sqrt x^ 2 +7 -2*=x-1​

The volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.

To find the volume of the solid generated by rotating the region enclosed by the curve of a function $f(x)$ and the x-axis around the x-axis, we use the formula:

$V = \int_{a}^{b} \pi [f(x)]^2 dx$

where $a$ and $b$ are the limits of integration.

Let's assume the function $f(x) = x^2 - 1$, then we have:

$V = \int_{-1}^{1} \pi [(x^2 - 1)]^2 dx$

$V = \int_{-1}^{1} \pi (x^4 - 2x^2 + 1) dx$

$V = \pi \left[\frac{x^5}{5} - \frac{2x^3}{3} + x\right]_{-1}^{1}$

$V = \pi \left[\left(\frac{1}{5} - \frac{2}{3} + 1\right) - \left(-\frac{1}{5} + \frac{2}{3} - 1\right)\right]$

$V = \pi \left[\frac{16}{15}\right]$

$V = \frac{16\pi}{15}$

Therefore, the volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.

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The maximum difference in radius for 295/75R22.5 trailer tires is 0.625 inches.

The tire size 295/75R22.5 represents certain measurements. The first number, 295, refers to the tire's width in millimeters. The second number, 75, represents the aspect ratio, which is the tire's sidewall height as a percentage of the width. The "R" stands for radial construction, and the number 22.5 denotes the diameter of the wheel in inches.

To calculate the maximum difference in radius, we need to determine the difference between the maximum and minimum radius values within the given tire size. The aspect ratio of 75 indicates that the sidewall height is 75% of the tire's width.

To find the maximum radius, we can calculate:

Maximum Radius = (Width in millimeters * Aspect Ratio / 100) + (Wheel Diameter in inches * 25.4 / 2)

For the given tire size, the maximum radius is:

Maximum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 388.98 mm

Similarly, we can find the minimum radius by considering the minimum aspect ratio value (in this case, 75) and calculate:

Minimum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 368.98 mm

The difference in radius between the maximum and minimum values is:

Difference in Radius = Maximum Radius - Minimum Radius ≈ 388.98 mm - 368.98 mm ≈ 20 mm

Converting this to inches, we have:

Difference in Radius ≈ 20 mm * 0.03937 ≈ 0.7874 inches

Therefore, the maximum difference in radius for 295/75R22.5 trailer tires is approximately 0.7874 inches, which can be rounded to 0.625 inches.

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Answer:

The answer the first question is: Always acute

The answer to the second is: 65 degrees

Step-by-step explanation:

:P

Answer:

To convert gallons to liters, we need to multiply the number of gallons by 3.78541, which is the conversion factor.

Capacity in liters = 16 gallons * 3.78541 liters/gallon

Capacity in liters = 60.56 liters (rounded to the nearest tenth)

Therefore, the capacity of the gas tank in liters is approximately 60.6 liters.

Answer:

60.6

Step-by-step explanation:

First, we find how many liters there are in a gallon. We find there are 3.78541178 liters in a gallon. 16*3.78541178 =60.5665885 Rounding to the nearest tenth, we get 60.6 as our answer.

The nurse will have to administer 3 milliliters with each dose.

When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:

medication f 0.05 mg/ml.

Milliliters will the nurse administer with each dose :

The conversion factor from mcg to mg is 1/1000.

Therefore, 150 mcg = 150/1000 = 0.15 mg.

The nurse has to administer 0.15 mg of medication f per dose.

The medication f available with the pharmacy is 0.05 mg/ml.

So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).

Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.

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Here is the summary of the relation J on all integers:

a. 1 J 2 : No

b. 2 J 1 : Yes

c. 3 J 6 : Yes

d. 17 J 51 : No

e. Another example of x and y in relation J: 4 J 12 (4 is related to 12 under relation J)

To define a relation J on all positive integers is following:

a. No, 1 is not a factor of 2, so 1 does not divide 2.

Therefore, 1 is not related to 2 under relation J.

b. Yes, 2 is a factor of 1 (specifically, 2 divides 1 zero times with a remainder of 1), so 2 divides 1.

Therefore, 2 is related to 1 under relation J.

c. Yes, 3 is a factor of 6 (specifically, 3 divides 6 two times with a remainder of 0), so 3 divides 6.

Therefore, 3 is related to 6 under relation J.

d. No, 17 is not a factor of 51, so 17 does not divide 51.

Therefore, 17 is not related to 51 under relation J.

e. Let's choose x = 4 and y = 12.

Then we need to check if x divides y. We can see that 4 is a factor of 12 (specifically, 4 divides 12 three times with a remainder of 0), so 4 divides 12.

Therefore, 4 is related to 12 under relation J.

To summarize:

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The solution to the system of equations using the substitution method is (7,2).

No, the substitution approach cannot be used to solve every system of equations. It can be challenging to replace one equation with another in some systems because they feature equations that are challenging or impossible to solve for one variable in terms of the other. Other approaches, such graphing or elimination, could be more useful in such circumstances.

Given that, the two equations are:

x= 4y - 1

3x + 2y = 25

Substitute x = 4y - 1 into the second equation:

3(4y - 1) + 2y = 25

12y - 3 + 2y = 25

14y - 3 = 25

14y = 28

y = 2

Substitute the value of y in equation:

x = 4y - 1

x = 4(2) - 1

x = 7

Hence, the solution to the system of equations using the substitution method is (7,2)

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Answer:

60%

Step-by-step explanation:

36/60 X 100 = 3600/60 = 360/6 = 60%

If you have been asked to assemble a two person team from among your five person team, then there are 10 different teams

Total number of members for the team = 5

Number of members that we need to assemble = 2

Here we have to use the combination

The combination is defined as the number of ways of selecting samples from the collection and the order of the collection does not matter

The number of combination of 2 members from a 5 member team = \(5C_2\)

= 5! / 2!(5-2)!

