Can someone help me on all of them I would appreciate it so much!

The equation P(t) = A - Bexp(-ct) can be used to model a worker's productivity after t hours on the job, where A, B, and c are positive constants.

We can then define the change in productivity over a brief period of time dt as

where P(t) is the productivity at time t. We can assume that dP(t) is negative because productivity is assumed to decrease over time.

As a result, the equation can be written as dP(t)/dt = -cP(t), or it can be rewritten as P(t) = Aexp(-ct), where A is a constant. P(t) = A - Bexp(-ct) can be obtained by adding a constant B to the right side of the equation to account for the fact that productivity can never be negative.

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The definite integral given is 2e1/x5 x6 dx.

To solve this integral, we need to use integration by parts. We will use u = 2e1/x5 and dv = x6 dx. Using integration by parts, we have:

∫ udv = uv - ∫vdu

Therefore, we have:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) ∫e1/x5 dx

We can solve this last integral by using the substitution x5 = u. Doing so, we have:

∫ e1/x5 dx = (1/5) ∫ eudu

Using integration by parts, we have:

∫ eu du = eu u - ∫ ueu du

Therefore, we have:

∫ e1/x5 dx = (1/5) [eu u - ∫ ueu du] = (1/5) [eu u - u2 eu/2]

Substituting x5 = u, we have:

∫ e1/x5 dx = (1/5) [ex5 x5 - x10 ex5/2]

Finally, we can substitute this result into the original integral and get the answer:

∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) [(1/5) [ex5 x5 - x10 ex5/2]]

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The height of the pile is increasing at a rate of approximately 0.630 feet per minute when the pile is 11 feet high.

We know that the rate of change of height dh/dt is approximately 0.630 feet per minute when the height h = 11 feet. We also know that the volume of a cone is given by:

\(V = (1/3)\pi r^{2} h\)

where r is the radius of the base and h is the height of the cone. Since the base diameter and height are always the same, we have:

r = d/2 = h/2

Substituting this into the formula for the volume, we get:

\(v=(1/3)\pi (h/2)^{2} h = (1/12)\pi h^{3}\)

Taking the derivative of both sides with respect to time t, we get:

\(dv/dt = (1/4)\pi h^{2} dh/dt\)

We know that dV/dt = 30 (since the height is increasing at a rate of 0.630 feet per minute and the volume of the pile is increasing at the same rate). Substituting this and h = 11 into the equation above, we get:

\(30 = (1/4)\pi (11)^{2} dh/dt\)

Solving for dh/dt, we get:

dh/dt = 240/(121π) ≈ 0.630 feet per minute

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Answer:Bottle B

Step-by-step explanation:

Given

Bottle A has 175 fluid ounce and cost \(\$19.25\)

So it cost \(\frac{175}{19.25}=9.09\ \text{ounce per}\ \$\)

Bottle B has 138 fluid ounce and cost \(\$8.97\)

So it cost \(\frac{138}{8.97}=15.38\ \text{ounce per}\ \$\)

Bottle C has 100 fluid ounce and cost \(\$8.0\)

So it cost \(\frac{100}{8}=12.5\ \text{ounce per}\ \$\)

Bottle D has 72 fluid ounce and cost \(\$7.56\)

So it cost \(\frac{72}{7.56}=9.52\ \text{ounce per}\ \$\)

So, Bottle B delivers more ounces at same price

Answer:

8x⩽112

Step-by-step explanation:

Width of the rectangle (in centimeters) = x

Therefore, the lenght of the rectable is 3x (in centimeters).  

The perimeter of the rectangle (in centimeters) is : 2x+2*3x=2x+6x=8x.

The perimeter of the rectangle is at most 112cm, therefore, 8x⩽112.

The linear approximation of the function at x = 5.1. We can calculate it in the following manner.

