Find the critical points of the function f (x) = x − 1 /x^2 + 3

The surface area of the triangular prism is approximately 44.29 square millimeters.

What is surface area?

Surface area is the total area that the surface of a three-dimensional object covers. It is a measure of the amount of space that the surface of an object occupies. Surface area is usually measured in square units such as square meters, square centimeters, square inches, or square feet.

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

The area of a plane figure is the space enclosed by its boundary.

According to the given information:

To find the surface area of a triangular prism, we need to add up the area of all the faces. A triangular prism has three rectangular faces and two triangular faces.

Let's start by finding the area of the triangular faces. The base of the triangular prism is a right triangle with base 4 millimeters, height 4 millimeters, and hypotenuse 5.7 millimeters. We can use the Pythagorean theorem to find the missing side:

[tex]a^2 + b^2 = c^2\\4^2 + 4^2 = 5.7^2[/tex]

16 + 16 = 32.49

32 = 32.49 - 0.49

32 = 32

So the missing side has length [tex]\sqrt{(5.7^2 - 4^2)} =3.69 millimeters.[/tex] This is the base of each triangular face.

The height of the triangular prism is 3 millimeters, so the height of each triangular face is also 3 millimeters.

The area of each triangular face is:

(1/2) × base × height

= (1/2) × 3.69 × 3

≈ 5.54 square millimeters

So the total area of the two triangular faces is:

2 × 5.54= 11.08 square millimeters

Now let's find the area of each rectangular face. The length of each rectangular face is the same as the base of the triangular face, which is 3.69 millimeters. The width of each rectangular face is the height of the triangular prism, which is 3 millimeters.

The area of each rectangular face is:

length × width

= 3.69 × 3

≈ 11.07 square millimeters

So the total area of the three rectangular faces is:

3 × 11.07

= 33.21 square millimeters

To find the surface area of the triangular prism, we add up the area of all five faces:

11.08 + 33.21

= 44.29 square millimeters

Therefore, the surface area of the triangular prism is approximately 44.29 square millimeters.

To know more about Surface Area visit: https://brainly.com/question/29298005

#SPJ1

The 90% confidence interval based on the data provided will be (0.6152, 0.7848)

It should be noted that standard error = ✓[(p * q) / n]

p = population proportion

q = 1 - p

n = sample size

sample proportion = x / n = 105 / 150 = 0.7

standard error = ✓(p * q) / n] = sqrt[(0.7 * 0.3) / 150] = 0.0516

margin of error = 1.645 * 0.0516 = 0.0848

Confidence interval = sample proportion ± margin of error

                 = 0.7 ± 0.0848

                 = (0.6152, 0.7848)

Learn more about confidence interval on

https://brainly.com/question/15712887

#SPJ1

Answer: ⬇️

Step-by-step explanation:

Given, u=(2,4,−5) and v=(1,−6,9).Now,3u−5v=3(2,4,−5)−5(1,−6,9)=(1,42,−60).

Therefore , the solution of the given problem of unitary method comes out to be once more administer maths and science quizzes on the same day.

The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.

Here,

List the multiples of each integer until we discover a common multiple as one method to determine the least common multiple:

=> 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are all multiples of 8.

=> 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60 are multiples of 6.

As an alternative, we can use the prime factorization technique to identify the smallest common multiple:

=> 8's prime factors are 2 x 2 x 2

=> 6's prime factors are 2 x 3

=> 2 x 2 x 2 x 3 = 24

We can see that 24 is the smallest common multiple once more, and in 24 days,

Mrs Hopkins will once more administer maths and science quizzes on the same day.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

Answer: 50 pounds

Step-by-step explanation:

The maximum weight of the luggage a passenger can bring without charge is 50 pounds.

Mary Ellen has decided to weigh each item as she packs her bag.

weight of Suitcase = 3.65 lbs

weight of clothing = 4.35 lbs

weight of shoes = 8.67 lbs

weight of toiletries = 11.35 lbs

weight of extras = 21.63 lbs

Now we will add the weights of each items

Total weight = 3.65 + 4.35 + 8.67 + 11.35 + 21.63 = 49.65

Rounding to the nearest to the one pound will be = 50 lbs

(Since 0.65 is greater than 0.5 so by rounding off 0.65 will become 1.)

Therefore the estimated weight is 50 pounds.

The first four elements of the sequence are:

a11 = 5350

a12 = 10702

a13 = 21406

a14 = 42814

Starting with a11 = 5350, we can use the recursive formula to find a12:

a12 = 2a11 + 2 = 25350 + 2 = 10702

a13 = 2a12 + 2 = 210702 + 2 = 21406

a14 = 2a13 + 2 = 221406 + 2 = 42814

Therefore, the first four elements of the sequence are:

a11 = 5350

a12 = 10702

a13 = 21406

a14 = 42814

Learn more about sequence on

https://brainly.com/question/6561461

#SPJ1

Step-by-step explanation:

Compounding formula

FV = PV ( 1 + i )^n      FV = Future value (4000)       PV = present value

                      i = decimal interest per PERIOD = .09/365

                      n = periods = 2 1/4 yrs * 365 days/yr = 821.25 periods

4000 = PV ( 1 + .09/365)^821.25

Solve for PV = $ 3266.83

The correct answers for the quadratic equation are:

Roots of a quadratic equation are the points where y = 0.

