this question uses the population growth model. a culture of bacteria starts at 4000 bacteria. after one hour the count is 5000. how many hours will the number of bacteria double?

The given vector field f(x,y) = 39x^2y^2i + 26x^3yj is conservative.

The vector field f(x,y) is given by:
f(x,y) = 39x^2y^2i + 26x^3yj

To check if the vector field is conservative, we need to verify if the curl of the vector field is zero. The curl of a 2D vector field is defined as:

Curl(f) = (∂(26x^3y) / ∂x) - (∂(39x^2y^2) / ∂y)

Calculate the partial derivative with respect to x for the second component (j):

∂(26x^3y) / ∂x = 78x^2y

Calculate the partial derivative with respect to y for the first component (i):

∂(39x^2y^2) / ∂y = 78x^2y

Subtract the second derivative from the first derivative:

Curl(f) = 78x^2y - 78x^2y = 0

Since the curl of the vector field f(x,y) is 0, the vector field is conservative.

The correct question should be :

Determine whether or not the vector field given below is conservative.

f(x,y) = 39x^2y^2i + 26x^3yj

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Answer:

something

Step-by-step explanation: they need numbers

Answer:

x=1

Step-by-step explanation:

2x+3=5

2x=5-3

=2

x= 2÷2

= 1

Answer:

x = 1

Step-by-step explanation:

2x + 3 = 5

2x = 2

x = 1

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Have a nice day!

Answer:

cost price of the bat: $3130.43

Step-by-step explanation:

3600/1.15 = 3130.43

Hope this helps

For solving the inequalities, there are more than four steps.

The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to  Subtract the same number from both sides and the third step is to  Multiply both sides by the same positive number, and the fourth step is to  Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.

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Answer:

On a coordinate plane, a trapezoid has points (0, 0), (0.5, 2), (1, 2), (1.5, 0). Step-by-step explanation: If a trapezoid is dilated with a scale factor between 0 and 1, the resulting trapezoid will look smaller than the original trapezoid.

Step-by-step explanation:

Answer:

never

Step-by-step explanation:

Any triangle can never be a parallelogram because it only has three sides.

quadrilateral with parallel sides is a parallelogram.

Answer:

  f'(x) = -2/√(x³)

Step-by-step explanation:

You want the derivative of f(x) = 4/√x.

The power rule for derivatives is ...

  \(\dfrac{d}{dx}(x^n)=nx^{(n-1)}\)

Applied to the given function, we have ...

  \(f(x)=\dfrac{4}{\sqrt{x}}=4x^{-\frac{1}{2}}\\\\f'(x)=4(-\frac{1}{2}x^{-\frac{3}{2}})\\\\\boxed{f'(x)=-\dfrac{2}{\sqrt{x^3}}}\)

__

Additional comment

The first attachment shows a calculator gives the same result.

The second attachment shows the derivative curve matches the one described by the function we found.

Answer:

B is the answer

Step-by-step explanation:

Rigid motion they don't change shape or size just move around.

Answer:

\(\sqrt{41}\)

Step-by-step explanation:

The part " d6 + i " threw me off track there, so I am going to assume that the question asks us to find the distance between 2 - 4i and 6 + i. This can be determined through a simple " distance formula, " as shown in the attachment below,

\(d = \sqrt{( 6 - 2 )^2 + ( 1 - ( - 4 )^2},\\d = \sqrt{( 4)^2 +( 5 )^2},\\d = \sqrt{41}\)

The distance is √41!

Answer:

41

Step-by-step explanation:

Hope I helped

The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

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Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

Answer:

12.5 % increase

Step-by-step explanation:

percent increase: \(\frac{final-initial}{initial}\) x 100

324-288 = 36/288 = 0.125 x 100 = 12.5 %

Answer:

33

Step-by-step explanation:

To find the mean of 5 numbers, you add the 5 numbers and divide by 5.

Let the unknown number = x.

(27 + 42 + 43 + 35 + x)/5 = 36

(x + 147)/5 = 36

x + 147 = 180

x = 33

Answer: 33

Answer:

200,000 x 1.09^14 =668345.4054

So, 668,345

Hope this helps!

SOLUTION

We want to find the interquartile range of the box and whisker plot in the picture.

Interquartile range is calculated as

In the box and whisker plot

Hence the answer is 6

The amount added each time increases because each initial population is larger. This type of growth is called exponential growth is the answer.

During each measured time period when the per capita growth rate of a population is positive (r > 0), a population will add a number to its population that equals exactly r times the initial population. This process continues with each succeeding time period. Exponential growth is a type of population growth that occurs when the number of individuals in a population increases at a constant percentage per unit of time. In exponential growth, the population increases by a fixed amount in each unit of time. Each time period, the amount added to the population increases because each initial population is larger. Population growth can be modelled by the equation dN/dt = rN, where N is the population size, t is time, and r is the per capita growth rate.

The solution to this differential equation is N = N₀e^(rt), where N₀ is the initial population size and e is the natural logarithm base (approximately 2.71828). The exponential growth model is useful in understanding the growth of populations with abundant resources and no natural limits on growth. However, in reality, no population can grow indefinitely because of environmental factors such as competition for resources, predation, disease, and other factors that limit population growth.