To find dy, we first need to calculate f'(x) (the derivative of f(x)):

f'(x) = e^x + xe^x

Now we can plug in x=5 to find f'(5):

f'(5) = e^5 + 5e^5

= 1680.25

Using dx=0.1, we can approximate the change in y (dy) as:

dy = f'(5)dx

= 1680.25 * 0.1

= 168.025

Therefore, when x=5 and dx=0.1, dy = 168.025.

To find the linear approximation using dy, we add dy to f(5):

f(5.1) = f(5) + dy

= (5*e^5) - 5 + 168.025

= 864.025

So the linear approximation using dy is f(5.1) = 864.025.

For the function y = f(x) = x * e^x - 5, we want to find the linear approximation at x = 5 when dx = 0.1.

First, we need to find the derivative f'(x), which represents the slope of the tangent line at any point x:

f'(x) = (x * e^x - 5)'

Using the product rule for derivatives, we get:

f'(x) = (1 * e^x + x * e^x)

Now, we can evaluate f'(5) to find the slope of the tangent line at x = 5:

f'(5) = (1 * e^5 + 5 * e^5) = 6 * e^5

Next, we use the given dx value to approximate the change in y, dy:

dy = f'(5) * dx = (6 * e^5) * 0.1

Now we can find the linear approximation at x = 5.1:

f(5.1) ≈ f(5) + dy

First, calculate f(5):

f(5) = 5 * e^5 - 5

Finally, add dy to f(5) to find the linear approximation:

f(5.1) ≈ (5 * e^5 - 5) + (6 * e^5) * 0.1

This is the linear approximation of the function at x = 5.1.

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The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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Answer:

Wooden Ruler

Step-by-step explanation:

Wood is rigid and cannot bend, stretch, or be changed and adapted.

Answer: x < 1

--------------------    

The two values of c are:

c = -4.6 (smaller value)

c = 5 (larger value)

What is value?

In mathematics, a value usually refers to a numerical quantity assigned to a variable or parameter in an equation, expression, or function.

To find the values of c in the interval (0, 5) such that Uf(P) = 24, where P = {0, c, 5}, we need to calculate the average value of the function f(x) = x over the interval [0, 5] and equate it to 24.

The formula for the average value of a function f(x) over an interval [a, b] is given by:

Uf([a, b]) = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, a = 0 and b = 5, so we have:

Uf([0, 5]) = (1 / (5 - 0)) * ∫[0, 5] x dx

Calculating the integral:

Uf([0, 5]) = \((1 / 5) * [x^2 / 2]\) evaluated from 0 to 5

\(= (1 / 5) * [(5^2 / 2) - (0^2 / 2)]\\\\= (1 / 5) * (25 / 2)\\\\= 5 / 2\\\\= 2.5\)

Now, we can set the average value Uf(P) equal to 24 and solve for c:

Uf(P) = 24

2.5 = 24 / (5 - c)

Multiplying both sides by (5 - c):

2.5 * (5 - c) = 24

12.5 - 2.5c = 24

Subtracting 12.5 from both sides:

-2.5c = 11.5

Dividing both sides by -2.5:

c = -11.5 / 2.5

c ≈ -4.6

We have one value of c as approximately -4.6.

To find the other value of c, we can use the fact that c should be within the interval (0, 5). Since c cannot be negative, the other value of c will be the larger value within the interval. Therefore:

c = 5

So, the two values of c are:

c = -4.6 (smaller value)

c = 5 (larger value)

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Answer:

Domain is all real numbers, x ≠ -5

Range is all real numbers, y ≠ 0

Step-by-step explanation:

Answer:

PART 1

In january she recives the discount but not in Febuary

25*12= 300 For Jan

59.99*10= 599.90 For Feb

Total: 899.90 dollars

PART 2

x stands for amount of months

59.99x=359.94

Divide both sides by 59.99

x= 6

Step-by-step explanation:

Answer:

30 minutes

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it says thousandths and a number group with a th at the end is on the right of the decimal.

