Part 3 of 4 The vertical scale on a cumulative relative frequency plot starts at what value and ends at what value? starting value ending value

the local minimum value of f is obtained at x = 3.

To find the intervals on which the function f(x) = 5x^4 - 20x^3 + 2 is increasing or decreasing, we need to analyze the behavior of the derivative of the function.

(a) Finding the interval(s) on which f is increasing:

To determine where the function is increasing, we need to find the intervals where the derivative is positive (greater than zero).

First, let's find the derivative of f(x):

f'(x) = 20x^3 - 60x^2

Now, we set f'(x) > 0 and solve for x:

20x^3 - 60x^2 > 0

20x^2(x - 3) > 0

We have two critical points: x = 0 and x = 3.

We create a sign chart to analyze the intervals:

Intervals: (-∞, 0), (0, 3), (3, +∞)

Test point: x = 1

20(1)^2(1 - 3) > 0

-40 < 0 (negative)

From the sign chart, we see that f(x) is increasing on the interval (0, 3).

(b) Finding the interval(s) on which f is decreasing:

To determine where the function is decreasing, we need to find the intervals where the derivative is negative (less than zero).

Using the sign chart from part (a), we see that f(x) is decreasing on the intervals (-∞, 0) and (3, +∞).

(c) Finding the local minimum and maximum values of f:

To find the local minimum and maximum values, we need to examine the critical points and the behavior of the function at those points.

The critical points are x = 0 and x = 3.

To determine if these critical points correspond to local minimum or maximum values, we can analyze the second derivative of f(x).

Taking the second derivative:

f''(x) = 60x^2 - 120x

For x = 0:

f''(0) = 0

For x = 3:

f''(3) = 60(3)^2 - 120(3) = 180 > 0

Since f''(3) > 0, we can conclude that x = 3 corresponds to a local minimum.

As for a local maximum, since f''(0) = 0, we cannot determine if x = 0 corresponds to a local maximum or another type of point (such as an inflection point).

In summary:

(a) The interval on which f is increasing: (0, 3)

(b) The intervals on which f is decreasing: (-∞, 0) and (3, +∞)

(c) The local minimum value of f: x = 3

(d) The local maximum value: DNE (cannot be determined without further information)

to more about intervals visit:

brainly.com/question/14641200

#SPJ11

The area of the green shaded region would be,

⇒ Area = 27 (7 - π)

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A solid figure is shown in image.

Since, The figure is shape of a trapezoid and it contain a circle.

Hence, The area of trapezoid is,

Area = (a + b) h / 2

Where, a and b are base and h is height of trapezoid.

Hence, We get;

The area of trapezoid is,

⇒ Area = (a + b) h / 2

⇒ A = (15 + 20) × 10/2

⇒ A = 35 × 5

⇒ A = 175

And, Area of circle is,

⇒ A = πr²

⇒ A = π × (10/2)²

⇒ A = π × 25

⇒ A = 25π

Hence, The area of the green shaded region would be,

⇒ Area = 175 - 25π

⇒ Area = 27 (7 - π)

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The two lighthouses will flash at the same time again in 21 minutes which is 4:26pm.

The least common multiple refers to the smallest multiple that two or more numbers have in common.

We will get time interval at which the two lighthouses flash simultaneously by finding the least common multiple (LCM) of 3 minutes and 7 minutes.

The prime factorization of 3 is 3

The prime factorization of 7 is 7.

The LCM is found by taking the highest power of each prime factor which is:

LCM(3, 7) = 3 * 7

LCM(3, 7) = 21 minutes

Therefore, the two lighthouses will flash simultaneously again after 21 minutes.

Read more about Lcm

brainly.com/question/233244

#SPJ1

Using Gaussian elimination, the given system of linear equations can be solved as follows:

x₁ = 3, x₂ = -2, x₃ = 1, x₄ = -1, x₅ = 0.