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Answer:

Step-by-step explanation:

We know that the for geometric sequence the terms are \(a,ar^2,ar^3,...\) , where a is the first term and r is the terms of common differences.Here the first term is a=2 and fourth term is 250. So the equation is :\(ar^3=250\implies2r^3=250\implies r^3=125\implies r=5\)

    So we came to know that common difference is 5. Hence the two terms between first and 4 th term is 10 and 50.

Final Answer: Two terms are 10 and 50.

The Function Header includes the name of the function .

it tells us  what type of data it expects to receive and the type of data it will return to the calling function or program.

The body of the function contains the instructions to be executed.

Three parts of function header,

1- return type

2- function name

3- argument list

The function's name is included in the header, which also provides information about the parameters and the type of data the function will return to the caller function or application. The instructions that must be followed are contained in the function's body.

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The complete question is :-

what is the function header and its parts?

Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a three-sided polygon that is also referred to as a trine on occasion (less frequently). There are three sides and three angles in every triangle, some of which may be equal.

Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You do this by twisting one form such that it is in alignment with the other. A rotation is the name given to such a change.

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Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

Answer:

x = 4

Step-by-step explanation:

The point (x, y) on the function f(x) = -4x - 9 that is closest to the point (3, 1) is (x, y) = (-37/17, -5/17).

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)

In this case, we want to minimize the distance between (x, y) on the function f(x) = -4x - 9 and (3, 1). Substituting the values into the distance formula, we have:

d = sqrt((3 - x)² + (1 - (-4x - 9))²)

Expanding the squared terms and simplifying, we have:

d = sqrt((3 - x)² + (1 + 4x + 9)²)

 = sqrt((3 - x)² + (4x + 10)²)

 = sqrt((9 - 6x + x²) + (16x² + 80x + 100))

Using x = -b/2a, we can find the value of x at the vertex:

x = -74 / (2 * 17)

x = -74 / 34

x = -37/17

Substituting this value back into the original expression, we can find the corresponding y-value:

y = -4x - 9

y = -4(-37/17) - 9

y = 148/17 - 9

y = 148/17 - 153/17

y = -5/17

Therefore, the point (x, y) on the function f(x) = -4x - 9 that is closest to the point (3, 1) is (x, y) = (-37/17, -5/17).

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The length of tangent CD is 2 unit.

Tangent of a circle is a straight line which touches the circle at only one point.

Therefore,

AB = AD = radius = 1.5

∠D = 90 degrees

Using Pythagoras theorem,

AC² = AD² + CD²

AC = 1.5 + 1 = 2.5

AD = 1.5

Therefore,

2.5² - 1.5² = CD²

CD² = 6.25 - 2.25

CD² = 4

CD = √4

CD = 2

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Answer:

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Step-by-step explanation:

We can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

To determine the number of practice trials out of 34 that would fall between 59 and 61 seconds, we can utilize the properties of a normal distribution with the given mean and standard deviation.

Given that Alejandro's finishing times are normally distributed with a mean of 60 seconds and a standard deviation of 1 second, we can represent this distribution as follows:

μ = 60 (mean)

σ = 1 (standard deviation)

To find the proportion of trials that fall between 59 and 61 seconds, we need to calculate the area under the normal curve within this range. Since the normal distribution is symmetrical, we can determine this area by calculating the area under the curve between the mean and the upper and lower limits.

Using a standard normal distribution table or a statistical calculator, we can find the z-scores for the values 59 and 61, based on the mean and standard deviation. The z-score represents the number of standard deviations a data point is away from the mean.

For 59 seconds:

z = (59 - 60) / 1 = -1

For 61 seconds:

z = (61 - 60) / 1 = 1

Next, we find the area under the curve between these z-scores. By referring to a standard normal distribution table or using a calculator, we can determine the area associated with each z-score.

The area to the left of z = -1 is approximately 0.1587.

The area to the left of z = 1 is approximately 0.8413.

To find the area between these two z-scores, we subtract the smaller area from the larger area:

Area between z = -1 and z = 1 = 0.8413 - 0.1587 = 0.6826

This means that approximately 68.26% of the trials will fall between 59 and 61 seconds.

To find the number of trials out of 34 that fall within this range, we multiply the proportion by the total number of trials:

Number of trials between 59 and 61 seconds = 0.6826 * 34 ≈ 23.23

Rounding this to the nearest whole number, we can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

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Answer:

y- 2x + 4

Step-by-step explanation:

Answer:

y- 2x + 4

Step-by-step explanation:

Answer:

35/87

Step-by-step explanation:

To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.

The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87

Answer:

a. 4x+8

c. 8x+12

d. 6x+6y+6z

b. 6x+8x

Step-by-step explanation:

The distributive property means that the term on the outside of the parentheses can be multiplied by each term on the inside. Take question C for example. You have to multiply 4 by 2x to get 8x, but also multiply 4 by 3 to get 12. These two terms are then connected by the addition as seen within the parentheses, which gives you 8x+12.

Answer:

98cm^2

Step-by-step explanation:

The triangle is equilateral and each side is 14cm

area of triangle: h*b/2