Answer:

C: 0.342

Step-by-step explanation:

Here's how it works:

.(tenth)(hundredth)(thousandth)

Therefore,

"Three hundred forty-two thousandths" is 0.342.

Answer:

The area of the parallelogram is 65 square units

Step-by-step explanation:

Do not worry! Sam is here to save you!!!

One way to find the area of a parallelogram is by using decomposition, which involves dividing the parallelogram into two triangles and then finding the area of each triangle. To do this, you can use the formula for the area of a triangle:

Area of a triangle = (base × height) / 2

where the base is one of the sides of the triangle and the height is the length of the perpendicular line segment from the base to the opposite vertex.

To apply this formula to a parallelogram, you can choose one of the sides as the base and the length of the perpendicular line segment from the opposite vertex to the base as the height. Then, you can calculate the area of each triangle and add them together to get the area of the parallelogram.

In your case, assuming that the base of the parallelogram is x units and the height is h units, we can divide the parallelogram into two triangles as shown:

       /        |\

      /        | \

     /          |   \

    /           |h    \

   /            |        \

  /            |           \

 /______|______\

    x              y

Sorry for the bad art.

Triangle 1: base = x, height = h, area = (x × h) / 2

Triangle 2: base = y, height = h, area = (y × h) / 2

Therefore, the total area of the parallelogram is:

Area of parallelogram = Area of triangle 1 + Area of triangle 2

= (x × h) / 2 + (y × h) / 2

= (x + y) × h / 2

= (8 + 2) × 13 / 2

= 65 square units

So the area of the parallelogram is 65 square units.

The least number of computers that must be shipped is 10.

In order to determine the least number of computers that must be shipped, the equation that represents the cost of shipping should be equal to the selling price of the computers.

3000 + 100x = 400x

In order to determine the value of x, take the following steps:

3000 = 400x - 100x

3000 = 300x

x = 3000 / 300

x = 10

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Answer:

y = 4

Step-by-step explanation:

Using the slope, m = 5, and the given point, (1, -6), plug in these values into the point-slope formula:  

y - y1 = m(x - x1)

y - (-6) = 5(x - 1)

y + 6 = 5x - 5

Subtract 6 on both sides of the equation to isolate y:

y + 6 - 6  = 5x - 5 - 6

y= 5x - 11

Therefore, the linear equation in slope-intercept form is y = 5x - 11.  

To find the value of the y-coordinate in point (3, y ):

Plug in the value of x = 3 into the equation, y = 5x - 11

y= 5x - 11

y= 5(3) - 11

y = 15 - 11

y = 4

Therefore, the value of the y-coordinate in point (3, y) is 4.

We can see that the y-intercept of the line is \(-2\) and its slope is \(-\frac{2}{3}\\\) since to get from \((-3,0)\) to \((0,-2)\) we have to run by \(3\) units to the right and rise by \(2\) units down. The the equation of your line in slope-intercept form is \(y = -\frac{2}{3}x -2\\\). All we have to do now is to rewrite it in standard form.

\(y = -\frac{2}{3}x -2\\ 3(y) = (-\frac{2}{3}x -2)3 \\ 3y = -2x -6 \\ 2x +3y = -2x -6 +2x \\ 2x +3y = -6 \)

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

Answer:

Step-by-step explanation:

Simplify step by step:

2( x+7 ) +3 ( x+1 )

We'll distribute:

= ( 2 ) ( x )  +  ( 2 ) ( 7 ) + ( 3 ) ( x ) + ( 3 ) ( 1 )

= 2x + 14  + 3x + 3

We'll Combine Like Terms:

= 2x + 14 + 3x + 3

= ( 2x + 3x ) + ( 14 + 3 )

= 5x + 17 Answer!

