what is functional residual capacity ?

The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

domain is x

range is y

domain is time

range is distance

domain is between 0 & 170 seconds

range is 0 & 60 meters

meters per seconds is like

miles per hour so

this graph is about SPEED !

speed is usually indicated by the graph's

SLOPE !

The transformed parent cube root function's equation is,

y = ∛(x-4) - 1.

The equation of the function is satisfied by all (and only those) points that lie on the graph of the function.

Hence, if a point fits on a function's graph, it must also fit the function.

The parent cube root function is transformed in the shown graph

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

At (0,0) in the parent function, the graph changes orientation.

We can observe from the above graph that it changes direction at (4,-1) meaning it is moved 4 units to the right and 1 unit down.

So, the value of h=4  and value of k=1

The equation of the transformed function is,

y = ∛(x-4) - 1

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The system of equations has no solution. Option A is the correct optio.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations is

3x - 9y =0 .....(i)

-x + 3y = -3 .....(ii)

Multiply -3 with equation (ii)

3x - 9y = 9 .....(iii)

Subtract equation (i) from (iii):

3x - 9y = 9

3x - 9y =0

________

        0 = 9

Which is a false statement.

Thus the system of equations has no solution.

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Answer:

the answer is A. 0

Suppose that a certain population obeys the logistic equation dy/dx= ry[1-(y/k)]

a) So if y0= K/3, then

dy/dx=  ry[1-(y/k)]

The above statement is equation 1.

Equation 2 is in the form of

dy/dx + P(t)y = yⁿQ(t)

which is a Bernoulli's differential equation with n=2. So 1- 2= -1

To solve it we put

Then dz/dx= -y⁻²(dy/dx)

This above statement is equation 3.

P(t)= -r, Q(t)= -(r/K)

and integrating factor is given by

IF= e ∫(1-n)P(t)dt= e ∫(-1)(-r)dt= ert

Then the solution is given by

z(IF)= ∫(1-n)Q(t)(IF)dt+C

If given y0= K/3, then

3/K= 1/K+C

Thus the solution to this part is

y⁻1ert= ert/K+2/K= 1/K(2+ert)

To find the time at which the initial population doubled that is 2K/3

Thus

2K/3= Kert/(2+ert)

For r=0.025, then r= 55.452

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Answer:

35xΔ2-67x-22

Step-by-step explanation:

The correlation coefficient for the data shown in the scatter plot is- 0.9.

The correlation coefficient is a measure of the strength of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. The correlation coefficient can be used to measure the strength of the linear correlation between two variables, as well as identify whether a relationship between two variables is positive or negative. It can also be used to compare the strength of different relationships between multiple variables.

The scatter plot shows a strong negative linear relationship between the two variables, indicating that as one variable increases, the other variable decreases. Therefore, the correlation coefficient is likely to be close to -1, making -0.9 the best estimate.

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The three internal angles of the triangle are α = 21.3°, β = 139.7°, and θ = 88.9°.

We can use the Law of Cosines to solve for the angles of the triangle:

cos(α) = (b² + c² - a²) / (2bc)

cos(β) = (a² + c² - b²) / (2ac)

cos(θ) = (a² + b² - c²) / (2ab)

Substituting the values given in the problem, we get:

cos(α) = (12.2² + 50.6² - 18.5²) / (2 x 12.2 x 50.6) = 0.929

α = cos⁻¹(0.929) = 21.3°

cos(β) = (18.5² + 50.6² - 12.2²) / (2 x 18.5 x 50.6) = -0.777 (note the negative value)

β = cos⁻¹(-0.777) = 139.7°

cos(θ) = (18.5² + 12.2² - 50.6²) / (2 x 18.5 x 12.2) = 0.056

θ = cos⁻¹(0.056) = 88.9°

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Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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Answer:

x = [tex]\frac{1}{19}[/tex]

Step-by-step explanation:

2 = 19x + 1  Subtract 1 from both sides

2 - 1 = 19x + 1 - 1

1 = 19x  Divide both sides by 19

[tex]\frac{1}{19}[/tex] = [tex]\frac{19x}{19}[/tex]

[tex]\frac{1}{19}[/tex] = x

The gradient of the surface can be described as a vector.

The gradient of a surface, which is a vector, represents the size and direction of the sharpest increase in value at a certain location. The magnitude of this vector, which denotes the direction of the greatest rate of rise of the surface, indicates how steep the rise is. The influence of this gradient is felt along a surface, which is the difference. It stands in for a unit that is level with the ground.