We can represent the given system of equations as an augmented matrix:

[ -2 -1 3 4 5 | 15 ]

[ 3 0 2 -9 -4 | 7 ]

[ 2 -2 4 -3 0 | 7 ]

[ 5 -5 -10 -5 -10 | -20 ]

[ 0 0 3 3 -9 | 9 ]

Applying Gaussian elimination, we perform row operations to transform the matrix into row-echelon form. After performing the necessary operations, we obtain the following matrix:

[ 1 0 0 0 0 | 3 ]

[ 0 1 0 0 0 | -2 ]

[ 0 0 1 0 0 | 1 ]

[ 0 0 0 1 0 | -1 ]

[ 0 0 0 0 1 | 0 ]

From the row-echelon form, we can determine the values of x₁, x₂, x₃, x₄, and x₅. Therefore, the solution to the system of equations is x₁ = 3, x₂ = -2, x₃ = 1, x₄ = -1, and x₅ = 0.


To learn more about Gaussian elimination click here: brainly.com/question/30400788

#SPJ11

The maximum absorbance error for a sample with a true absorbance of 2 is [tex]0.0001\%[/tex], and for a true absorbance of 3 is [tex]0.00015\%[/tex].

What is Error analysis?

A branch of mathematics called error analysis, commonly referred to as uncertainty analysis or error propagation, deals with quantifying and analysing the uncertainties or errors connected with measurements, computations, and experimental data. It entails evaluating measurement precision and accuracy, estimating uncertainty, and comprehending how errors spread across calculations and mathematical procedures.

To calculate the maximum tolerated stray light and maximum absorbance error, we can use the formula:

Maximum Absorbance Error = (Stray Light Level) * (True Absorbance)

a) To find the maximum tolerated stray light for an absorbance error not exceeding 0.001 at a true absorbance of 2, we can rearrange the formula:

Stray Light Level = (Maximum Absorbance Error) / (True Absorbance)

Given:

Maximum Absorbance Error = 0.001

True Absorbance = 2

Plugging in the values, we get:

Stray Light Level = 0.001 / 2 = 0.0005 = 0.05%

Therefore, the maximum tolerated stray light is 0.05%.

b) For a research-quality spectrophotometer with a stray light level of <0.00005% at 340 nm, we can use the same formula to calculate the maximum absorbance error.

Given:

Stray Light Level = 0.00005%

True Absorbance = 2 or 3 (two different cases)

For True Absorbance of 2:

Maximum Absorbance Error = (Stray Light Level) * (True Absorbance) = [tex]0.00005\% * 2 = 0.0001\%[/tex]

For True Absorbance of 3:

Maximum Absorbance Error = (Stray Light Level) * (True Absorbance) = [tex]0.00005\% * 3 = 0.00015\%[/tex]

Therefore, the maximum absorbance error for a sample with a true absorbance of 2 is [tex]0.0001\%[/tex], and for a true absorbance of 3 is[tex]0.00015\%[/tex].

To learn more about Error analysis:

https://brainly.com/question/31939499

#SPJ4

The values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally are p > 0.

To determine the values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally, we can apply the alternating series test.

According to the alternating series test, a series of the form ∑((-1)^n * b_n) converges conditionally if:

1. The terms b_n are positive and decreasing (|b_n+1| ≤ |b_n|), and

2. The limit of b_n as n approaches infinity is 0 (lim(n→∞) b_n = 0).

In this case, our terms are b_n = 1 / (n^p). Let's check these conditions:

1. The terms are positive and decreasing:

  To satisfy this condition, we need to show that |(1 / ((n+1)^p))| ≤ |(1 / (n^p))| for all n.

  Taking the ratio of consecutive terms:

  |(1 / ((n+1)^p)) / (1 / (n^p))| = (n^p) / ((n+1)^p) = (n / (n+1))^p.

Since (n / (n+1)) is less than 1 for all n, raising it to the power p will still be less than 1 for p > 0. Therefore, the terms are positive and decreasing.

2. The limit of the terms as n approaches infinity is 0:

  lim(n→∞) (1 / (n^p)) = 0 for p > 0.

Based on the conditions of the alternating series test, the series converges conditionally for p > 0.

Therefore, the values of p for which the series ∑(n=1)^(∞) ((-1)^n / (n^p)) converges conditionally are p > 0.

To know more about conditionally convergent refer here:

https://brainly.com/question/31064900#

#SPJ11

Answer:

2.25 in²

Step-by-step explanation:

area of square = L X W

= 1.5 X 1.5

= 2.25 (in²)

50% of the prospective customers surveyed would be willing to pay a maximum of $7.01 to $8.