Answer:

Step by step Explanation:

2(x+7) +3(x+1)

Open the brackets (multiply outside number by the numbers and letters inside the brackets)

2x + 14 + 3x+ 3

Collect like terms (collect ones that look alike in one side )

2x + 3x + 14 + 3

Add the like terms (add the ones that look alike)

= 5x + 17 (Answer)

I hope you understand it, it's really simple just work step by step.

Good luck ✅.

Answer:

CCCC YES BY SASA

Step-by-step explanation:

Answer:

1,4

Step-by-step explanation:

2 + 1 is 3. 3 + 4 is 7

3 + 1 is 4. 7 + 4 is 11. so it's 1 up and 4 across

Answer: 1/4

Step-by-step explanation:

rise y over run x

The difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m. Then the correct option is B.

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

A frequency generator sends a 550 Hz sound wave through both water and ice.

The wavelength is given as

\(\lambda = \dfrac{v}{f}\)

f = frequency

v = velocity

Then the wavelength in the water will be

\(\rm \lambda _w = \dfrac{1500}{550}\\\\\lambda _w = 2.73\)

The wavelength in the ice will be

\(\rm \lambda _I = \dfrac{3200}{550}\\\\\lambda _I = 5.82\)

Then the difference in wavelength between the wave produced in ice and the wave produced in water will be

\(\rightarrow \lambda _I - \lambda_w \\\\\rightarrow 5.82 - 2.73 \\\\\rightarrow 3.09 \approx 3.1\)

Thus, the difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m.

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Answer:

3.1

Step-by-step explanation:

B

Both still have the same profit. $2 for sandwiches and $3 for wraps. The only reason why there is a difference in the total amount is the change in number of sandwich or wrap sold in a given month. Therefore, next month's total sale is higher than last month's total sale making it safe to assume that the sale of sandwich or wrap is higher than last month's sale.

{hope this helps}

Answer:

4/16 because 5/20 is equivalent to 1/4. 4/16 is also equivalent to 1/4

Step-by-step explanation:

Divide 5/20= 1/4

Multiply 4 times the numerator and the denominator:

4 × 1 = 4

4 × 4 = 16

so we know 4/16 is equivalent to 5/20

The numerical value of each expression,

a. sech(0) = 1

b. coshaA¹ = 0.

(a) The hyperbolic secant function, sech(x), is defined as sech(x) = 1/cosh(x). Therefore, sech(0) = 1/cosh(0) = 1/1 = 1.

(b) The inverse hyperbolic cosine function, coshaA¹(x), is defined as the value y such that cosh(y) = x. Therefore, we want to find y such that cosh(y) = 1. Using the definition of the hyperbolic cosine function, we get:

cosh(y) = (\(e^y\) + \(e^{(-y)}\))/2 = 1

Multiplying both sides by 2 and rearranging, we get:

\(e^y\) + \(e^{(-y)}\) = 2

Multiplying both sides by \(e^y\), we get:

\(e^{(2y)}\) - 2\(e^y\) + 1 = 0

This is a quadratic equation in \(e^y\). Using the quadratic formula, we get:

\(e^y\) = (2 ± √(4 - 4))/2 = 1

Therefore, y = coshaA¹(1) = 0.

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Answer:

60%

Step-by-step explanation:

The importance and advantage of using graph representation when organizing your data are that it makes data presentable, summarizing, better way of comparison of data.

An organized diagram or pictorial representation of the relationship between values or data is referred to as a graph. it is a a diagram that depicts a variable's variation in comparison to that of one or more other variables, such as a series of points, lines, line segments, curves, or areas.

The following are the three advantages of graphs:

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The total amount spent on the 2 pizzas including tip as required to be determined is; 26 dabloons.

It follows from the task content that the total amount spent on ordering the pizzas including tips is to be determined.

First, since each of the pizzas costs; 11 dabloons; it follows that the cost of 2 pizzas would be;

= 2 × 11 dabloons

= 22 dabloons.

Also, since a 4 dabloon tip is given to the delivery person;

Total amount spent is; 22 + 4 = 26 dabloons.

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Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function