Find the value of x. Then find the angle measures of the polygon.

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

To learn more about the absolute value of a number from the link

https://brainly.com/question/24368848

#SPJ4

For the normal distribution, 99.7% of the data falls within 3 standard deviations of the mean, the given statement is false.

According to the Empirical rule, approximately 99.7% of all of the data values will lie within 3 standard deviations of each side of the mean. Therefore given statement is false.

The empirical rule likewise alluded to as the three-sigma rule or 68-95-99.7 rule, is a measurable decision that expresses that for a typical conveyance, practically completely noticed information will fall inside three standard deviations (indicated by σ) of the mean or normal (signified by µ).

Specifically, the exact decision predicts that 68% of perceptions fall inside the primary standard deviation (µ ± σ), 95% inside the initial two standard deviations (µ ± 2σ), and 99.7% inside the initial three standard deviations (µ ± 3σ).

To learn more about statistics and probability,

https://brainly.com/question/8058700

#SPJ4

The slope is 2 and the y-intercept is (0,6) or just 6.

Let f be a differentiable function on one variable, and let z=f(x²+y²).

Find y ∂x ∂z −x ∂y ∂z.

Since f is a function of one variable, we can let u=x²+y² and z=f(u) where u is another variable.

Therefore, the Chain Rule gives:

y=zufu and x=zufv,

where fu and fv are the partial derivatives of f with respect to u and v, respectively.

Furthermore, the total differential of z=f(u) is dz=f'(u)du.

From the chain rule, we have du/dx=2x and du/dy=2y.

Substituting the values, we have:

y = fu(2x)z and x = fv(2y)z

Therefore, it follows that:

∂z/∂x=fu(2x),∂z/∂y=fv(2y)

Differentiate the first equation with respect to y and the second equation with respect to x to get:

∂2z/∂y∂x=2fu(fuv)(2x) and ∂2z/∂x∂y=2fv(fuv)(2y)

Simplifying the above, we have:

∂2z/∂y∂x=4xfufv and ∂2z/∂x∂y=4yfvfu.

Using the quotient rule, we obtain:

y∂x/∂z−x∂y/∂z=y/((4xfufv)/4(yfvfu))−x/((4yfvfu)/4(xfufv))=(yfufv)/(x²+y²)−(xfvfu)/(x²+y²)=(yfufv−xfvfu)/(x²+y²).

Therefore, y∂x/∂z−x∂y/∂z=(yfufv−xfvfu)/(x²+y²).

To know more about Variable visit:

https://brainly.com/question/15078630

#SPJ11

∂x/∂z = 1 / (∂z/∂x) = 1 / (2x * ∂f/∂u), and ∂y/∂z = 1 / (∂z/∂y) = 1 / (2y * ∂f/∂u).

∂f/∂u represents the partial derivative of the function f with respect to u.

To find ∂x/∂z and ∂y/∂z for the function z = f(x^2 + y^2), we can use the chain rule.

First, let's differentiate z = f(x^2 + y^2) with respect to x while treating y as a constant:

∂z/∂x = ∂f/∂u * ∂u/∂x

= 2x * ∂f/∂u [where u = x^2 + y^2]

Now, let's differentiate z = f(x^2 + y^2) with respect to y while treating x as a constant:

∂z/∂y = ∂f/∂u * ∂u/∂y

= 2y * ∂f/∂u [where u = x^2 + y^2]

Therefore, ∂x/∂z = 1 / (∂z/∂x) = 1 / (2x * ∂f/∂u), and ∂y/∂z = 1 / (∂z/∂y) = 1 / (2y * ∂f/∂u).

∂f/∂u represents the partial derivative of the function f with respect to u.

