A rocket is launched in the air. Its height in feet is given by
ℎ
=
−
16
�
2
+
80
�
h=−16t
2
+80t where
�
t represents the time in seconds after launch. Interpret the coordinates of the vertex in context

Answer:

31.4 in

Step-by-step explanation:

the formula for circumference is 2*\(\pi\)*radius. Since the diameter (which is the radius multiplied by 2) is labeled we can divide 10 by 2 to get the radius. 10/2 is 5. Since pi is an infinite number, we round it to 3.14. Then, plug in the numbers. The expression will be 2*3.14*5. 2* = 10 and 10 * 3.14 you can just move the decimal so the answer is 31.4.

Explanation: To solve this question first we need to know that the terminal point pair (little red point in the image) represented by the coordinates represent the (cosine, sine) as shown bellow

We also need to understand that the "tan" formula can be expressed as follows

So all we need to do is to substitute and calculate.

Step 1: Let's substitute the values and calculate as follows

Step 2: Now let's rationalize the result as follows

Final answer: So the final answer is

.

Answer:

a dollar 1.50

Step-by-step explanation:

you take 4 and multiple by 1.25 which is 5 then you the remaining 3 and divide by 2 which is 1.50

Hope this helps:)

A. Triangle ABC is similar to triangle DEF.

B. The value of x is 21.

What are similar triangles?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are items that feature more than two figures that are the same shape but different sizes.

Here, we have

Given a triangle and we have to show both triangles are similar.

A. ABC will be similar to DEF if two sides along with their corresponding angle of ABC is equal to two sides and their corresponding angle of DEF. ABC will be similar to DEF if the corresponding ratios of all sides of both triangles are equal to each other.

Hence, triangle ABC is similar to triangle DEF.

B. By the property of similar triangles,

= AB/DE = AC/DF

= 14/x = 10/15

x = 21.

Hence, the value of x is 21.

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The calculated measure of angle y is 60 degrees

from the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

using the above as a guide, we have the following:

y = 60

Hence, the value of y is 60 degrees

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1.-

Circumference = 2 pi r

= 2 * 3.14 * 28.1/2

= 44.1 yd letter B

2.- Circumference = 2*pi* r

= = 2*3.14*11

= 69.08 in letter H

3.- Area = pi*r^2

= 3.14*(9)^2

= 254.34 mm^2 Letter B

Answer:

False

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 3x - 3

y = -4x + 4

Step 2: Solve for x

Substitution

Here we see that our x-value would equal 1.

∴ (-3, 0) is NOT a solution to the systems.

To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

To find the zeros of the function y = tan(2x), we can utilize the fact that tan(x) is equal to sin(x)/cos(x).

Given y = tan(2x), we can rewrite it as:

y = sin(2x) / cos(2x)

Now, let's consider the numerator of this expression, which is sin(2x). If we set sin(2x) equal to zero, we can determine the values of x that make the numerator zero:

sin(2x) = 0

By solving this equation, we can find the zeros of sin(2x). The solutions will be the values of x for which sin(2x) equals zero.

Similarly, we can look at the denominator of the expression y = sin(2x) / cos(2x), which is cos(2x). If cos(2x) equals zero, the denominator will be zero, which leads to undefined values for y. These points will be vertical asymptotes of the function tan(2x).

To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

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Answer:

3 angles?

Step-by-step explanation:

The expected value of the random variable, representing the number of green marbles drawn, is 0.53 (option d).

To calculate the expected value, we need to multiply each outcome by its corresponding probability and then sum them up. Let's break down the problem:

There are three possible outcomes for the number of green marbles drawn: 0, 1, or 2.

For the outcome of 0 green marbles:

The probability of drawing 0 green marbles can be calculated by selecting both marbles from the non-green marbles in the bag. The probability of drawing a non-green marble on the first draw is (5+6)/(5+6+4) = 11/15. Since the first marble is replaced before the second draw, the probability of drawing a non-green marble on the second draw is also 11/15. Therefore, the probability of getting 0 green marbles is (11/15) * (11/15) = 121/225.

For the outcome of 1 green marble:

The probability of drawing 1 green marble can be calculated by selecting one green marble and one non-green marble. The probability of drawing a green marble on the first draw is 4/15. The probability of drawing a non-green marble on the second draw is 11/15. Since the first marble is replaced, the probability of drawing a non-green marble on the second draw is still 11/15. Therefore, the probability of getting 1 green marble is (4/15) * (11/15) = 44/225.

