a rectangle is constructed with its base on the diameter of a semicircle with radius 12 and with its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum​ area?

the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v is 10[tex]\sqrt{14}[/tex]

The surface element is

dS = || ∂r/∂u  x  ∂r/dv || du dv

where

r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k

r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k

is the vector parameterization for the surface S.

The normal vector to the surface is

∂r/∂u  x  ∂r/dv

… = (i + j + 2 k)  x  (i - j + k)

… = 3 i + j - 2 k

and has norm

|| ∂r/∂u  x  ∂r/dv || = √(3² + 1² + (-2)²) = √(14)

Now compute the integral:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv

… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv

… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv

… = √(14) ∫₀¹ (8 + 2v) dv

… = √(14) (8v + 2v²) |₀¹

… = 10 √(14)

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The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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Answer:

x = - 25

Step-by-step explanation:

the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is

| - a | = | a | =a

given

| x + 10 | = 15 , then

x + 10 = 15 ( subtract 10 from both sides )

x = 5

OR

-(x + 10) = 15

- x - 10 = 15 ( add 10 to both sides )

- x = 25 ( multiply both sides by - 1 )

x = - 25

solutions are x = 5 , x = - 25

Answer: -25

Step-by-step explanation:

Answer: y= -4x -24

Step-by-step explanation:

The equation is y=mx + b

We know the b is -24 because it already tells us the coordinate of the y-intercept is (0, -24), so we only need to find x by looking at the rise over run.

The rise is -24, and the run is 6, so -24/6 = -4

So the equation is y= -4x -24

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when we pay n pesos, then recurrence relation for all the number are in a ways to pay a bill is in this order:[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

A recurrence relation is an equation which represents a chain primarily based totally on a few rule. It enables in locating the following time period (subsequent time period) established upon the previous time period (preceding time period). If we recognise the preceding time period in a given series, then we will without difficulty decide the following time period.

Recurrence family members are used to lessen complex issues to an iterative procedure primarily based totally on less difficult variations of the trouble. An instance trouble wherein this technique may be used is the Tower of Hanoi puzzle. Recurrent is some thing that happens frequently or repeatedly. However, in case you are speakme approximately a recurrence relation, then you definitely have a mathematical shape which you are handling and it's miles really specific than a recursive formula. Recursion is the repeated use of a process or action.

pay 1 pesos coin , then n-1 pesos

pay 2 pesos coin , then n-2 pesos if n ≥ 2

pay 5 pesos coin , then n-5 pesos if n ≥ 5

pay 10 pesos coin , then n-10 pesos if n ≥ 10

pay 5 pesos bill , then n-5 pesos if n ≥ 5

pay 10 pesos bill , then n-10 pesos if n ≥ 10

pay 20 pesos bill , then n-20 pesos if n ≥ 20

pay 50 pesos bill , then n-50 pesos if n ≥ 50

pay 100 pesos bill , then n-100 pesos if n ≥ 100

a0=1

so i have recurrence relation as follows:

[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

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The probability of getting exactly 0 heads is, 0.031.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

A fair coin is tossed 5 times.

So, the the total number of possibilities are,

[tex]2^5= 32[/tex]

We have to find the probability of getting exactly 0 heads.

The only possible set of flips that yields 0 heads is {T, T, T, T, T}.

So,

The probability is, [tex]\frac{1}{32}=0.03125[/tex]

Probability ≈ 0.031

Hence, the probability of getting exactly 0 heads is, 0.031.

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The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).

The center of the object is represented by the centroid. The centroid of a triangle is the location where the triangle's three medians cross. The intersection of all three medians is another definition of it. The median is a line that connects the middle of a side to the opposite vertex of a triangle. The region bounded by the curves is a triangle with the tip at (0, e^0) and the base at (3, 0). The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).

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Answer:

They took 3 vans and 3 buses.

Step-by-step explanation:

Given:

To find:

The number of vans and the number of buses they took.

Explanation:

Let the number of vans = v

Let the number of buses = b

The total number of vans and buses is 6:

[tex]v+b=6[/tex]

⇒[tex]v=6-b....[/tex]Equation(1)

Each van holds 6 students and each bus hold 50 students.

The number of students on the trip is 168.