To know more about partial derivative, visit:

https://brainly.com/question/32387059

#SPJ11

Answer:

A is the answer ,I am very sure

Step-by-step explanation:

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft

Answer:

one monke plus two monke that's 4 monke

Answer:

MONKE SLAP

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation for a circle is

\((x-h)^2+(y-k)^2=r^2\)

We have our h and k from the center as h = -1 and k = -3, and we also know the radius, which is 6. We also have an x/y coordinate as (-6, -6) and we want to know if that coordinate lies in, on, or outside of the circle. The way we will do that is plug everything into the circle equation and solve. If what we solve for is less than the radius, then the point is inside the circle; if what we solve for is equal to the radius, then the point is on the circle; if what we solve for is greater than the radius, then the point in outside the circle.  Here we go:

\((-6-(-1))^2+(-6-(-3))^2?36\) .  There's a question mark there intentionally. The left side is the one we are solving for to see if it is less than, equal to, or greater than, 36.  Continuing,

\((-6+1)^2+(-6+3)^2? 36\) and

\((-5)^2+(-3)^2?36\) and

25 + 9 ? 36

34 ? 36

We know that 34 is less than 36, so the point lies INSIDE the circle.

Answer:

a

Step-by-step explanation:

because it is in the circle

Answer:

You deposit $1000 in a savings account that earns ... Balance at. End of Year. = Principal + Annual. Interest. = $1000 + $1000(0.06) ... balance in an account that earns interest compounded annually after t years. P = Principal (initial deposit) ... 15. 4.8. —. 12. 16. 268.68 ⋅72. 17. MULTIPLE CHOICE Which graph represents ...

Step-by-step explanation:

Answer:

y = 1/3x -3

Step-by-step explanation:

Answer:

7/25 of a chance or a 28% chance as said in the questiom

Step-by-step explanation:

So, the question says it's a 28% chance or a 28/100 chance.

All you have to do is simplify the fraction or just still right 28% chance.  But for the fraction:

Divide the numerator and denominator by 2 to get 14/50.

Divide both by two again to simplify fully to 7/25

Answer:

y = 3x + 2

Step-by-step explanation:

For this question we have to use the equation y=mx+c

m represents the gradient

c represents where the line crosses the y-axis (the y-intercept)

1) Find the gradient

To find the gradient we have to divide the change in y by change in x

In this question that means we have to divide 3 by 1

3 ÷ 1 = 3

2) Find the y-intercept

We can see that the line crosses the y-axis on the point (0,2) meaning the y-intercept is 2

y = 3x + 2

Hope this helps, have a lovely day! :)

Answer:

Step-by-step explanation:

y=3x+2

Answer:

c. Yes, she is correct because 0.45 and 0.333 are rational numbers. The sum of two rational numbers is a rational number.

Answer:

c

Step-by-step explanation:

ΔABD is congruent with ΔCDB.

Option B is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

A figure that contains two triangles.

Two triangles ΔABD and ΔCDB

AB = CD (given)

BAD = DCB (given)

AD = CB (given)

By SAS rule

ΔABD ≅ ΔCDB

Thus,

ΔABD ≅ ΔCDB

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ2

The Solution.

The triangle that can be used with sine, cosine, and tangent ratios must have the following characteristics:

1. The triangle must be a right-angled triangle.

2. The triangle must have one of its angles as 90 degrees.

3. Another angle must be indicated as the angle of interest.

4. At least two sides and an angle must be identified/represented with values.

5. The ratios under consideration can be used to find all the angles and all the sides.

The Correct option Will be  An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem i.e. A.

The likelihood of an event is expressed by probability. The occurrence of a random event is the subject of this mathematical field of study. The value is between zero and one. In mathematics, probability is a tool for calculating the likelihood that certain events will take place.

Probability is the possibility of something happening. The probability distribution also makes use of this central concept in probability theory. We must first ascertain the total number of possibilities before calculating the likelihood that a specific event will occur.

When something unusual happens, it does not happen frequently in terms of sight or sound.

The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.

Now,

As an unusual event has low probability because it does not happen often and The same cutoff should not be used to detect unexpected events all of the time. Choosing a cutoff is subjective, and it should consider the repercussions of erroneously labelling an occurrence as rare.

Hence,

            An event is unusual if it has a low probability of occurring The choice of a cutoff should consider the context of the problem.

To know more about probability visit the link

https://brainly.com/question/30034780

#SPJ1

The exponential function best represents the growth of the investment.