In mathematics, the vector grad f(x,y,z) = (df/dx, df/dy, df/dz) represents the gradient of a three-variable function with scalar values, f(x,y,z). Variables like optimization and electromagnetism employ the gradient of a surface, which is a crucial notion in vector calculus. In particular, the gradient of a surface is frequently used to compute the normal vector to a surface or to identify the direction of the steepest rise or drop in a landscape.

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Answer:

m = 3

Explanation:

the slop is 3

The equivalent of 1/4 acre in square feet according to the relation between the two is 10,890.

Square feet and acre are the units which are representative of area covered by a land. The conversion of square feet and acre is simple and can be performed through simple formula -

1 acre is equal to 43, 560 square foot

So, using this relationship to find the square feet equivalent of 1/4 acre.

Area covered by 1/4 acre = amount of area covered in acre × equivalent of one acre in square foot

Area covered by 1/4 acre = 1/4 × 43, 560

Performing multiplication on Right Hand Side of the equation

Area covered by 1/4 acre = 10, 890 square feet

Hence, 10, 890 square feet is occupied by 1/4 acre.

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Answer:

Step-by-step explanation:

256. You can make this observation because they pattern has a rule that you multiply by 2 to get the next number.

Answer:

Another observation we can make about this number pattern is that each term is obtained by doubling the previous term. This means that the pattern is an example of exponential growth, where the growth factor is 2.

We can also observe that the sequence is a power of 2, where the first term is 2^2, the second term is 2^3, the third term is 2^4, and so on. In other words, the nth term in the sequence can be represented by the formula 2^(n+1).

Additionally, we can see that the sequence is an increasing sequence, where each term is greater than the previous one. This is because we are multiplying each term by 2, which means that each subsequent term will be twice as large as the previous one.

Answer:

I hope u understand my handwriting

Answer:

9 Paper Clips

Step-by-step explanation:

See picture below :)

MaryAnn can order a total of 213 prints for cost $35, including shipping.

Each print costs $0.15, so MaryAnn can order $35/$0.15 = 233.33 prints, but since she can only order whole prints, she can order a maximum of 233 prints.

The shipping charge is a flat fee of $3.00 per order, regardless of how many prints MaryAnn orders.

Let's say MaryAnn orders x prints, then her total cost would be:

Cost = $0.15 x + $3.00

Since her total cost can't exceed her budget of $35, we can set up the following inequality:

$0.15 x + $3.00 ≤ $35.00

Subtracting $3.00 from both sides, we get:

$0.15 x ≤ $32.00

Dividing both sides by $0.15, we get:

x ≤ 213.33

Since MaryAnn can only order whole prints, she can order a maximum of 213 prints.

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The height of cliff is 62.50 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, the angle of elevation from point A to the top of a cliff is 38°, the point A is 80 feet from the base of the cliff,

Refer to figure attached,

The scene is making a right triangle, with an acute angle 38°, and base (distance from point to base of the cliff) 80 ft, we need to find the length of perpendicular line which is the height of the cliff,

Therefore,

We know that,

tan β = ratio of the perpendicular side to base of a triangle,

Therefore,

tan 38° = AB / 80

AB = 62.50

Hence, the height of cliff is 62.50 ft

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sinθ = -0.9798 (rounded to two decimal places).

What is the Trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

We can use the identity sin²θ + cos²θ = 1 to find sinθ, since we know cosθ:

sin²θ + cos²θ = 1

sin²θ + 0.2² = 1 (substituting cosθ = 0.2)

sin²θ = 0.96

Taking the square root of both sides, we get:

sinθ = ± 0.9798

Since θ is in the second quadrant, sinθ is negative.

Hence, sinθ = -0.9798 (rounded to two decimal places).

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Answer:

484ft

Step-by-step explanation:

Split the shape into different shapes like triangles and squares.

area of a triangle: [tex]A=\frac{ab}{2}[/tex]

Area of a square: A = l x w

Answer:

it will have one real solution

Step-by-step explanation:

The slope of a line that is parallel to the line containing the points (3, 4) and (2, 6) is -2.

To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line containing these points. We can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where:

m = slope

(x1, y1) = coordinates of the first point (3, 4)

(x2, y2) = coordinates of the second point (2, 6)

Substituting the given values, we get:

m = (6 - 4) / (2 - 3)

m = -2

The slope of the line containing the points (3, 4) and (2, 6) is -2.

Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2.

Therefore, the slope of the parallel line is -2.

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The correct statement about position of 2 is the 2 in 142 represents 10 times the value of the 2 in 124.

We know about the place value of digits. It states that the first digit on the Right Hand Side is the units place. Moving to the left, the next digit holds the value of tens. Moving further left the value increases 10 times.

Based on this, 142 has 2 at the leftmost place. Thus, it's value is 2. But, in the number 124, the two is at second position. It makes it value 20 (as 2 × 10 = 20). Therefore, the number in 124 is ten times of the number is 142.

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Answer:

I'd say the first and third options would be correct.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

If it is a fair spinner then

First option is true

second option is true

third option cannot be determined from info given  

4th option is true

The coordinates of triangle A'B'C' after a translation of triangle ABC based on the transformation rule (x, y) → (x - 4, y + 3) are A' (-2, 7), B' (-2, 0), and C' (3, 0).

The coordinates of quadrilateral Q'R'S'T' after a translation based on the transformation rule are Q' (-2, 0), R' (4, 0), S' (-2, -8), and T' (-2, -8).

In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit to the value on the x-coordinate (x-axis) of the pre-image of a function.

By translating the coordinate of triangle ABC to the left by 4 units and vertically upward by 3 units, the coordinates include the following:

(x, y)                               →                          (x - 4, y + 3)

Coordinate A = (2, 4)   →    Coordinate A' (2 - 4, 4 + 3) = (-2, 7).

Coordinate B = (2, -3)   →    Coordinate B' (2 - 4, -3 + 3) = (-2, 0).

Coordinate C = (7, -3)   →    Coordinate C' (7 - 4, -3 + 3) = (3, 0).

By translating the coordinate of quadrilateral QRST vertically downward by 4 units, the coordinates include the following:

(x, y)                               →                          (x, y - 4)

Coordinate Q = (-2, 4)   →    Coordinate Q' (-2, 4 - 4) = (-2, 0).

Coordinate R = (4, 4)   →    Coordinate R' (4, 4 - 4) = (4, 0).

Coordinate S = (-4, -4)   →    Coordinate S' (-4, -4 - 4) = (-2, -8).

Coordinate T = (-2, -4)   →    Coordinate T' (-2, -4 - 4) = (-2, -8).

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The number of ways the adults and the kids can be served is 831600

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

Volume = 1 gallon 3 pints

By conversion

1 gallon = 8 pints

So, we have

Volume = 8 pints +  3 pints

Volume = 11 pints

Also, we have

Adult = 2 cups

Kid = 1 cup

Convert to pints

Volume = 11 pints

Adult = 4 pints

Kid = 2 pints

The number of ways is then calculated as

Ways = 11!/(4! * 2!)

Evaluate

Ways = 831600

Hence, the number of ways is 831600

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The weight of th baby elephant in the month of March would be 247.5 Kg.

Weight of a body is the force exerted by the earth on the body on the surface of the earth towards its center.

Given is that in January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜.

Assume the weight of the baby elephant in March would be {x} Kg. We can write -

{x} = 180 + 3/8 of 180

{x} = 180 + 3/8 x 180

{x} = 180 + 67.5

{x} = 247.5 Kg

Therefore, the weight of th baby elephant in the month of March would be 247.5 Kg.

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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A geometric progression is the sum of the terms of a geometric progression. The nth partial sum of a geometric sequence can be calculated from the first term a1 and the common quotient r as: Sn=a1(1−rn)1−r.

A geometric progression is a sequence of numbers formed by multiplying the common quotient 'r' by each of the preceding numbers. The first term in this series is a1. And the nth partial sum of the series, Sn is calculated by multiplying the first term a1 by the magnitude (1-rn) divided by (1-r).

This equation gives us the sum of the first n terms of a geometric progression. For example, if a1 = 2 and r = 2, then partial sum S3 of the first three terms in the series is 2*(1-2^3)/(1-2)= 2/1 = 2. In other words is the sum of the first three terms of series '2.' The subsumed equation is very useful tool for computing sum of any number of terms in a geometric series.

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No,Sarah would have 16 small stones and 14 large stones on the sixth day, since it's +4 small stones and +3 large stones per day. You must show your working if you want the marks. Best of luck!