.

Hence, the minimum contract capacity is 10800 persons/hr.

(c) Average highest call reversal floor (H) and the average number of stops (S):

The formula for the average highest call reversal floor isH = [n/(n – 1)] × [∑f/(n × P)].

Where, n = number of lifts; ∑f = sum of the products of the number of floors served and the corresponding number of calls; and P = ∑f/number of floors served. Thus, H = [n/(n – 1)] × [∑f/(n × P)]For S, the formula is given by

S = ∑f/(n × P).

Thus, for calculating H and S, the traffic calculation is done, and the calculations are provided below:

For traffic design, let n = 3. Then, Np = UPPHC/up-peak hour= (120 × 3600)/3600=120 persons/hr.

Let the average number of stops be S. Then the number of floors served on the average during the up-peak hour is given by 24/S.

From the traffic flow diagram, the average highest call reversal floor is (3/2) H

= [3/(3 – 1)] × [((1 × 2) + (2 × 4) + (3 × 7) + (4 × 8) + (5 × 9) + (6 × 10) + (7 × 10) + (8 × 9) + (9 × 8) + (10 × 7) + (11 × 6) + (12 × 5) + (13 × 4) + (14 × 2))/(3 × 12)] = (3/2) × 7.63 = 11.45 ≈ 11 th floor.

∴ Average highest call reversal floor, H = 11th floor.∴ The average number of stops,

S = ∑f/(n × P)= [(1 × 2) + (2 × 4) + (3 × 7) + (4 × 8) + (5 × 9) + (6 × 10) + (7 × 10) + (8 × 9) + (9 × 8) + (10 × 7) + (11 × 6) + (12 × 5) + (13 × 4) + (14 × 2)]/3 × 12 × 1= 526/36= 14.61 ≈ 15.

(d) Round trip time (RTT):The formula for RTT is given by RTT = 2 × [L × (h/S) × Single floor flight time + Door open and closing time + Passenger loading and unloading time].

Where, L = number of lifts required to provide the UPPHC during the up-peak hour.

Thus, the calculation for L is done first as:

L = UPPHC/[(h/S) × Single floor flight time × 3600/up-peak hour]Now, substituting the given values in the above formula, we get,L = 120/[(8/4) × 5 × 3600/240] = 5 lifts(approx.)

Now, substituting the above value of L in the formula for RTT, we get

RTT = 2 × [5 × (8/4) × 5 + 2 + 0.8 + 0.8] = 94 s(approx.).Thus, the round trip time (RTT) is 94 s.

(e) Number of lifts required (L): We have already calculated the value of L, which is equal to 5 lifts.

(f) Real up peak interval (UPPINT):The formula for the real up-peak interval is given by:

Real up peak interval = (RTT × Number of cycles per hour)/(60 × Number of lifts required)Where the number of cycles per hour is given by 3600/RTT.

Hence, the value of the number of cycles per hour is equal to 3600/94, which is approximately equal to 38.298.

Now, substituting all the above values in the formula, we get

Real up peak interval = (94 × 38.298)/(60 × 5) = 30.06 s(approx.).Hence, the real up-peak interval (UPPINT) is 30.06 s.

The quality of the lift system is excellent since the real up-peak interval is less than the up-peak interval of 32 s, which was the expected value.

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The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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Answer: 5.657

Step-by-step explanation:

Split it into two right triangles, with the hypotenuse being the diagonal.

Then, a square plus b square = c square

So, 4 square + 4 square = c square

16 + 16 = c square

32 = c square

square root of 32 = c

square root of 32 = ~5.657

c = ~5.657

Answer:

w = 6 units

Step-by-step explanation:

The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:

\(P=2w+2l\)

Where w represents width and l represents length.

To find the width, rearrange the equation so it is in terms of w:

\(P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}\)

Now, plug in the known values!

\(w=\frac{20-2(4)}{2}\)

Simplify!

\(w=\frac{12}{2} \\w=6\)

Answer:

The answer is 3w - g - 4

Step-by-step explanation:

(8w - 4g + 1) - (5w + 3g - 5)

8w - 4g + 1 - 5w + 3g - 5

Rearrange terms

8w - 5w - 4g + 3g + 1 - 5

Combine like terms

(8w - 5w) = 3w   ( -4g + 3g) = -g  (1 - 5) = - 4

Answer:

3w - g - 4

Answer:

R___S___T

RT=RS+ST

39 = (23 - 2x) + (9x - 5)

39 =7x + 18

7x = 39 - 18

7x = 26

x = 26/7

x= 3.7

RS= 23 - 2x = 23 - 2(3.7) = 23 - 7.4 = 15.6

If went ST = 9x -5 = 9(3.7)- 5 = 33.3 - 5 = 28.3

I hope I helped you^_^

Answer:

\(\displaystyle 13,834311042... = x\)

Step-by-step explanation:

\(\displaystyle \frac{x}{13} = csc\:70 \hookrightarrow 13csc\:70 = x \\ \\ 13,834311042... = x\)

OR

\(\displaystyle \frac{13}{x} = sin\:70 \hookrightarrow xsin\:70 = 13 \hookrightarrow \frac{13}{sin\:70} = x \\ \\ 13,834311042... = x\)

Information on trigonometric ratios

\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ\)

I am joyous to assist you at any time.