To determine the percentage of prospective customers willing to pay a maximum of $7.01 to $8,

Number of respondents willing to pay $7.01 to $8: 10

Total number of respondents: 20

To find the percentage, we can use the formula:

Percentage

= (Number of respondents willing to pay $7.01 to $8 / Total number of respondents) x 100

= (10 / 20) x 100

= 50%

Therefore, 50% of the prospective customers surveyed would be willing to pay a maximum of $7.01 to $8.

Learn more about Percentage here:

https://brainly.com/question/25704420

#SPJ1

Answer:

Step-by-step explanation: 22

tan30° = [tex]\frac{12}{x}[/tex] ⇒ [tex]\frac{\sqrt{3} }{3}[/tex] = [tex]\frac{12}{x}[/tex] ⇒ x = 12√3

c = √(12√3)² + 12² = 24

P= a+b+c = 12√3 + 12 + 24 = 36+12√3

The solution to the equation 30 = w/2 + 10 for w is w = 40

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

30=w/2 (fraction) +10

Express properly

So, we have the following representation

30 = w/2 + 10

Subtract 10 from both sides

This gives

w/2 = 20

Multiply through by 2

w = 40

Hence, the solution to the equation is w = 40

Read more about equation at

https://brainly.com/question/148035

#SPJ1

Answer:

Step-by-step explanation o:

[tex]\displaystyle \int x^2\cos(4x)dx\hspace{5em}\textit{let's use integration by parts} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ u=x^2\implies \cfrac{du}{dx}=2x\hspace{7em}v=\displaystyle \int \cos(4x)dx\implies v=\cfrac{\sin(4x)}{4} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int x^2\cos(4x)dx\implies \cfrac{x^2\sin(4x)}{4}-\cfrac{1}{2}\int x\sin(4x)dx\leftarrow \stackrel{ \textit{now let's again for this, use} }{\textit{integration by parts}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~ \hspace{5em}\displaystyle \int x\sin(4x)dx \\\\[-0.35em] ~\dotfill\\\\ u_1=x\implies \cfrac{du}{dx}=1\hspace{7em}\displaystyle v_1=\int \sin(4x)dx\implies v_1=\cfrac{-cos(4x)}{4} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int x\sin(4x)dx\implies \cfrac{-x\cos(4x)}{4}+\cfrac{1}{4}\int \cos(4x)dx \\\\\\ \displaystyle \int x\sin(4x)dx\implies \cfrac{-x\cos(4x)}{4}+\cfrac{1}{4}\left( \cfrac{\sin(4x)}{4} \right)[/tex]

[tex]\displaystyle \int x\sin(4x)dx\implies \cfrac{-x\cos(4x)}{4}+\cfrac{\sin(4x)}{16} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{now let's put together both the outer and nested integration by parts}}{\displaystyle \int x^2\cos(4x)dx\implies \cfrac{x^2\sin(4x)}{4}-\cfrac{1}{2}\left[ ~~ \cfrac{-x\cos(4x)}{4}+\cfrac{\sin(4x)}{16} ~~ \right]} \\\\\\ \displaystyle \int x^2\cos(4x)dx\implies \cfrac{x^2\sin(4x)}{4}+\cfrac{x\cos(4x)}{8}-\cfrac{\sin(4x)}{32}+C[/tex]

The slope of the line forming the smallest right triangle, when a line is drawn through the point (1, 2), is 2.

The slope of the line forming the smallest right triangle with the positive x and y axes, when a line is drawn through the point (1, 2), can be determined as follows.

First, let's consider the two axes as the legs of the right triangle, and the line drawn through (1, 2) as the hypotenuse. The slope of the hypotenuse can be calculated by finding the difference in y-coordinates divided by the difference in x-coordinates between the two endpoints.

Since the x-coordinate of the point where the line intersects the x-axis is 0 (positive x-axis), and the y-coordinate of the point where the line intersects the y-axis is 0 (positive y-axis), the difference in y-coordinates is 0 - 2 = -2, and the difference in x-coordinates is 0 - 1 = -1.

Therefore, the slope of the line forming the smallest right triangle is -2/-1 = 2.

Learn more about hypotenuse here: https://brainly.com/question/16893462

#SPJ11

The area of the region R is 24.

To find the area of the region R bounded by the curves f(x) = -x^2 - 4x + 5, g(x) = 2x + 10, and the x-axis over the interval [-5, 1], we need to integrate the difference between the two curves over that interval.