For the outcome of 2 green marbles:

The probability of drawing 2 green marbles can be calculated by selecting both marbles from the green marbles in the bag. The probability of drawing a green marble on the first draw is 4/15. Since the first marble is replaced, the probability of drawing a green marble on the second draw is also 4/15. Therefore, the probability of getting 2 green marbles is (4/15) * (4/15) = 16/225.

Now, we can calculate the expected value by multiplying each outcome by its probability and summing them up:

Expected Value = (0 * (121/225)) + (1 * (44/225)) + (2 * (16/225))

= 0 + (44/225) + (32/225)

= 76/225

≈ 0.337

Rounded to two decimal places, the expected value of the random variable, representing the number of green marbles drawn, is approximately 0.34 (option d).

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(a) To break even, the number of calendars that must be sold is 102. (b) The profit from selling 206 calendars at a 20% discount is $746.22.

(a) To calculate the number of calendars that must be sold to break even, we need to consider the total costs and the selling price per calendar. The total costs consist of the sum of space rental and wages per day, which is $185.00 + $271.00 = $456.00.

The profit per calendar is the selling price minus the purchase price, which is $11.21 - $3.26 = $7.95. To break even, the total profit should cover the total costs, so we divide the total costs by the profit per calendar: $456.00 / $7.95 = 57.48. Since we cannot sell a fraction of a calendar, we round up to the nearest whole number, which is 58. Therefore, 58 calendars must be sold to break even.

(b) To calculate the profit from selling 206 calendars at a 20% discount, we first need to determine the discounted selling price. The discount is 20% of the regular selling price, which is 0.20 * $11.21 = $2.24. The discounted selling price is then $11.21 - $2.24 = $8.97 per calendar.

The profit per calendar is the discounted selling price minus the purchase price, which is $8.97 - $3.26 = $5.71. Multiplying the profit per calendar by the number of calendars sold gives us the total profit: $5.71 * 206 = $1,176.26. Therefore, the profit from selling 206 calendars at a 20% discount is $1,176.26.

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The sequence an = ln(3n^2 + 4) − ln(n^2 + 4) converges to ln(3) as n approaches infinity.

To find the limit of the sequence an = ln(3n^2 + 4) − ln(n^2 + 4) as n approaches infinity, we can use algebraic manipulation and properties of limits

an = ln(3n^2 + 4) − ln(n^2 + 4)

= ln[(3n^2 + 4)/(n^2 + 4)]

= ln[3 + 4/n^2]/[1 + 4/n^2]

= ln(3) + ln[1 + (4/n^2)] − ln[1 + (4/n^2)]

= ln(3)

As n approaches infinity, the expression inside the natural logarithm approaches 3, so the limit of the sequence is ln(3):

\(\lim_{n \to \infty} a_n\)  = ln(3)

Therefore, the sequence converges to ln(3).

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The given question is incomplete, the complete question is:

A) Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

an = ln(3n^2 + 4) − ln(n^2 + 4)

lim n→∞ an = ?

It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.

Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.

The driver's shift includes both driving and non-driving time.

Therefore, it is necessary to consider the total amount of time spent on the job.

The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.

Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:

Time for the trip = (Distance ÷ Average Speed) + Breaks

Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2

Time for the trip = 9 + 1

Time for the trip = 10 clock hours

Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.

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The first choice is the correct result

12 months in a year

2 years

2x12=24

74.16x24=1779.84

Heather's total cost of repayment is $1,779.84.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

Given,

Principal = $1,500

Rate = 17% per year (or 0.17 as a decimal)

Time = 2 years

Total interest = (principal × rate × time) / 12

Substitute the given values, and we get:

Total interest = (1500 × 0.17 × 2) / 12 = $51

So, Heather will pay a total of $51 in interest over the two years.

Total repayment = monthly payment × number of months

Here,

Monthly payment = $74.16

Number of months = 2 years × 12 months/year = 24 months

Substitute these values, and we get:

Total repayment = $74.16 × 24 = $1,779.84

Therefore, Heather's total cost of repayment is $1,779.84.