[tex]6v+50b=168[/tex]....Equation(2)

Substitute equation (1) into equation (2):

[tex]6v+50b=168[/tex]

[tex]6(6-b)+50b=168[/tex]

Then solve the equation for b:

[tex]36-6b+50b=168[/tex]

[tex]44b=168-36[/tex]

[tex]44b=132[/tex]

[tex]\frac{44b}{44}=\frac{132}{44}[/tex]

[tex]b=3[/tex]

Then, solve for v:

[tex]v=6-b=6-3=3[/tex]

Answer:

They took 3 vans and 3 buses.

The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).

The past step makes six void spots in which three Is might be sorted out, however just three spots should be picked. Request doesn't make any difference, as every one of the three Is are something similar. Along these lines, there are (63) approaches to picking those spots.

Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!

So such plans where the sets of indistinguishable letters are discernable. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe

∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)

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Answer:

You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.

Step-by-step explanation:

From the given average the number of students are more in the afternoon quiz as compare to the morning quiz .

As given in the question,

Combined average score of the two classes = 84.

Average score of students in the morning quiz = 80

Let 'x' be the number of students in the morning quiz

80 = ( Sum of all number of students in the morning quiz) / x

⇒  Sum of all number of students in the morning quiz = 80x __(1)

Average score of students in the afternoon quiz = 86

Let 'y' be the number of students in the afternoon quiz

86 = ( Sum of all number of students in the afternoon quiz) / y

⇒  Sum of all number of students in the afternoon quiz = 86y __(2)

Average score of combined classes = ( 80x + 86y ) / (x + y)

⇒ 84 = ( 80x + 86y ) / (x + y)

⇒ 84x + 84y = 80x + 86y

⇒4x = 2y

⇒ y = 2x

Number of students in the afternoon are double  the number of students in the morning.

Therefore, from the given averages afternoon class has more number of students than morning class

The complete question is :

Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean) score for the two classes combined was 84. Which class had more students?(1) The average score for the students in the morning class was 80

(2) the average score for the students in the afternoon class was 86

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Answer:

  remaining zeros: {-1/2, √3}

Step-by-step explanation:

Given the polynomial function f(x) = 2x³ +x² -6x -3 has one zero at x = -√3, you want the remaining zeros.

A polynomial with rational real coefficients and zeros that are roots or complex numbers will have all such roots in conjugate pairs.

The root that is the conjugate of -√3 is +√3.

The product of the roots of an odd-degree polynomial will be the opposite of the ratio of the constant to the leading coefficient. Here, that means the product of roots is ...

  -(-3/2) = 3/2

We already know that two of the three roots are ±√3, so their product is -3. The remaining root will be ...

  (3/2)/(-3) = -1/2

The remaining zeros of f(x) are √3 and -1/2.

__

Additional comment

When the degree of the polynomial is even, the constant term will be the product of the roots. This odd/negative, even/positive behavior comes from the fact that each zero (q) corresponds to a factor (x -q).

The product of these binomial factor constants is the constant in the standard-form polynomial. It will have a negative sign if there are an odd number of factors.

Answer:

628 m

Step-by-step explanation:

We need to find the circumference, C, of the circle.

C = πd

C = 3.14 × 100 m

C = 314 m

Walking around the circular path twice is twice the length of the circumference.

distance = 2C = 2 × 314 m = 628 m

The odds against selecting a history are 31/16.

Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.

Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.

Probability(Event) = favorable outcome/Total outcome = x/n

Number of playwrights = 47

Number of tragedies = 16

Therefore, the odds against selecting tragedies are

(47 - 16) / 16

= 31/16

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The complete question is:

Of the 47 plays attributed to a​ playwright, 11 are​ comedies, 16 are​ tragedies, 20 are histories. If one play is selected at​ random, find the odds against selecting a tragedy.

Answer:

2.5x103

Step-by-step explanation:

Six candies would cost $1.44.

Answer:

$1.44

Step-by-step explanation:

We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.

1 piece of candy = $0.24

So we do 0.24*6= 1.44

I hope this helps!!!

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When the car is acquired for $22600 and depreciates at an 11.5% rate, it will take 6.7 years for its worth to reach $5200.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

Cost of car=$22600

Rate of depreciation=11.5%

After n years, value of car=$5200

Annual depreciation expense=22600*11.5%

=$2599

Value of the Car = Purchase cost - (Annual depreciation expenses * n)

5200=22600-(2599*n)

2599n=22600-5200

2599n=17400

n=6.695

n=6.7 years

The number of years until the value of the car is 5200 dollars at depreciation rate of 11.5% when purchased at 22600 dollars will be 6.7 years.

