for the differential equation a. find all equilibrium solutions and use the first derivative test to draw the phase line for the de. b. classify each equilibrium solution as asymptotically stable , unstable or semi-stable. c. use the second derivative test for concavity and the phase line to produce a phase portrait and sketch one typical solution curves in each region determined by the equilibrium solutions.

The piece of pasta he started with was 34 inches long.

Defining a problem, identifying its underlying cause, locating, ranking, and selecting potential solutions, as well as putting those ideas into practice, are all steps in the issue-solving process. Diagnose the circumstance to keep your attention on the issue and not merely its symptoms.

Let x be the length of the original piece of pasta.

After taking bites, he has (x - 3) pieces of pasta, each 17/10 inches long.

So, the total length of all pieces of pasta is (x - 3) * 17/10 = 17 inches.

Therefore, x = 10 * 17/7 + 3 = 34 inches.

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There are 66 ways to choose two vehicles from the dealer's inventory.

A combination is a grouping of items from a larger set in which the order of the items is irrelevant. In other words, it is a method of selecting a subset of items from a larger set without regard for their order of selection.

The formula C(n, k) = n! / (k! (n - k)!) can be used to calculate the number of combinations.

where n represents the total number of items in the set and k represents the number of items in the combination.

The exclamation mark (!) represents the factorial function, which is the sum of all positive integers up to a certain number.

The number of ways to select two vehicles from 8 cars and 4 trucks is 8 + 4 = 12 vehicles.

To find the number of combinations, we use the formula for combinations, which is:

C(n, k) = n! / (k! (n - k)!)

where n is the total number of vehicles and k is the number of vehicles we want to choose.

So, for n = 12 and k = 2,

we have:

So, putting the value in above formula:

We will get it as:

C(12, 2) = 12! / (2! (12 - 2)!) = (12 * 11) / (2 * 1) = 66

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Answer: The answer would be

Step-by-step explanation:

28/3

in decimal form- 9.3 (3 keeps going)

Mixed Number- 9 1/3

Andy is using wooden boards that are 0. 45 feet wide to build a deck. The number of rows of boards are needed to completely cover a space is 47 rows of boards.

Divide the total width (21 feet) by the width of each board (0. 45 feet):

21 / 0. 45 = 46. 666666

Round the result up to the next whole number:

47 rows of boards

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

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The quotient is x³-3x²-3x+9 and the remainder is -33.

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor.

When we divide a polynomial p(x) by a linear factor (x - a) (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R is the remainder.

p(x)/q(x) = p(x)/(x- a) = Quotient + (Remainder/(x - a))

p(x)/(x - a) = Q(x) + (R/(x - a))

Given that, (x⁴-12x²-6)/(x+3)

Here, (x⁴+0x³-12x²+0x-6)/(x+3)

Now,

-3| 1   0   -12   0   -6|

  |     -3    9   9   -27|

________________

    1  -3   -3   9    |-33

So, remainder = -33 and quotient = x³-3x²-3x+9

Therefore, the quotient is x³-3x²-3x+9 and the remainder is -33.

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Answer:

1,500

Step-by-step explanation:

It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!

Answer: $115

Step-by-step explanation:  

92 is the price after a 20% discount, so it is 80% of the original value.

So, solve, 92÷0.80=115

So the original price was $115

Answer:

x = 40 and y = 100

Step-by-step explanation:

random number 100

40% of 100 = 0.40 * 100 = 40

It will take 48 hours, to fill the tank if both pipes are left open simultaneously.

We are given the following data -

The time taken to fill the tank by inlet pipe = 12 hrs

so, the rate of filling = 1/12

The time taken to empty the tank by drain pipe = 16 hrs

so, the rate of emptying = - 1/16

Therefore, the total work done by both pipes can be given by the following formula -

(1/rate of filling) + (1/rate of emptying) = (1/rate of net change)

1/12 + (-1/16) = (1/Rn)

Therefore, (1/Rn) = 1/12 - 1/16 = 1/48

To find how long it will take to fill the tank, we need to find the reciprocal of the rate of net change:

1/Rn = 1/(1/48)

Rn = 48

So it will take 48 hours, to fill the tank if both pipes are left open.

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The total length in feet of the two bulletin boards side by side is 9 feet.

