Prove or disprove
For function f :→ R→→ R f(x) = x² and every onto function g(x) : [0, [infinity]) → [0, [infinity]) holds
a) f o g = g o f b) f o g is onto [0, [infinity])

The other two solutions of the equation are approximately -0.433 and 2.433, given that one solution is -2.

To find the other two solutions of the equation x^4 + 3x^3 - 3x^2 - 7x + 6 = 0, we can use polynomial factoring or numerical methods.

First, let's divide the polynomial by (x + 2) using polynomial long division or synthetic division.

```

      x^3 - x^2 - 5x + 3

(x + 2) / x^4 + 3x^3 - 3x^2 - 7x + 6

      -x^4 - 2x^3

-----------------

          x^3 - 3x^2 - 7x

          x^3 + 2x^2

-----------------

                -5x^2 - 7x

                -5x^2 - 10x

-----------------

                          3x + 6

                          3x + 6

-----------------

                                 0

```

After the division, we are left with the quadratic equation x^3 - x^2 - 5x + 3 = 0.

To find the remaining solutions, we can use numerical methods such as factoring, completing the square, or using the quadratic formula. In this case, since factoring might not yield integer solutions, we can use numerical methods.

Using numerical methods like the Newton-Raphson method or a graphing calculator, we can find the approximate solutions to be x ≈ -2, x ≈ -0.433, and x ≈ 2.433.

Therefore, the other two solutions of the equation x^4 + 3x^3 - 3x^2 - 7x + 6 = 0 are approximately -0.433 and 2.433.

To learn more about quadratic equation click here

brainly.com/question/30098550

#SPJ11

Answer:

81.25%

Step-by-step explanation:

58-32=26

26/32=0.8125

0.8125x100=81.25

Sorry I'm not that good at explaining but here is something that helped me.

Step-by-step explanation:

hypotenuse = √3^2+8^2

= 8.5

x= √(8.5)^2-9= 7.9

Area = 1/2 x base x height.

Base is 6 units long, height is 7 units long.

Area = 1/2 x 6 x 7 = 21 square units.

Answer:

y = (x - 5)² - 6

Step-by-step explanation:

The parabola y = x² is shifted down by 6 units

⇒ we get the parabola of the equation : y = x² - 6

Then , The parabola y = x² - 6 is shifted to the right by 5 units

⇒ the equation of the new parabola is y = (x - 5)² - 6

Answer:

Step-by-step explanation:

\(4a-3\left(4-a\right)\\\\\mathrm{Expand}\:-3\left(4-a\right):\quad -12+3a\\\\=4a-12+3a\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\\mathrm{Simplify}\:4a-12+3a:\quad 7a-12\\\\=7a-12\)

Circumference = Diameter x PI

The units is the same units as the diameter = cm.

The diameter is shown as 14 cm

Circumference = 14 x PI = 14PI cm.

Answer:

(3,4,5) is the answer

Step-by-step explanation:

Answer:

The answer is 6î + 9j – 15k

Step-by-step explanation:

So,

A = 2î + 3j – 5k

Multiply The value of A with 3 we get,

3A = 3(2î + 3j – 5k)

3A = 6î + 9j – 15k

Thus, The value of 3A is 6î + 9j – 15k

-TheUnknownScientist 72

Step-by-step explanation:

in my opinion

total area = the width × the length

= (3x-4)(-8x+2)

= -24x²+6x+32x -8

= -24x² + 38x -8

Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

Know more about mean delivery time here:

https://brainly.com/question/14268332

#SPJ11

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

To know more about trigonometric visit :

https://brainly.com/question/29156330

#SPJ11

The value of the limit is:

lim(x→a) (5x^2 - 1) / (x + 10)

The limit of a function as x approaches some value. Here's a step-by-step explanation using the given terms:

1. Identify the function: It appears that the function is f(x) = (5x^2 - 1) / (x + 10).

2. Determine the value x is approaching: Since it's unclear what value x is approaching, let's use the symbol 'a' to represent it. We want to find lim(x→a) f(x).

