Find the critical values of:f(x) = x^3 - 3x^2 + 29

The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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Answer:

Robert's salary = $ 9426.65

Step-by-step explanation:

First we need to solve for n ( noel's salary)

And from there we can just sub n value into Robert's salary equation which is (n - 512) [ he earns $512 less than noel]

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Answer:

7/20

Step-by-step explanation:

The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

This is called absolute sign | | or something near to that...

Any number inside the | | will always be positive in the output. For example |3|= 3 and also |-3|= 3

|-x| = x (notice that)

That's the bottom line and the idea of this equation

You will substitute with the value of function g(x) in the function f(g(x)) = x

The value of g(x) is known as it states g(x) = -x

So when substituting it's going to be like that

f(-x) = -x (right)?

But notice they told you that

f(x) = |x| so as we stated earlier if it's

Anything inside the | | is always positive

So f(-x) = x ###

Why?

Because when we substitute

|-x| =x

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:i think its 3.25 miles

Step-by-step explanation:

Answer:

5.2

Step-by-step explanation:

13÷2.5=5.2

The tangent identity is: tan x = sin x / cos x. It relates the tangent, sine, and cosine of an angle in a right triangle.

The Pythagorean identity is: sin² x + cos² x = 1. .

The length of the hypotenuse of a right triangle with legs of equal length is √2 times the length of either leg.

The 30-60-90 triangle theorem states that the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b): c² = a² + b².

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Answer:

1.2in

Step-by-step explanation:

Answer:

(1) 1.2 inches

Answer:

x=15

Step-by-step explanation:

3*5=15

Answer:

x = 15

Step-by-step explanation:

x/3 = 5

3* x/3 = 3*5

x=15

In simplified form... multiply both sides by 3 to get x by itself and you should get, x = 15

Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Step-by-step explanation:

non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa. From the example, Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent. So if Jon got a face card, he would not have eight of clubs

Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Given,

Statements .

Here,

Non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa.

For instance,

Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent.

So if Jon got a face card, he would not have eight of clubs .

Thus option B is correct statement .

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A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Work Shown:

9+15 = 24 students total

9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.

Answer:

=x2-100

Step-by-step explanation:

When I said x2 I mean (x*x)

Answer:

x=-5

Step-by-step explanation:

(8x+4)/2=6x+12

4x+2=6x+12

-2x=10

x=-5

Answer:

x = -5

Step-by-step explanation:

Given equation:

\(\dfrac{1}{2}(8x+4)=6(x+2)\)

Multiply both sides of the equation by 2 to eliminate the fraction on the left side:

\(\implies 2\cdot\dfrac{1}{2}(8x+4)=2\cdot6(x+2)\)

\(\implies (8x+4)=12(x+2)\)

\(\implies 8x+4=12(x+2)\)

Distribute the right side of the equation:

\(\implies 8x+4=12\cdot x+12 \cdot 2\)

\(\implies 8x+4=12x+24\)

Switch sides:

\(\implies 12x+24=8x+4\)

Subtract 8x from both sides of the equation:

\(\implies 12x+24-8x=8x+4-8x\)

\(\implies 4x+24=4\)

Subtract 24 from both sides of the equation:

\(\implies 4x+24-24=4-24\)

\(\implies 4x=-20\)

Divide both sides of the equation by 4:

\(\implies \dfrac{4x}{4}=\dfrac{-20}{4}\)

\(\implies x=-5\)

Therefore, the value of x is -5.

The inverse of a matrix A is A^-1. And I, the identity matrix, is equal to A.A^-1.

The square matrix needs to be non-singular and have a non-zero determinant value in order to get the inverse matrix. Let's think about the 2 x 2 square matrix A.

Inverse of  matrix:

A^(-1)=Adj A/|A|

A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for calculating the inverse of a 2 × 2  matrix. In order to find the inverse of a matrix of order 3 or higher, we also need to be aware of the matrix's determinant and adjoint. When multiplied by the provided matrix, the other matrix that serves as the inverse of that matrix yields the multiplicative identity.

There are two ways to find a matrix's inverse. Through the use of an adjoint of a matrix and simple processes, it is possible to derive the inverse of a matrix. Row or column transformations can be used to carry out the basic operations on a matrix. Additionally, the adjoint and determinant of the matrix can be used to apply the inverse of matrix formula in order to get the inverse of a matrix.