Abscissa of a quadratic equation are the points where x = 0.

If the equation of a quadratic equation is in the vertex form,

         y = a(x - h)² + k

         Vertex of the U-shaped curve will be (h, k)

Given in the question, where the equation of the u-shaped curve is
y = 2x(x - 11)

Convert the equation in the vertex form,

y = 2x² - 22x

y = 2(x² - 11x)

y = 2 *  (x² - 2 ( 5.5x) + (5.5)² - (5.5)²)

y = 2[(x - 5.5)² - 30.25]

y = 2(x - 5.5)² - 60.5

Hence, the vertex of the U-shaped curve will be (5.5, -60.5).

For x-intercepts,

Substitute y = 0,

0 = 2x(x - 11)

⇒ x = 0, 11

   Therefore, roots of the parabola will be (0, 0) and (11, 0).

and the  ordinate of the vertex is x = 5.5

Learn more about the quadratic equations:
https://brainly.com/question/30098550
#SPJ1

Answer:

270

Step-by-step explanation:

I am showing my mental math, hope this helps you:

45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:

4 x 6 = 24

5 x 6 = 30

Therefore, the answer is:

2 (4 + 3) 0

270

The value of the expression 45 x 6 is 270.

We have,

To calculate the product of 45 multiplied by 6, you can follow these steps:

- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.

- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.

- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 2 to this result: 24 + 3 = 27.

- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.

- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 5 to this result: 24 + 2 = 26.

- Write down the hundred digit of the result, which is 6.

- Combine the hundreds, tens, and units digits together: 6, 7, 0.

- The final product of 45 multiplied by 6 is 270.

So, 45 x 6 = 270.

Thus,

The value of the expression 45 x 6 is 270.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Answer:

The answer is -5

Step-by-step explanation:

Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.

The volume of the inside of the giant sugar cube would be = 3.375cm³

To calculate the volume of a cube, the side length should first be determined from the surface area given.

But the formula for surface area of a cube = 6a²

That is;

surface area = 13.5cm²

a = ?

13.5 = 6(a)²

13.5/6 = a²

a = √13.5/6

= √2.25

= 1.5cm

Therefore the volume of the cube = a³

= 1.5³

= 3.375cm³

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

Complete question:

A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5m² of material to build the cube. What is the volume inside the giant sugar cube? Give an exact answer (do not round).

The calculated value of x in the right triangle is 8.7

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

The right triangle

The value of x in the right triangle can be calculated using the following sine ratio

sin(75) = x/9

Cross multiply the equation

So, we have

x = 9 * sin(75)

Evaluate the products

x = 8.7

Hence, the value of x in the right triangle is 8.7

Read more about right triangle at

https://brainly.com/question/2437195

#SPJ1

Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).

The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:

(y - k)²   = 4p( x -  h)

If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....

y² = 4px

where p is still a nonzero real number.

Learn more about parabolas:
https://brainly.com/question/31142122
#SPJ1

Answer: IN ORDER FROM TOP LEFT OVER

Step-by-step explanation:

1. Example

2. Already correct

3. 43

4. 82

5. Supplementary

6. 68

7. 33

8. Adjacent (could be wrong)

9. 51

10. 128

11. 54

12. Complimentary

13. Parallel

14. 29

15. 117

HOPE THIS HELPS. I MAY HAVE GOTTEN 1 OR 2 WRONG.

To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.

Expanding -10(x-1.7), we get

-10x + 17 = -3

Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation

-10x + 17 + 10x = -3 + 10x

Simplifying, we get

17 = 10x - 3

Next, we add 3 to both sides of the equation

17 + 3 = 10x - 3 + 3

Simplifying, we get

20 = 10x

Finally, we divide both sides of the equation by 10 to isolate x

20/10 = 10x/10

Simplifying, we get

2 = x

Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.

To know more about distributive property here

https://brainly.com/question/6276874

#SPJ1

Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

Exponential function:

A decaying exponential function is modeled by:

⇒ A (t) = A (0) (1 - r)ⁿ

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem:

In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000

Emissions will decrease 2.5% in each successive year, hence r = 0.026

Then, the equation for the amount emitted each year is:

⇒ A (t) = A (0) (1 - r)ⁿ

⇒ A (t) = 80000 (1 - 0.025)ⁿ

⇒ A (t) = 80,000 (0.975)ⁿ

The total amount emitted over the course of the 11 year period is:

T = ∫ 0 to 11 ( A (t) ) dt

Hence:

T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt

Applying the Fundamental Theorem of Calculus:

T = 763,968 kilotons

Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

You can learn more about exponential functions at brainly.com/question/25537936

#SPJ1

Answer:

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{-1-0}{0+3}[/tex]

m = [tex]\frac{-1}{3}[/tex]

Answer: -[tex]\frac{1}{3}[/tex]

87.5% of those who passed the first test also passed the second test.
The given statement in the question is an example of conditional probability rather than supplementary probability. Therefore, the statement is false.