What is exponential function?

An exponential function can be used to depict the investment's growth. The formula for an exponential function is y = a * b^x, where an is the starting point (in this case, 45,000), b is the growth factor (in this case,

1 + 0.018 = 1.018), and x is the number of time periods (in this case, the number of months).

For example, if we let x represent the number of months, the function would be:

y = 45,000 * 1.018^x

This function represents the growth of the investment as a function of the number of months. As the number of months increases, the value of the investment will grow exponentially according to the formula.

Hence, the exponential function best represents the growth of the investment.

To know more about exponential function, click on the link,

https://brainly.com/question/2456547

#SPJ1

The sum of forecast errors is also known as total forecast error. Therefore, the correct answer is option A, which is "2."

The absolute error of the given data is calculated by subtracting the actual value from the forecasted value, followed by the absolute value.

The errors are then summed up to get the mean absolute deviation. The value used for ||18−20|| in the calculation of MAD and summing up the forecast errors is 2.

Therefore, the correct answer is option A, which is "2."Formula for calculating MAD:MAD = Σ ( | A_i - F_i | ) / n

Where: MAD is the mean absolute deviation|A_i - F_i| represents the absolute error between the actual value (A) and the forecasted value (F)n is the total number of observations, Sum of forecast errors:Σ ( A_i - F_i )Where: A_i is the actual valueF_i is the forecasted value

The sum of forecast errors is also known as total forecast error.

Learn more about absolute deviation here:

https://brainly.com/question/32547820

#SPJ11

When x=8, the ratio of the population of Town A to Town B is 2.98.

Given that, the function p(x)=9x²+10x+400 represent the population of town A and the function Q(x)= 4x² + 12x represents the population of town B.

a. From 2012 to 2014, the population of Town A had a greater average rate of change. The average rate of change of Town A's population can be calculated by taking the change in the population (P(2014) - P(2012)) and dividing it by the change in years (2014 - 2012). This gives the following expression:

[P(2014) - P(2012)] / [2014 - 2012]

Substituting in the values of P(2014) and P(2012) yields:

[9(14²) + 10(14) + 400 - (9(12²) + 10(12) + 400)] / [2014 - 2012]

Simplifying this expression gives us:

[630] / [2]

Therefore, the average rate of change of Town A's population from 2012 to 2014 is 315.

To calculate the average rate of change of Town B's population from 2012 to 2014, we can use the same expression:

[Q(2014) - Q(2012)] / [2014 - 2012]

Substituting in the values of Q(2014) and Q(2012) yields:

[4(14²) + 12(14) - (4(12²) + 12(12))] / [2014 - 2012]

Simplifying this expression gives us:

[336] / [2]

Therefore, the average rate of change of Town B's population from 2012 to 2014 is 168.

Since 315 is greater than 168, Town A's population had a greater average rate of change from 2012 to 2014.

b. Find (P/Q)(X). Evaluate and interpret the expression when X=8

The expression (P/Q)(X) represents the ratio of the population of Town A to Town B as a function of the number of years since 2010.

Substituting in the values of P(x) and Q(x) yields:

(P/Q)(X) = [9x² + 10x + 400] / [4x² + 12x]

When X = 8, this expression simplifies to:

(P/Q)(8) = [9(8²) + 10(8) + 400] / [4(8²) + 12(8)]

= [576 + 80 + 400] / [256 + 96]

= [1056] / [352]

= 2.98

Therefore, when x=8, the ratio of the population of Town A to Town B is 2.98.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ1

Using the information about the rate of change of snow that fell on the ground, a set of data is found and the points are plotted on a graph as shown below.

What is meant by rate of change?

How quickly something changes over time is referred to as its rate of change. So, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The amount of snow when the storm began = 4 in.

The rate at which snow fell till 4 in. = 2in / hr

The storm stopped for the next 5 hours.

The rate at which snow fell for the next 4 hours = 3 in/hr

The rate at which snow melted for the next 4 hours when the sun came out

                                = 5 in/hr

We are asked to make a graph showing the inches of snow on the ground over time using the data that Casho collected.