3. Substitute the value of 'a' into the function: Since we don't have a specific value for 'a', let's find the general limit expression:

lim(x→a) (5x^2 - 1) / (x + 10)

4. Analyze the function: As x approaches 'a', we need to check if the function is continuous at that point. If it is continuous, we can directly substitute the value of 'a' into the function.

5. If there is no specific value of 'a' provided, the answer will be expressed in terms of 'a'. In this case, the limit of the function as x approaches 'a' is:

lim(x→a) (5x^2 - 1) / (x + 10)

Without knowing the specific value of 'a', this is the most concise answer I can provide. If you can clarify the question, I'd be happy to help further!

To know more about limit, refer here:

https://brainly.com/question/8533149

#SPJ11

The value that should be entered in range 16 to 20 is 4.

Range is the difference between the highest and lowest values.

Given is a data,

The disparity between values in a data collection can be measured most simply using the range. The range can be calculated by simply disregarding the other values and subtracting the lowest value from the highest value.

The number from 16 to 20 has been occurred for 4 times in the given data, that are 17, 17, 18, 19

Hence, The value that should be entered in range 16 to 20 is 4.

For more references on range, click;

https://brainly.com/question/28135761

#SPJ1

Answer:

Step-by-step explanation:

To solve for the measure of Angle N with the given side lengths, you need to find the inverse tangent (tan^-1). You use the tangent because you have the opposite and adjacent side lengths of the angle.

The step by step solution:

tan(<N)=1.7/6.7

<N=tan(^-1)1.7/6.7

<N=14 degrees

Question 1 below on day 1 city A

on day 3 city B

Question 3 city A has more crimes

for question 2 i need to know the options

Using a moving average of order p = 3, a forecast for time period 6 is 46.

The moving average is a mathematical method for calculating a series of averages using various subsets of the full dataset. It is also known as a rolling average or a running average. The moving average smoothes the underlying data and lowers the noise level, allowing us to visualize the underlying patterns and patterns more readily. In other words, a moving average is a mathematical calculation that employs the average of a subset of data at various time intervals to determine trends, eliminate noise, and better forecast future outcomes. Answer: 46.

More on moving average: https://brainly.com/question/32464991

#SPJ11

The number of visitors that we must sample to construct a 95% confidence interval is (b) 1,030 visitors.

In order to construct the 95% confidence interval with a margin of error of  ±3%, we need to find the sample size that will give us a margin of error of 0.03 or less.

The formula used to find desired sample-size is :

⇒ n = (Z² × p × (1-p)) / (E²)

Where, n = required sample size

Z = Z-score for required level of confidence (1.96 for 95% confidence)

p = proportion of visitors who favor proposal;

E = margin of error = (0.03);

We don't know the value of p, So, we use the sample proportion as an estimate:

⇒ p' = 89/150 = 0.5933;

Substituting the values,

we get,

⇒ n = (1.96² × 0.5933 × (1-0.5933)) / (0.03²)
⇒ 1029.67 ≈ 1030.

Therefore, the number of visitors to sample is (b) 1,030 visitors.

Learn more about Confidence Interval here

https://brainly.com/question/29647810

#SPJ4

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

Learn more about Proportion here :

https://brainly.com/question/26974513

#SPJ1

Answer:

Step-by-step explanation:

To solve this problem, we can use the formula distance = rate x time, or d = rt. We are given the rate and the distance, and we need to find the time. We can rearrange the formula to get t = d/r. Then we can plug in the given values and simplify.

t = d/r

t = 952/357

t = 2.6667

We can round the answer to two decimal places and add the appropriate units. The final answer is:

t = 2.67 hours

As per th presented informations and the given informations, the cylinder's volume can be found out being approximately 45638.3 cubic meters.

To calculate the volume of a cylinder with a given height and radius, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

putting in the present values, we will be getting:

V = π(9²)(18)

V = π(81)(18)

V = 14526π

Rounding the achieved value to the nearest tenth, we get:

V ≈ 14526π ≈ 45638.3

Therefore, the volume of the cylinder is found out to be  nearly 45638.3 cubic meters.

Learn more about volume of cylinder :

https://brainly.com/question/24159177

#SPJ4

The complete question is :

Find the volume of the cylinder. Round your answer to the nearest tenth. Having radius 9m and height 18 m.