The total length of the bulletin boards when calculated side by side will be done using addition operation. The expression that will form for calculation is -

The total length = length of one bulletin board + length of second bulletin board

Keep the values in formula -

The total length = 1.25 + 1.75

Performing addition on Right Hand Side of the equation

The total length of the two bulletin boards = 3 yards

The total length in feet = 3 × (3 feet)

Performing multiplication

Total length = 9 feet

The total length in feet is 9 feet.

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The perimeter of the rectangle  = (6 x + 8) meters. and the Area is  

2x² +10x.

step 1: The first side's length is (x+ 5) metres, while the second side's breadth is (2x+ 1) metres.

Now, the RECTANGLE'S PERIMETER = 2 (LENGTH + WIDTH).

Here, perimeter is equal to 2 ((x+ 5) m + (2x + 1) m) or 2 (x + 5 + 2x +1) = 2(3x + 4) = 6x + 8

Therefore, the rectangle's perimeter is equal to (6 x + 8) metres.

step 2:

Area of a rectangle equals length times breadth

Given:

Size = x+5

Thickness = 2x+1

Area of rectangle = length breadth = (x+5) (2x+1) = 2x (x+5) (2x+1) =2x2+5+4x+1 =2x2+10x, according to the query.

The area is therefore 2x2 + 10x.

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A sentence constructed up of variables, numbers, or both is known as an expression in mathematics.

A mathematical expression is a sentence with at least two numbers or variables, at least one mathematical operation, and at least single mathematical operation. Math allows for addition, subtraction, multiplication, and division.

Using variables, numbers, or both, a mathematical expression is a phrase. A symbol in an expression can never be equal. Examples include these expressions. Equations are mathematical statements that demonstrate the equality of two expressions.

Let the equation be 2x + 10

Where, x = 15

substitute the values in the above equation, we get

= 2(15) + 10

= 40

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Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts? Show your work.

Given expression is:

2x + 10

Answer:

Ariel's plant is 1.6 inches taller than Dyani's.

It doesn't seem that you can multiply the measurement of Dyani's plant anymore than Ariel's. So I believe that would be 0 inches.

Step-by-step explanation: You can multiply Dyani's measurement with number like 1.0, 1.2, etc. You still wouldn't be able to multiply it anymore.

I hope this helps!

Nasim have to pay for 3 pounds of coffee is  $10.75.

The  expression for p pounds of coffee is 4.75p - 3.5.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount.

and, Nasim have to pay to buy 3 pounds of coffee.

So, Nasim have to pay for 3 pounds of coffee.

= 3 x 4.75 - 3.50

= 14.25 - 3.5

= $10.75

and, the expression for p pounds of coffee is

= 4.75p - 3.5

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Answer: x = 33°

Step-by-step explanation: 2x° + 24°-24 = 90°-24 2x/2 = 66/2 x = 33°

Solving exponential and logarithmic equations requires a strong understanding of the properties of exponents and logarithms, as well as the use of logarithmic identities and inverse operations. It is important to simplify expressions and isolate the variable using basic algebraic operations, logarithmic identities, and inverse functions.

When solving exponential or logarithmic equations, there are several important steps to consider:

Simplify the equation using basic algebraic operations, such as multiplication, division, addition, and subtraction.

Isolate the exponential or logarithmic expression on one side of the equation.

Use the properties of exponents or logarithms to simplify the expression, if possible.

Use logarithmic identities such as logarithmic rules and change-of-base formula to simplify the expression.

Solve for the variable by using inverse operations.

Check your answer by substituting it back into the original equation and verifying that both sides are equal.

Identities and logs can be helpful in solving exponential and logarithmic equations because they provide a set of rules that can be used to simplify expressions. For example, logarithmic identities such as log(a * b) = log(a) + log(b) and log(a/b) = log(a) - log(b) can be used to simplify expressions containing products and quotients.

However, identities and logarithms can also be confusing because they involve complex concepts and require a solid understanding of logarithmic properties. This can make solving exponential and logarithmic equations challenging for some students.

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Answer:

  305 miles

Step-by-step explanation:

You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.

Distance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.

  distance = speed · time

  total distance = speed1 · time1 + speed2 · time2

  = (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi

Dylan travelled a total of 305 miles.