First, let's find the x-values where the two curves intersect:

-f(x) = g(x)

-x^2 - 4x + 5 = 2x + 10

Rearranging the equation:

x^2 + 6x - 15 = 0

Factoring the quadratic equation:

(x + 5)(x - 3) = 0

So the intersection points are x = -5 and x = 3.

Now, let's set up the integral to find the area:

Area = ∫[a, b] (g(x) - f(x)) dx

Since the region is bounded by the x-axis, we take the absolute value of the difference between g(x) and f(x).

Area = ∫[-5, 1] |(2x + 10) - (-x^2 - 4x + 5)| dx

Simplifying:

Area = ∫[-5, 1] |3x^2 + 6x - 5| dx

Since the expression inside the absolute value is non-negative over the interval [-5, 1], we can simplify the integral further:

Area = ∫[-5, 1] (3x^2 + 6x - 5) dx

Integrating term by term:

Area = [x^3 + 3x^2 - 5x] evaluated from -5 to 1

Evaluating the integral at the limits:

Area = (1^3 + 3(1^2) - 5(1)) - (-5^3 + 3(-5^2) - 5(-5))

Calculating the values:

Area = (1 + 3 - 5) - (-125 + 3(25) + 5(5))

Simplifying:

Area = -1 - (-125 + 75 + 25)

Area = -1 + 25

Area = 24

Therefore, the area of the region R is 24.

Learn more about area at https://brainly.com/question/30689896

#SPJ11

The angles are classified as;

angle 1 angle of elevation

angle 2 angle of depression

angle 3 angle of elevation

angle 4 angle of depression

The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point which is above the observer.

Usually measured from the observer's eye to the object or point of interest, and is expressed in degrees or radians.

The angle of elevation is used in trigonometry to solve problems involving right triangles and heights of objects.

The angle of depression is the angle between the horizontal plane and the line of sight or downward direction to an object or point below, the observer, which is measured from the observer's eye to the object or point of interest and is also expressed in degrees or radians.

Learn more about the angle of depression at:

brainly.com/question/17193804

#SPJ1

The complete question is attached below.

Long answer: According to the International Telecommunication Union (ITU), there were an estimated 5 billion unique mobile phone users in the world as of January 2018. However, it is important to note that this number does not necessarily equate to the number of individual subscribers, as some people may have more than one mobile phone or SIM card. Additionally, the number of cell phone subscribers can vary by country and region. For example, according to Statista, the number of mobile phone users in the United States was approximately 266 million in 2018. Overall, while there is not a definitive global estimate for the number of cell phone subscribers in 2018, it is clear that mobile technology continues to have a significant impact on the way people communicate and access information worldwide.

The work required to stretch the spring from 7 cm to 15 cm past equilibrium is 0.268 J (joules).

What is work?

Work is a physical quantity that measures the amount of energy transferred to or from an object due to the application of a force over a displacement. It is the product of the magnitude of the force applied to an object and the distance over which the force is exerted.

The work done to stretch or compress a spring can be calculated using the formula: W = (1/2) * k * Δx².

Given that the spring constant (k) is 140 kg/s² and the displacement (Δx) is 15 cm - 7 cm = 8 cm = 0.08 m, we can substitute these values into the formula:

W = (1/2) * 140 kg/s² * (0.08 m²)

W = 0.5 * 140 kg/s² * 0.0064 m²

W = 0.448 J

learn more about Work here:

https://brainly.com/question/30640810

#SPJ4

The missing variable is given as follows:

B) 105º.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

The polygon in this problem has 4 sides, hence the sum of the interior angle measures is given as follows:

S(4) = 180 x (4 - 2)

S(4) = 360º.

The interior angle measures are given as follows:

Then the value of x is obtained as follows:

85 + 110 + 90 + x = 360

285 + x = 360

x = 75º.

Then, applying the exterior angle theorem, the value of b is given as follows:

b = 180 - 75

b = 105º.

More can be learned about the sum of the interior angle measures of a polygon brainly.com/question/224658

#SPJ1

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

To know more about hypotheses visit:-

https://brainly.com/question/14758286

#SPJ11

The Laplace transform of the solution y(t) to the given initial value problem y"+y=g(t), y(0) = -4, y'(0) = 0, where g(t) = t, t<6; 5, t>6 is represented by the function Y(s) (in terms of s).