Answer:

false

Step-by-step explanation:

not 100% certain though

If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

Know more about zero product property here:

https://brainly.com/question/1626209

#SPJ11

Answer:

The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)

correspond to the x-intercepts of the function graph

Step-by-step explanation:

The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)

are x = 2, x = 3, x = 5

which are located at points (2, 0), (3, 0), (5,0)

These points are the x-intercepts of the graph of the equation
So the x-intercepts of the equation are the roots of the equation

I have graphed this using Geogebra which I am familiar with. You should probably use Desmos as per the instructions

In terms of pi means to include pi in your answer. In other words, don't use 3.14 or 22/7 for pi.

The functions y1 = e^(6x) and y2 = e^(2x) are linearly independent because the Wronskian, which is the determinant of the matrix formed by their derivatives, is nonzero for all x.

To determine the linear independence of the functions y1 and y2, we can compute their Wronskian, denoted as W(y1, y2), which is defined as:

W(y1, y2) = det([y1, y2; y1', y2']),

where y1' and y2' represent the derivatives of y1 and y2, respectively.

In this case, we have y1 = e^(6x) and y2 = e^(2x). Taking their derivatives, we have y1' = 6e^(6x) and y2' = 2e^(2x).

Substituting these values into the Wronskian formula, we have:

W(y1, y2) = det([e^(6x), e^(2x); 6e^(6x), 2e^(2x)]).

Evaluating the determinant, we get:

W(y1, y2) = 2e^(8x) - 6e^(8x) = -4e^(8x).

Since the Wronskian, -4e^(8x), is nonzero for all x, we can conclude that the functions y1 = e^(6x) and y2 = e^(2x) are linearly independent.

Therefore, the linear independence of these functions is demonstrated by the fact that their Wronskian is nonzero for all x.

Learn more about linearly independent  here:

https://brainly.com/question/12902801

#SPJ11

The point on the graph of the function where the slope of the tangent line is 5 is (-3, -28).

We have,

function f(x) = x³ + 9x² + 32x + 14 at which the slope of the tangent line is 5.

So, the slope of the tangent line represents the derivative of the function. So, we need to find the derivative of f(x) and set it equal to 5.

f(x) =  x³ + 9x² + 32x + 14

Taking the derivative of f(x) with respect to x:

f'(x) = 3x² + 18x + 32

Setting f'(x) equal to 5 and solving for x:

3x² + 18x + 32 = 5

3x²+ 18x + 27 = 0

Dividing both sides by 3:

x² + 6x + 9 = 0

Factoring the quadratic equation:

(x + 3)²= 0

x + 3 = 0

x = -3

Now, substitute it into the original function

f(-3) = (-3)³ + 9(-3)² + 32(-3) + 14

f(-3) = -27 + 81 - 96 + 14

f(-3) = -28

Therefore, the point on the graph of the function where the slope of the tangent line is 5 is (-3, -28).

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ4

r = 4/(cos(theta) - (3/4)sin(theta)), This is the polar form of the rectangular equation.

To convert a rectangular equation into polar form, we use the following equations:

x = r cos(theta)
y = r sin(theta)

where r is the distance from the origin to the point (x,y), and theta is the angle between the positive x-axis and the line segment connecting the origin to the point (x,y).

Let's say we have the rectangular equation:

3x - 4y = 12

To convert this into polar form, we first need to solve for y:

y = (3/4)x - 3

Now we substitute the equations for x and y in terms of r and theta:

r sin(theta) = (3/4)r cos(theta) - 3

Simplifying this equation, we get:

r = 4/(cos(theta) - (3/4)sin(theta))

This is the polar form of the rectangular equation. To check our work, we can convert this back into rectangular form:

r = 4/(cos(theta) - (3/4)sin(theta))
r(cos(theta) - (3/4)sin(theta)) = 4
rcos(theta) - (3/4)rsin(theta) = 4
x - (3/4)y = 4

This is the same equation we started with, so our conversion is correct. It's important to be detailed and show all work when converting rectangular equations into polar form to avoid making mistakes.

Learn more about the equation here:

brainly.com/question/29657983

#SPJ11