Answer:

ch.1 = 12x1.2=14.4

ch.2=10.5x1.2=12.6

ch.3=39.3x1.2=47.16

Step-by-step explanation:

You just have to multiply all the chapters by 1.2

i think if im wrong im sorry

Answer: 14.4, 12.6, 49.16

Step-by-step explanation:

Multiply each number by 1.2

12x1.2=14.4

10.5x1.2=12.6

39.3x1.2=49.16

chapter 1 : 14.4

chapter 2: 12.6

chapter 3: 49.16

The temperature at 6 PM at greater than morning temperature at 6 AM by 1.3° C.

We know initially the temperature is 19.4° C.

The new temperature at noon will be = Temperature at 6 AM + temperature after noon

Keep the values

The new temperature at noon will be = 19.4 + 3.8

Performing addition

The new temperature at noon will be = 23.2° C

Temperature at 6 PM = Temperature at noon - temperature fall between noon and 6 PM

Keep the values

Temperature at 6 PM = 23.2 - 2.5

Performing subtraction

Temperate at 6 PM = 20.7° C

The difference between the temperature = 20.7 - 19.4

Performing subtraction

The difference between the temperature is 1.3° C.

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Constants are fixed values that never change, whereas variables are values that can change but are often initialized to “0” or another default value because the program's user will supply the actual values.

In programming, a variable is a value that may vary depending on outside variables or data that has been provided to the program. A program normally consists of instructions that tell the computer what to do and data that it utilizes while running.

The correct values for the variables x and y are 8 and 5, respectively.

[tex]3 \times 8 + 2 \times 5=34[/tex]

[tex]24 + 10 =34[/tex]

[tex]\frac{1}{2}\times 8+2 \times 5=14[/tex]

[tex]4 + 10 =14[/tex]

Constants and variables are typically categorized as certain data kinds. Each data type specifies and restricts the data's shape.

An integer expressed as a decimal number or a string of text characters with a set maximum length are examples of data types. Each object in object-oriented programming includes the data variables of the class of which it is an instance.

Therefore, The methods of the object are made to deal with the actual values that are presented to it when it is utilized.

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Answer:

1480

Step-by-step explanation:

To the nearest 10, is the 10s place. 76 is closes to 80, so round 1476 to 1480. Hope this helps!

The equation that can be used to determine the price of the dress

is x + 0.06x + 35 = 126.16.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Assuming the cost of the dress Francesca bought to be 'x'.

We know, 6% = 0.06 in decimal and  She also paid $35 which was not taxed to have the dress altered.

Therefore, The equation to determine the cost of the dress would be,

x + 0.06x + 35 = 126.16.

1.06x = 126.16 - 35.

1.06x = 91.16.

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The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Let x = number of vegetarian meals

Let y = number of meats.

The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

In this case, the daily budget is 600.

Subtract the equations

y = 275

Number of meats = 275

Number of vegetarian meals = 325 - 275 = 50

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Answer:

-72

Step-by-step explanation:

Assuming it is -x^2 - x and not (-x)^2, then you simply plus in -9 for x:

-(-9)^2-(-9) = -72

Answer:

see graph attached

Step-by-step explanation:

Suppose the prediction of an annual drop in magazine subscriptions of 8% is correct. In that case, the number of subscribers that a magazine with 85,630 subscribers will have in 8 years, using an exponential function, is 43,947.

The exponential function is an expression in the form of f(x) = bˣ, where the b constant is called the base and the x variable is called the exponent.

Exponential functions may describe exponential growth or exponential decay.

Exponential decay refers to a decrease or drop, where the decay rate is known.

The annual drop in magazine subscriptions = 8%

The number of current magazine subscribers = 85,630

The number of years for the prediction = 8 years

Decay factor = (1 - 8%) = 0.92

The number of magazine subscribers in 8 years = 85,630 x 0.92^8

= 85,630 x 0.5132189

= 43,947

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(A) The British literature class is most likely larger, because the standard deviation is lower.

A high standard deviation suggests that the observed data is very variable around the mean. This suggests that the observed data is widely dispersed. Instead, a modest or low standard deviation would suggest that the majority of the observed data is closely packed around the mean.

The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed.

Hence, when standard deviation is lower the class is most likely to be larger in number.

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