To solve the initial value problem y"+y=g(t) with the given initial conditions, we can take the Laplace transform of both sides of the equation. This transforms the differential equation into an algebraic equation in the Laplace domain.

Applying the initial conditions to the transformed equation, we can find the Laplace transform, Y(s), of the solution y(t). The exact expression for Y(s) can be obtained by using the table of Laplace transforms and the properties of Laplace transforms.

By substituting the Laplace transform of the input function, g(t), into the transformed equation, we can solve for Y(s) in terms of the Laplace variable s.

Learn more about  Laplace transform

brainly.com/question/30759963

#SPJ11

The value of y is 5/4.

To solve the ratio equation 12:3 = 5:y, we need to find the value of y.

The ratio 12:3 can be simplified by dividing both sides by their greatest common divisor (GCD), which is 3.

Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. So, the simplified ratio becomes 4:1.

Now we have the equation 4:1 = 5:y. To solve for y, we can set up a proportion:

4/1 = 5/y

Cross-multiplying, we get:

4y = 5 × 1

Simplifying further:

4y = 5

To isolate y, we divide both sides of the equation by 4:

y = 5/4

Therefore, the value of y is 5/4.

for such more question on ratio

https://brainly.com/question/2328454

#SPJ11

Answer: The answer above is true.

Step-by-step explanation:

Both can help you to visualize  time series data.

Have a great day! I hope that this helps! :)

The identity S curl F · dS = 0 holds, given the conditions of the Divergence Theorem and the assumption of continuous second-order partial derivatives for the scalar functions and components of the vector fields.

The identity S curl F · dS = 0 can be proven using the Divergence Theorem and the assumption of continuous second-order partial derivatives.
The Divergence Theorem states that the flux of a vector field through a closed surface S is equal to the triple integral of the divergence of the vector field over the region enclosed by S. Mathematically, it can be written as:

∫∫(curl F) · dS = ∫∫∫(∇ · curl F) dV,

where ∇ is the del operator, curl F is the curl of vector field F, dS is the outward-pointing differential surface element, and dV is the differential volume element.

If we assume that the scalar functions and components of the vector fields have continuous second-order partial derivatives, then we can apply the Divergence Theorem.

Since the curl of F is a vector field, its divergence (∇ · curl F) is a scalar function. According to the Divergence Theorem, if the surface S is closed (i.e., it encloses a region), the flux of curl F through S is equal to the triple integral of the divergence of curl F over the region enclosed by S.

However, in this case, S is not closed but instead represents an open surface. Since the Divergence Theorem is not applicable to open surfaces, we cannot directly equate the flux of curl F through S to the triple integral of the divergence of curl F over the region enclosed by S.

Therefore, we cannot conclude that S curl F · dS equals zero based solely on the conditions of the Divergence Theorem and the assumption of continuous second-order partial derivatives.

For more questions like Divergence Theorem click the link below:

https://brainly.com/question/31272239

#SPJ11

The point-slope form of a line, we can write the equation of the tangent line with slope -1/2 passing through the point (2,1):

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

To find the equation of the tangent line to the curve x^2 + 2xy + 4y^2 = 12 at the point (2,1) on the ellipse, we can use implicit differentiation. By taking the derivative of the equation with respect to x and solving for dy/dx, we can obtain the slope of the tangent line. Then, using the point-slope form of a line, we can determine the equation of the tangent line.

To find the derivative dy/dx, we differentiate both sides of the equation x^2 + 2xy + 4y^2 = 12 with respect to x. Using the chain rule and product rule, we get:

2x + 2y + 2x(dy/dx) + 8y(dy/dx) = 0

Next, we can solve this equation for dy/dx by isolating the terms involving dy/dx:

2x(dy/dx) + 8y(dy/dx) = -2x - 2y

Factoring out dy/dx, we have:

(2x + 8y)(dy/dx) = -2x - 2y

Dividing both sides by (2x + 8y), we get:

dy/dx = (-2x - 2y) / (2x + 8y)

Now, we can substitute the coordinates of the given point (2,1) into the derivative to find the slope of the tangent line at that point:

m = dy/dx = (-2(2) - 2(1)) / (2(2) + 8(1)) = -6/12 = -1/2

Using the point-slope form of a line, we can write the equation of the tangent line with slope -1/2 passing through the point (2,1):

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

Simplifying this equation gives the final equation of the tangent line to the ellipse at the point (2,1).