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Answer:

Step-by-step explanation:

30

Step-by-step explanation:

以下の情報を添えて、このチラシを当社の登録従業員の 1 人に渡してください。 より多くのチラシを提出した先生がピザ パーティーを勝ち取ります。

Answer: D) a V shaped graph with vertex at(2,4) which opens up

Step-by-step explanation:

Answer:

d

any more help just ask :)

There are 360 lbs of protein in a ton of feed. Given:Weight of ration = 2000 lbsWeight of corn = 1600 lbsWeight of distillers grain = 400 lbsThe percentage of protein in corn = 9%The percentage of protein in distillers grains = 27%Now, to find out how many pounds of protein are contained in a ton of feed,

we first need to convert the weight of the feed to tons:1 ton = 2000 lbsSo, the weight of the feed in tons = 2000/2000 = 1 tonNow, we need to find out how much protein is contained in 1 lb of corn and distillers grains respectively:In 1 lb of corn, the protein content is 9%.So, the protein content in 1600 lbs of corn = 9% of 1600= 0.09 x 1600= 144 lbsIn 1 lb of distillers grains, the protein content is 27%.So, the protein content in 400 lbs of distillers grains = 27% of 400= 0.27 x 400= 108 lbsTherefore, the total weight of protein in 1 ton of feed = 144 + 108= 252 lbsBut we need the weight of protein in a ton, which is 2000 lbs.

So, we can set up a proportion as follows:1 ton of feed contains 252 lbs of proteinTherefore, x tons of feed contain 2000 lbs of protein.So, x = (2000/252) x 1 = 7.936507936507937 (rounded to 3 decimal places)Therefore, the answer is that there are 360 lbs of protein in a ton of feed.

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a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.

An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

   2x⁴ − 3x³ − 2x² − 4x − 1

 +---------------------------------------

x  |   2x⁵    -3x⁴    -2x³    -4x²   -x

 |

3  |   6x⁴    -9x³    -6x²    -12x    -3

 +---------------------------------------

c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.

    x + 8      x - 5

 +--------------------

x  |  x² + 8x   x² - 5x

 |

-5 | -5x + -40   -5x + 25

 +--------------------

The final total area can be found by adding up the areas of the smaller rectangles:

Total area = x² + 8x + x² - 5x - 5x - 40 + 25

= 2x² - 10x - 15

= 2x² - 10x - 15.

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The rectangular array is represented by the equations "3*(5 + 2a)" and "3*2a*5 + 3*5".

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or an algebraic expression.

given, two rectangles whose one side is equal that is 3.

expression for the area of the rectangle for the first rectangle = 3 * 2a

expression for the area of the rectangle for the second rectangle =

3*(5 + 2a)

Since Expressions are equivalent

3*2a*5 + 3*5 = 3*(5 + 2a)

therefore, two equivalent expressions representing the rectangular array are "3*(5 + 2a)" and  "3*2a*5 + 3*5".

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Answer:

(Choice B) B It decreases.

Step-by-step explanation:

According to the situation, the solution of the value of the expression is as follows

Let us assume

r         80 -2r

5        80 - 10 = 70

4        80 - 8 = 72

3        80 - 6 = 74

2        80 - 4 = 76

1         80 - 2 = 78

As we can from the above calculation that expression value risen if r value decreased

Therefore the correct option is B.

Answer:

It increases

Step-by-step explanation:

The components of the force are approximately Fx = 10.61 N and Fy = 10.61 N. The magnitude of the force is approximately 7.07 N, and its direction is approximately 45 degrees.

a) To find the components of a force at an angle of 45 degrees with a magnitude of 15 N, we can use trigonometry.

Let's assume the force has components Fx and Fy.

Fx = F * cos(θ) = 15 N * cos(45°) = 15 N * (√2/2) ≈ 10.61 N

Fy = F * sin(θ) = 15 N * sin(45°) = 15 N * (√2/2) ≈ 10.61 N

So, the components of the force are approximately Fx = 10.61 N and Fy = 10.61 N.

b) Given the components of a force as (5, 5) Newton, we can use the Pythagorean theorem and trigonometry to find the magnitude and direction.