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Answer:

9 + 4i

Step-by-step explanation:

5 + 4 + 9i - 5i

=> 9 + 4i

The vertex and range of the function y = |x - 5| + 5 is (5, 4) and  [4, ∞) respectively

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

In the given function;

y = |x - 5| + 4

Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.

vertex = (5, 4)

Range = [4, ∞)

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Answer and explanation in one:

(4+9)/(-2-1) = 13/-3 = -13/3

y=-13x/3 + b

4=26/3 + b

b = 4-26/3 = (12-26)/3 = -14/3

y=-13x/3 -14/3 is the line through the two given points

find the line perpendicular and through (14,-6)

y=3x/13 + b, plug in the point to find b

-6 = 3(14)/13 + b

b = -6 -42/13 = -78/13 - 42/13 = -120/3

y= 3x/13 - 120/13

find the intersection point of the two lines, set them equal

3x/13 -120/13 = -13x/3 - 14/3

multiply by 39

9x - 360 = -169x - 182

178x = 360-182 = 178

x = 1

y= -27/3=-9

the point is (1,-9)

calculate the distance from (1,-9) to (14,-6)

d^2 = 9+169 = 178

d = sqr178 = about 13.34

Using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an equation.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.

So, we begin the week with 30 units of orange juice.

We purchase more than 50 units of orange juice.

Total: 30 + 50 = 80 units

Our ending inventory was 30 units.

Units of orange juice sold: 80 - 30 = 50 units

Therefore, using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.

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Complete question:

You begin the week with 30 units of orange juice. You purchase 50 units. Your ending inventory for the week is 30 units. How many units did you sell?

a) 5

b) 15

c) 49

d) 50

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

From the graph,

x axis represents the arm length of the catapult and the y axis represents the distance.

The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line

The coordinates of the intersecting point = (-30, 90)

Here arm length represents -30, but the arm length cannot be a negative value

Therefore, there is no arm length that gives equal distance

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Answer:

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

Step-by-step explanation:

The required balance at the beginning of the incomplete register is $38.25.

Given that,
To determine the beginning balance in the incomplete register.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
In the table, in the register, the balance starts with an entry of $38.25 paycheck. So, the 1 st entry of the register shows the balance in the beginning.

Thus, the required balance at the beginning of the incomplete register is $38.25.

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Answer:

8.9

Step-by-step explanation:

Answer:

0.34

Step-by-step explanation:

[tex] {0.5 }^{2} + {0.3}^{2} \\ 0.25 + 0.09 \\ = 0.34[/tex]

(I'm not sure if this is what you meant)

The rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

For the shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

Given that Trapezoid 1 with vertices

A(-4, 3), B(1, 3), C(0, 0), D(-3, 0)

Trapezoid 2 with vertices are;

A'(-1, 1), B'(4, 1), C'(3, -2), D'(0, -2)

It can be observed by comparison that the x-values have increased by 3 units and the y-values have decreased by 2 units

So the rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)

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The co-ordinates of the point P that divides the line segment AB in the ratio 3:2 are (3,0)

What is Line Geometry?

A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.

Solution:

To find the co-ordinates of point P we wil use section formula

(x,y) = (m*x2 + n*x1 / m+n), (m*y2 + n*y1 / m+n)

(x,y) = (3*3 + 2*3)/5 , (3*2 + 2*(-3))/5

(x,y) = 15/5 , 0/5

(x,y) = 3,0

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Answer:3

Step-by-step explanation:3

Using the percentage method, we know that the original price of the TV set was $400.

Percentages are just fractions with a denominator of 100.

To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the percentage is always out of 100.

Then we automatically know that:

100% - 15% = 85%

We know:
85% = $340

15% = ?

Now, calculate the reduced price as follows:
85/340 = 15/x

85x = 15(340)

85x = 5,100

x = 5100/85

x = $60

Original price of the TV set:

Sold cost + Reduced cost

$340 + $60

$400

Therefore, using the percentage method, we know that the original price of the TV set was $400.

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