Learn more about equation of tangent here:

https://brainly.com/question/6617153

#SPJ11

Cos∠W value is 3/√34 from the given right angle triangle

The given triangle VWX is a right angled triangle

At the vertice V the angle is 90 degrees

We have to find the value of cosW

We know that cosine function is a ratio of adjacent side and hypotenuse

The adjacent side is 3 and hypotenuse is √34

Plug in these values in cosw

Cos∠W=3/√34

Hence, Cos∠W is 3/√34 from the given right angle triangle

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

We have the angles as;

A = 40 degrees

B = 126 degrees

C = 14 degrees

To solve a triangle means to find the measures of all its angles and sides based on the given information. The information needed to solve a triangle depends on the specific problem, but generally, you need at least three known values, including side lengths or angles.

We know that;

[tex]c^2 = a^2 + b^2 - 2abCos C\\9 = (8)^2 + (10)^2 - 2(8 * 10)Cos C[/tex]

9= 164 - 160 Cos C

9 - 164 = - 160 Cos C

C = 14 degrees

Then;

a/Sin A = c/Sin C

8/Sin A = 3/Sin 14

A = Sin-1 (8Sin 14/3)

A = 40

Then;

B = 180 - (40 + 14)

B = 126 degrees

Learn more about triangle:https://brainly.com/question/2773823

#SPJ1

To determine which function has a larger maximum, we need to compare the vertex points of both functions.

For Function 1, the equation is f(x) = -3x^2 + 4x + 2. The coefficient of the x^2 term is negative, indicating that the parabola opens downward. The vertex of the parabola can be found using the formula x = -b / (2a), where a is the coefficient of x^2 (-3) and b is the coefficient of x (4).

Using the formula, we find that the x-coordinate of the vertex is x = -4 / (2 * -3) = 2/3. Substituting this value into the equation, we can find the corresponding y-coordinate: f(2/3) = -3(2/3)^2 + 4(2/3) + 2 = 4/3.

For Function 2, the given information states that the graph is a parabola that opens downward and passes through the points (-1/2, 0), (1/2, 4), and (2, 0). The vertex of this parabola can be found as the midpoint between the x-coordinates of the two known points with equal y-values. In this case, it would be the midpoint between (-1/2, 0) and (2, 0), which is (3/4, 0). Therefore, the maximum value is y = 0.

Comparing the y-values of the vertices, we see that f(2/3) = 4/3 and f(3/4) = 0. Since 4/3 is greater than 0, we can conclude that Function 1 has a larger maximum.

Therefore, the correct answer is:

a) Function 1 has a larger maximum.

The missing step in solving the inequality is Subtract 8x from both sides of the inequality is

The given inequality is 8x<2x+3

eight times of x less than two times of x plus three

x is the variable in the inequality which we have to solve

Subtract 2x from both sides

8x-2x<3

6x<3

Divide both sides by 6

x<1/2

Where as they solved inequality by Subtract 3 from both sides of the inequality:

8x-3<2x

Now to isolate the x term we have Subtract 8x from both sides of the inequality:

Hence, Subtract 8x from both sides of the inequality is the missing step in solving the inequality

To learn more on Inequalities click:

https://brainly.com/question/28823603

#SPJ1

The circumference is :

Solution:

To calculate the circumference, we will use the formula C = 2πr.

Diagram for better understanding

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 33\ ft}\end{picture}[/tex]

Now plug in the values. We shouldn't forget to use 3.14 for pi.

[tex]\bold{Circumference = 2 \times 3.14 \times 33}[/tex]

[tex]\bold{Circumference = 6.28 \times 33}[/tex]

[tex]\bold{Circumference = 207.24\:ft}[/tex]

If the radius of a circle is 33 feet, the circle's circumference is 207.24 feet.

Given: Radius of a circle, r = 33 feet

and taking π = 3.14

The circumference of the circle can be calculated using the formula,

C =  2πr.......(i)

where, C ⇒ circumference of a circle, and

            r ⇒ radius of a circle

Therefore, putting the given values in equation (i), we get,

C = 2 x 3.14 x 33

⇒ C = 207.24 feet

Thus, if the radius of a circle is 33 feet, the circle's circumference is 207.24 feet.

Read more about the circumference of a circle on :

https://brainly.com/question/27447563