Magnitude of the force:

|F| = √(Fx² + Fy²) = √(5² + 5²) = √50 ≈ 7.07 N

Direction of the force:

θ = tan⁻¹(Fy / Fx) = tan⁻¹(5 / 5) = tan⁻¹(1) ≈ 45°

So, the magnitude of the force is approximately 7.07 N, and its direction is approximately 45 degrees.

c) To find the resultant velocity of two children pulling a cart, we can use vector addition.

Let's assume the velocity of child A is Va = 5 m/s (east) and the velocity of child B is Vb = 7 m/s (north).

The resultant velocity (Vr) can be found by adding the vectors Va and Vb:

Vr = Va + Vb = 5 m/s (east) + 7 m/s (north)

To find the magnitude and direction of Vr, we can use the Pythagorean theorem and trigonometry:

Magnitude of Vr:

|Vr| = √(Vx² + Vy²) = √((5 m/s)² + (7 m/s)²) ≈ √74 ≈ 8.60 m/s

Direction of Vr:

θ = tan⁻¹(Vy / Vx) = tan⁻¹((7 m/s) / (5 m/s)) ≈ 54.47°

So, the resultant velocity is approximately 8.60 m/s at an angle of 54.47 degrees north of east.

d) Given the components of VA as (5, 1) and VB as (7, 7), we can find the resultant vector VR by adding VA and VB.

VR = VA + VB = (5 + 7, 1 + 7) = (12, 8)

To find the magnitude and direction of VR, we can use the Pythagorean theorem and trigonometry:

Magnitude of VR:

|VR| = √(Vx² + Vy²) = √((12)² + (8)²) = √(144 + 64) = √208 ≈ 14.42

Direction of VR:

θ = tan⁻¹(Vy / Vx) = tan⁻¹(8 / 12) ≈ 33.69°

So, the magnitude of the resultant vector is approximately 14.42, and its direction is approximately 33.69 degrees.

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None of the statements A, B, or C can be determined to be true based on the given information. we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

To determine which statement is true, let's analyze the given information.  We have:

P(B) = 4/1

P(A∪B) = 2/1

P(A|B) = 3/2

Let's evaluate each statement:

A) P(A) = 3/1

This statement is not directly supported by the given information. We cannot determine the value of P(A) solely based on the provided probabilities.

B) P(A∩B) = 12/1

This statement is also not supported by the given information. We do not have enough information to determine the value of P(A∩B).

C) P(B|A) = 5/1

This statement is not supported by the given information. We do not have any direct information about P(B|A), so we cannot determine its value.

D) A and B are not independent.

To determine whether A and B are independent, we can check if P(A∩B) = P(A) * P(B). However, as mentioned earlier, we do not have enough information to determine the value of P(A∩B). Therefore, we cannot conclude whether A and B are independent based on the given information.

In summary, none of the statements A, B, or C can be determined to be true based on the given information. The only conclusion we can draw is that we do not have enough information to determine the values of P(A), P(A∩B), or P(B|A) from the given probabilities.

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All times in the interval 0 ≤ t ≤ π/2 are π/8, π/6, π/4 respectively.

What is the general form of velocity?

The general form of a velocity function is \(v(t) = v_0 + at\)

where,

v(t) is the velocity of an object at time t, \(v_0\) is the initial velocity of the object, a is the acceleration of the object

This formula assumes constant acceleration. If the acceleration is not constant, then the formula becomes more complex, involving calculus and integration.

We can start by integrating the acceleration function to get the velocity function:

v(t) = ∫ a(t) dt = ∫ 8 cos (4t) dt = 2 sin (4t) + C

We know that v(π/8) = 1, so we can use this information to solve for the constant C:

1 = 2 sin (4π/8) + C

1 = 2 sin (π/2) + C

1 = 2 + C

C = -1

Therefore, the velocity function is v(t) = 2 sin (4t) - 1

To determine when the particle is moving to the right, we need to find when its velocity is positive. We can write:

v(t) > 0

2 sin (4t) - 1 > 0

sin (4t) > 1/2

4t > π/6 or 4t < 5π/6

t > π/24 or t < 5π/24

Since we are only interested in the interval 0 ≤ t ≤ π/2, we need to check which of these solutions fall within this interval:

π/24 < π/8 and 5π/24 > π/8

So the particle is moving to the right at times t = π/8, t = π/6, and t = π/4, which are the solutions that fall within the given interval.