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Answer:

A bat

Step-by-step explanation:

Answer:

The bat flies faster by 7 feet

Step-by-step explanation:

first, you need to find some common ground. 84 and 4 can both be divided by two 84/2=42 so now we know that:

-The bat flies 42 feet in two seconds

-The dove flies 35 feet in two seconds

So we know that the bad flies faster because the number is greater, but by how much?

To find this just subtract 35 from 42 to get 7.

So to summarize

The bat flies faster by 7 feet

Answer:

24

Step-by-step explanation:

Let total number of the chocolates be x.

25% of x = 6 (because 100 - 75 = 25% of chocolates left).

25/100 x x = 6

x = 600/25

x = 24

Hence, 24 is the total amount of chocolates.

Hope it helps :)

The formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) can be proven using the trigonometric identities.

Starting with the definition of cosecant:

cosec (A + B) = 1/sin (A + B)

Using the sum-to-product identity:

sin (A + B) = sinA cosB + cosA sinB

Substituting this expression into the definition of cosecant:

cosec (A + B) = 1 / (sinA cosB + cosA sinB)

Using the difference-to-product identity:

sinA - sinB = 2sin((A - B)/2)cos((A + B)/2)

Dividing both numerator and denominator by 2sin((A - B)/2)cos((A + B)/2), we get:

cosec (A + B) = (sinA cosB - cosA sinB) ÷ (sinA + sinB)(sinA - sinB)

Therefore, the formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) has been proven.

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Answer:

the anwser is 7 buddy hope it helps

Answer:

6 times

Step-by-step explanation:

Turn that fraction into a decimal. 3/4=0.75

Divide!

4.5/0.75=6

A number 4.5 is 6 times of number 3/4.

We have to given that,

To find how many times does 3/4 go into 4.5.

Let us assume that,

x times does 3/4 go into 4.5.

Hence, It can be written as,

⇒ x × 3/4 = 4.5

Solve for x,

⇒ 3x /4 = 4.5

⇒ 3x = 4.5 × 4

⇒ 3x = 18

Divide by 3;

⇒ x = 18/3

⇒ x = 6

Therefore, 4.5 is 6 times of number 3/4.

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Answer:

Option 4

Step-by-step explanation:

The central angles are "Angles in the center"

So,

Central Angles are <AOB, <BOC and <AOC

Answer:

<AOB, <BOC and < AOC

Step-by-step explanation:

There are 3 angles at center O . The largest is <AOC ( = 180 degrees). Thn you have 2 more each equal to 90 degrees.

The measure of the print is 2 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1' = 1/8''

This means,

12 inch = 1/8 inch

Now,

16 feet = 12 x 16 inch = 192 inch

So,

12 inch = 1/8 inch

Multiply 16 on both sides.

16 x 12 inch = 16/8 inch

192 inch = 2 inch

Thus,

2 inches is the measure of the print.

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Answer:

2x + y = 26

Step-by-step explanation:

The standard form of a linear equation is   A x + By = C.

Simplify -2(x - 8)

Multiply -2 by -8

y - 10 = -2x + 16

2x + y - 10 = 16

Add 10 to both sides.

Add 16 and 10

Answer= 2x + y = 26

Equation of parabola in vertex form is 13x² + 26x + 17

Define Parabola

A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.

Given,

vertex (h,k) = (-1, 4)

points (x,y) = (-2, 17)

We know, The equation in vertex form is

y = a(x - h)² + k

put the (h,k) values,

y = a(x - (-1))² + 4

y = a(x + 1)² + 4                     --------- eq(i)

Next, find the value of 'a' by plug in the points of (x, y) in eq(i)

y = a(x + 1)² + 4

⇒17 = a(-2 + 1)² + 4

⇒17 = a(-1)² + 4

⇒17 = a + 4

⇒a = 13

Now, substitute 'a' value in eq(i) to find the equation of parabola

y = a(x + 1)² + 4

⇒ y = 13(x + 1)² + 4

⇒ y = 13(x² + 1 +  2x) + 4

⇒ y = 13x² + 13 + 26x + 4

⇒ y = 13x² + 26x + 17

Therefore, equation of parabola in vertex form is 13x² + 26x + 17

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Answer:

proportional

Step-by-step explanation:

test = 100%

Answer: The correct answer is that it is proportional?