So let's write the data as follows

Time            Inches of snow

0                        4

1                          4+2 = 6

2                          6+2 = 8

3                          8

4                          8

5                           8

6                            8

7                            8

8                           8 + 3 = 11

9                           11+3 = 14

10                          14 +3 = 17

11                          17 + 3 = 20

12                           20-5 = 15

13                           15-5 = 10

14                           10-5 = 5

15                           5 -5 = 0

Therefore using the information about the rate of change of snow that fell on the ground, a set of data is found and the points are plotted on a graph as shown below.

To learn more about the rate of change, follow the link.

https://brainly.com/question/8728504

#SPJ1

Answer:

B. y = -6

Step-by-step explanation:

As you can see the graph I done is perpendicular

Answer:

B

Step-by-step explanation:

A line perpendicular to the y- axis is a horizontal line parallel to the x- axis, with equation

y = c ( where c is the value of the y- coordinates the line passes through )

The only equation in this form is

y = - 6 → B

The basis for v is {1, x}.

Let's start by breaking down the problem. We need to find the dimension and a basis for the vector space v, which is defined as:

v = {p(x) in 2 : xp'(x) = p(x)}

To find the dimension of v, we need to determine how many linearly independent vectors there are in v. In other words, we need to find the maximum number of vectors in v that can be combined in a linearly independent manner.

Let p(x) = a + bx be an arbitrary polynomial in v. Then, we have:

xp'(x) = p(x)

x(b) = a + bx

x(b) - bx = a

x(b - 1) = a

So, any polynomial in v can be written in the form a + (b - 1)x. This means that v is isomorphic to R^2, the vector space of 2-tuples of real numbers. The dimension of R^2 is 2, so the dimension of v is also 2.

To find a basis for v, we can use the standard basis for R^2, which is {(1,0), (0,1)}. We can then map each element of the basis to a polynomial in v as follows:

(1,0) -> 1

(0,1) -> x

These polynomials satisfy the condition xp'(x) = p(x), and they are linearly independent, since no linear combination of them can give us the zero polynomial. Therefore, the basis for v is {1, x}.

To learn more  about vectors, refer below:

https://brainly.com/question/24256726

#SPJ11

Answer:

76ft

Step-by-step explanation:

The range is the highest number minus the lowest number.

53ft - (-23ft) = 76ft

Answer:

34%

Step-by-step explanation:

LammettHash is right just take it as a whole number (for those of you using acellus)

The final answer:

c=29

Step-by-step explanation:

(21^2+20^2)

(441+400)

\(\sqrt{841}\)

= 29

The linear functions defined in this problem are given as follows:

1. y = -x + 3.

2. y = x - 3.

3. y = 3x + 1.

4. y = -2x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients and their meaning are given as follows:

From the second bullet point above,  the intercepts for each function in this problem are given as follows:

The slopes are given as follows:

The problem is incomplete, hence we just define the linear functions.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

CD is the altitude to side AB of right \(\triangle\)ABC, where m\(\angle\)ACB = \(90^o\) The value of BC is 7.28 units.

Value in math is a concept that describes the magnitude, or size, of a number. It can refer to absolute value, which is the actual number, or it can refer to relative value, which is the number compared to other numbers. Value is important in math because it is used to compare and measure different quantities. For example, in addition and subtraction, the value of the numbers being added or subtracted determines the answer. In multiplication, the value of the factors determines the product. Value is also important for performing calculations, such as finding averages, which requires knowledge of numbers and their relative values.
The given triangle is a right triangle, with ∠acb as the right angle. Using the Pythagorean Theorem, we can find the length of the side BC. The Pythagorean Theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Therefore, BC² = AC² + BD²
Substituting the given values in the equation,
BC² = 52 + (5 1/3)²
Simplifying the equation,
BC² = 25 + 27.69
Therefore, BC² = 52.69
Taking the square root of both sides,
BC = √52.69
Therefore, BC = 7.28 units.
To know more about value click-
brainly.com/question/843074
#SPJ1