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Answer:

in fraction form it is X= 1/3

in decimal form it is X= 0.3 rep.

Step-by-step explanation:

The possible values of ml for each value of l are as follows:
- For l = 0, ml = 0
- For l = 1, ml = -1, 0, 1
- For l = 2, ml = -2, -1, 0, 1, 2
- For l = 3, ml = -3, -2, -1, 0, 1, 2, 3.

The values of ml represent the orientation of the orbital in a given subshell. The possible values of ml depend on the value of l, which is the angular momentum quantum number. The values of l determine the shape of the orbital.

For l = 0, which corresponds to the s subshell, there is only one possible value of ml, which is 0. This indicates that the s orbital is spherical in shape and has no orientation in space.

For l = 1, which corresponds to the p subshell, there are three possible values of ml, which are -1, 0, and 1. This indicates that the p orbital has three orientations in space, corresponding to the x, y, and z axes.

For l = 2, which corresponds to the d subshell, there are five possible values of ml, which are -2, -1, 0, 1, and 2. This indicates that the d orbital has five orientations in space, corresponding to the five axes that can be derived from the x, y, and z axes.

For l = 3, which corresponds to the f subshell, there are seven possible values of ml, which are -3, -2, -1, 0, 1, 2, and 3. This indicates that the f orbital has seven orientations in space, corresponding to the seven axes that can be derived from the x, y, and z axes.

It is important to note that the values of ml are always integers, and they range from -l to +l. The ml values describe the orientation of the orbital in space and play an important role in understanding the electronic structure of atoms and molecules.

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The mean score for the test is 80.

We have,

To find the mean score for the test, we can use the relationship between the mean, the standard deviation, and the z-score.

The formula for the z-score is:

z = (x - μ) / σ

Where:

z is the z-score,

x is the given score,

μ is the mean, and

σ is the standard deviation.

In this case, we know that Cathy's score (x) is 74 and it is 1 standard deviation below the mean (z = -1).

The standard deviation (σ) is given as 6.

Plugging these values into the z-score formula, we can solve for the mean (μ):

-1 = (74 - μ) / 6

Multiplying both sides by 6:

-6 = 74 - μ

Rearranging the equation:

μ = 74 + 6

μ = 80

Thus,

The mean score for the test is 80.

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Answer:

f(x) =  -2x -2 ;  -∞ < x < -4  and  -4 < x < ∞

               6      ;    x = -4

Step-by-step explanation:

         (-1,0)  and  (0 ,-2)

Find the slope using the points.

      \(\sf slope =\dfrac{y_2-y_1}{x_2-x_1}\)

               \(\sf = \dfrac{-2-0}{0-(-1)}\\\\=\dfrac{-2}{0+1}\\\\=-2\)

m = -2

Equation of line in slope y-intercept form: y =mx + b

 y = -2x + b

Plugin any of the point in the above equation. (0, -2)

 -2 = 0 + b

 b = -2

Equation:   y = -2x - 2

Hollow circle is the break point.

Function:

  f(x) =  -2x -2 ;  -∞ < x < -4  and  -4 < x < ∞

               6      ;    x = -4

The function graphed on the axes below as a piecewise function is \($f(x)=\left\{\begin{array}{l}-x-1, \text { for }-6 \leq x < 2 \\ -\frac{1}{2} x-4, \text { for } 2 < x < 6\end{array}\right.$\)

The upper piece of the graph is defined on the interval \($-6 \leq x < 2$\). It has a slope of -1 and a y-intercept of -1, so its equation is \($y=-x-1$\).

The lower piece of the graph is defined on the interval \($2 < x < 6$\). It has a slope of -1 / 2 and would cross the y-axis at -4 if it were extended. Its equation is

\(y=-1 / 2 x-4\)

The two pieces together give the function.

\(f(x)=\left\{\begin{aligned}-x-1, & \text { for }-6 \leq x < 2 \\-\frac{1}{2} x-4, \text { for } 2 < x < 6\end{aligned}\right.$$\)

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

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The half-life of Potassium-42 can be calculated using the following formula:

t1/2 = (ln 2) / λ

where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.

Substituting the values given, we get:

t1/2 = (ln 2) / 0.055

t1/2 ≈ 12.6 hours

Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.

It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.

To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:

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