The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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Carla works Monday, Wednesday, Saturday

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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Answer: m∠2 =60

60=4x+12

subtract 12 from both sides

60-12=4x+12-12

60-12=4x

48=4x

divide both sides by 4

48÷4=4x÷4

48÷4=x

x=12

Plug it into the equation

4(12)+12=

48+12=

m∠2 =60

another proof is that they are congruent

I hope this is good enough:

Answer: 1

Step-by-step explanation:

For every three its going down, its going three to the left.

So it's going -3/-3

            OR

-1/-1 = 1/1 = 1

Answer:

y = \(\frac{1}{3}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation

- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )

0 = c

y = \(\frac{1}{3}\) x + 0 , that is

y = \(\frac{1}{3}\) x

An equation of the question is 250 × 0.94^n = 150 and in approx 8 years it will have about 150 students.

The population of its high school decreases by 6% each year.

The senior class has 250 students now.

Each year decrease in population = 6% = 0.06

So it can be = 1 - 0.06 = 0.94

Total student now = 250

Let n be the number of years before the class will have  students.

So the equation should be = 250 × 0.94^n

After years left students = 150.

Now the equation should be

250 × 0.94^n = 150

Now solving the equation.

Divide by 250 on both side, we get

0.94^n = 150/250

0.94^n = 3/5

Taking log on both side, we get

log(0.94^n) = log(3/5)

Using the formula log(m^n) = n logm and log(m/n) = log m - log n

n log(0.94) = log3 - log5

Now finding the value of log using calculator

n (-0.062) = 1.099 - 1.61

(-0.062)n = -0.511

Divide by (-0.062) on both side, we get

n = 8.242

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The complete question is:

As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 250 students now. In how many years will it have about 150 students? Write an equation. Then solve the equation without graphing. Write an equation to represent this situation. Let n be the number of years before the class will have  students.

Answer:125x^6y^6 (Red)

Step-by-step explanation: To find the answer we need to do first 5^3 which is 125. Then according to exponent rule, we multiply the exponents inside by the exponent outside, so it would be x^6 and y^6.

It would be 125x^6y^6.

Hope this helps you!

Answer:

The point A has the ordered pair of (-4, 2)

Step-by-step explanation:

In mathematics, an ordered pair is a pair of objects.

When finding a point you start with the x then the y.

(-4, 2)

-4 means to the left 4

and 2 means up 2.

According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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Answer:

5.5 hours

Step-by-step explanation:

Answer:

----------------------

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

Answer:

7 and 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first step is to find the √58.

The answer is 7.61577310586.

Since this is between 7 and 8, the correct answer is 7 and 8.

***NOTE*** we are going to use the rise over run formula to solve this problem

Joe climbed a mountain with a rise of 1, 200 feet and a run of 1, 500 feet.

So, the slope would be:

1, 200 over 1, 500

which can be simplified...

1,200/1,500 = 12/15 = 4/5

When we solve for slope for Bob, we do the same thing.

He climbed a mountain with a rise 900 feet and a run of 1, 000 feet.

So, it would look like this after we simplify it...

900/1,000 = 9/10

Finally, since Bob's mountain has the largest slope (or fraction), that means that he climbed the steepest mountain.

I hope this helps! :) Let me know if you need help with anything else! I'd be happy to help you!!

Did it hurt when you fell from heaven? because i think you may have fell on your face.

~ Keiji ❤

I'm not too good at comebacks, but have a good day and remember to eat~

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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There is need of total of 25 boxes of same size for the next lower level.

A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.

Some examples for sequence are :

2,4,6,8,10,12

3,9,27,81,243

The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.

In a sequence , first term always known as initial term.

and difference between two terms are known as common difference. It is denoted by d.

General form of sequence is :

\(a_1,a_2,a_3,----,a_n\)

where , \(a_n\) = last term in sequence.

According to question,

The boxes in each of successive levels make a sequence.

Also, number of boxes at level n = \(n^2\)

As upto four level the number of boxes are 16.

at level 5 , n = 25

Thus, the total  boxes of equal or same size need for next lower level is 25.

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The complete question is :

Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.

a. How many boxes of same size would need for next lower level?

b. How many boxes of same size would need to add the 3 levels?

c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?

Answer:

3.2

Step-by-step explanation:

to solve this equation, you need to first separate the coefficient 5.5 from x. To do this, you must divide BOTH sides. 5.5x ÷ 5.5 = 17.6 ÷ 5.5

x= 3.2

The transfer function U(s)/Y(s) for the given system modeled by the differential equation y'' + 3y' + 2y = 21 + u is 1/(s^2 + 3s + 2).

To find the transfer function U(S)/Y(S) for the given system modeled by the differential equation y'' + 3y' + 2y = 21 + u, we need to take the Laplace transform of both sides of the equation.

Taking the Laplace transform, and assuming zero initial conditions:

s^2Y(s) + 3sY(s) + 2Y(s) = 21 + U(s)

Now, let's rearrange the equation to solve for Y(s):

Y(s)(s^2 + 3s + 2) = 21 + U(s)

Dividing both sides by (s^2 + 3s + 2):

Y(s) = (21 + U(s))/(s^2 + 3s + 2)

Therefore, the transfer function U(s)/Y(s) is:

U(s)/Y(s) = 1/(s^2 + 3s + 2)

The transfer function U(s)/Y(s) for the given system modeled by the differential equation y'' + 3y' + 2y = 21 + u is 1/(s^2 + 3s + 2).

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