We are given the following information:
- 70% of the class passed both tests.
- 80% of the class passed the first test.
We want to find the percentage of those who passed the first test and also passed the second test.
To do this, we will use the concept of conditional probability.
Let A be the event of passing the first test, and B be the event of passing the second test.

We are asked to find the conditional probability P(B|A), which is the probability of passing the second test given that the student has passed the first test.
Using the formula for conditional probability, we have:
P(B|A) = P(A ∩ B) / P(A)
We know that P(A ∩ B) = 0.7 (since 70% of the class passed both tests) and P(A) = 0.8 (since 80% of the class passed the first test).
Now, we can calculate P(B|A):
P(B|A) = 0.7 / 0.8 = 0.875.

For similar question on conditional probability.

https://brainly.com/question/10739947

#SPJ11

Answer:

A) Sequence 2: 15,13,11,9,7

A) Ordered pairs (12,15), (16,13), (19,11), (22,9), (25,7)

B)  Sequence 1: 1,5,17,53,161

B) Sequence 2: 6,15,33,69,141

B) Ordered pairs (1,6), (5,15), (17,33), (53, 69) (161,141)

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

A) Sequence 2: 15,13,11,9,7

A) Ordered pairs (12,15), (16,13), (19,11), (22,9), (25,7)

B)  Sequence 1: 1,5,17,53,161

B) Sequence 2: 6,15,33,69,141

B) Ordered pairs (1,6), (5,15), (17,33), (53, 69) (161,141)

Step-by-step explanation:

Helping in the name of typing.

Answer:

430

Step-by-step explanation:

Let's call the price of the television set before taxes "x".

The total cost including tax is $451.50, which is equal to x plus 5% of x (the tax). In other words:

x + 0.05x = $451.50

Simplifying the left side by factoring out x, we get:

1.05x = $451.50

Dividing both sides by 1.05, we get:

x = $430

Therefore, the price of the television set before taxes was $430.

It is true that the product of the index [tex](b^9)^3 = b^2^7[/tex]

Indices track asset performance in finance and specify array elements in math and programming; their use varies by subject. Different methods refer to list, vector, or matrix elements. Power law of indices: larger number or letter must match.

This can be expressed mathematically as am+n.

Additionally, there are several Laws of Indices that provide rules for simplifying calculations or expressions involving powers of the same base.

The given question is true or false is [tex](b^9)^3[/tex]= [tex]b^27(b^9)^3[/tex] = [tex](b^9)^3 = b^2^7[/tex]

Learn more about the multiplication law of indices on https://brainly.com/question/28521253#SPJ1

Step-by-step explanation:

For  f(3)     3 is >= 2   so you use the second portion of the function :

f(3)   =  5x+2  = 5(3) + 2   = 17

Answer:

x=109 y=100

Step-by-step explanation:

Answer:

x=100

y=109

Step-by-step explanation:

For any quadrilateral (4-sided shape) inscribed in a circle (all 4 vertices of the quadrilateral are on the edge of the circle),  there is a special relationship between certain pairs of angles within the quadrilateral.

Specifically, opposite angles (angles across from each other) must sum (add) to 180 degrees.

The angle measuring 80 degrees is opposite the angle measuring x degrees, so x + 80 = 180, implying x = 100.

In this case, the angle measuring 71 degrees is opposite the angle measuring y degrees.  So, 71 + y = 180, which implies y = 109.

Answer:

160

Step-by-step explanation:

The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp)

Adjacent = 80

Hypotenuse = x

therefore, cos(60) = 80/x

1/2 = 80/x

x = 80 x 2 = 160

Answer:

it’s 86.6%

Step-by-step explanation:

could be wrong

Answer:

Step-by-step explanation:

Law of sines states that the lengths of the sides of a triangle are proportional to the sines of the corresponding angles.

sinM/17 = sinx/10

sin M = .94551

.94551/17 = sin x /10

cross mulitply and then divide.

.954551 · 10/17 = sin x

9.4555/17 = .5562

sin inverse is 33.793 ° or rounded to 33.8°

The x intercepts are (-2, 0), (2, 0) and (3, 0) and it has vertical asymptotes at x = 4 and x = -4

The x intercepts are the points where the graph intersect with x-axis

In this case, the points are (-2, 0), (2, 0) and (3, 0)

So, the x intercepts are (-2, 0), (2, 0) and (3, 0)

The graph has no horizontal asymptotes

However, it has vertical asymptotes at x = 4 and x = -4

From the graph, the local maxima or minima are

Minima (3, -1) and Maxima (-1, 12)

This is the points where the graph changes it concave-ness

From the graph, we have the point to be (1, 13/2)

Read more about functions at

https://brainly.com/question/4138300

#SPJ1