= 5! / 2! × 3!

= (5 × 4 × 3!) /(2! × 3!)

= (5 × 4) / 2

= 20 / 2

= 10

Therefore, there are 10 different teams

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The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Answer: 6.75 or 6 3/4

Step-by-step explanation: 3 3/8 x 2 = 6.75 Brainliest please?

Solution a needed 70 ounces and solution b needed 50 ounces

What does "1 ounce" mean?

One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.

One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.

So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:

50% * x + 20% * (100-x) = 41% * 100

Dropping the ‘%’ we get

50x + 2000 - 20x = 4100

30x = 2100

x = 2100/30 = 70

Hence 70 ounces will be needed

Solution a = 70 ounces

Solution b = 50 ounces

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Answer:

3,600 seconds

Step-by-step explanation:

multipy how many hours by 3,600

(so 1 times 3,600)

Answer:

3,600 seconds

Step-by-step explanation:

\(\frac{60 seconds}{1 minute} (\frac{60 minutes}{1 hour} )=\frac{3,600 seconds}{1 hour}\)

Answer:

1/2 or .5

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:hope this helps! :)

Answer:

A,C,D

Step-by-step explanation:

The only one you might use it the triangle

The third approximation to 63 using Newton's method with initial approximation x = 3 is equal to 8.625.

Use Newton's method to find the root of a function,

Follow these steps,

Choose an initial approximation x_0.

Calculate the function value f(x_0) and the derivative f'(x_0).

Use the formula,

x_1 = x_0 - f(x_0)/f'(x_0)

To calculate a new approximation x_1.

Repeat steps 2 and 3 with x_1 as the new initial approximation,

until we obtain the desired accuracy.

For this problem, we want to find the square root of 63,

which is equivalent to finding the root of the function f(x) = x^2 - 63.

Starting with x_0 = 3, we have,

f(x) = x^2 - 63

⇒f'(x) = 2x

At x_0 = 3,

f(x_0) = 3^2 - 63

         = -54

f'(x_0) = 2×3

          = 6

Using the formula for Newton's method, we get,

x_1 = x_0 - f(x_0)/f'(x_0)

      = 3 - (-54)/6

      = 3 + 9

      = 12

So, the second approximation to the square root of 63 is 12.

To obtain the third approximation, we repeat the process with x_1 as the new initial approximation,

At x_1 = 12,

f(x_1) = 12^2 - 63

        = 81

f'(x_1) = 2× 12 = 24

Using the formula for Newton's method, we get,

x_2 = x_1 - f(x_1)/f'(x_1)

= 12 - 81/24

= 8.625

Therefore, the third approximation to the square root of 63 using Newton's method, rounded to five decimal places, is Xs = 8.625.

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well, for the piece-wise function, we'd like to know f(-2), or namely what is f(x) when x = -2?

well, f(x) is 2 for x = -1

f(x) is 4 for x > -1

keeping in mind that in the negative side of the number line, the closer to 0, the larger, thus -1 is much larger than -1,000, so  hmmm -2 is farther from 0 than -1 is, so -1 is larger than -2, so when x = -2, x < -1, and the function that applies when x < -1 is -(x+1)² + 4, so then

\(f(x)= \begin{cases} -(x+1)^2 + 4&\stackrel{-2}{x} < -1\\\\ 2&x=-1\\\\ 4&x > -1 \end{cases} \\\\\\ f(-2)\implies -(~~(-2)+1~~)^2 + 4\implies -(-1)^2+4\implies -(-1)(-1)+4 \\\\\\ -(1)+4\implies -1+4\implies \text{\LARGE 3}\)

Answer: f(-2)=3

Step-by-step explanation:

\(f(x)=\left\{\begin{array}{ccc}-(x+1)^2+4\ for\ x < -1\\2\ \ \ \ for\ \ x=-1\\4\ \ \ for \ \ \ x > -1\end{array}\right\)

\(-2\in(-\infty,-1)\\Hence,\)

\(f(-2)=-(-2+1)^2+4\\f(-2)=-(-1)^2+4\\f(-2)=-1+4\\f(-2)=3\)

Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

Answer:

de qye hablas xd

Step-by-step explanation:

cual es la pregunta.?

Answer:

las opciones?

Step-by-step explanation:

the options?

Answer:

75

Step-by-step explanation: 100 divided by 4 = 25.

100 - 25 = 75.

Answer:

75$

Step-by-step explanation:

Original Price of the Item: $

100

Discount Percent (% off):

25

%

Results:

Amount Saved (Discount): $

25

Sale / Discounted Price: $

75

Answer: To find the dimensions of the rug, we need to subtract the width of the floor strip from both the length and the width of the room. Let x be the width of the floor strip in feet. Then the dimensions of the rug will be 18-2x by 26-2x.

The area of the rug is given by:

(18-2x)(26-2x) = 180

Expanding the right-hand side gives:

468 - 72x + 4x^2 = 180

Rearranging the equation gives:

4x^2 - 72x + 288 = 0

We can use the quadratic formula to find the solutions for x:

x = (-b ± √(b^2-4ac)) / 2a

where a = 4, b = -72, and c = 288

x = (72 ± √(72^2 - 4(4)(288))) / 2(4)

x = (72 ± √(72^2 - 4(1152))) / 8

x = (72 ± √(72^2 - 4608)) / 8

x = (72 ± √(5184)) / 8

x = (72 ± 72) / 8

x = (144 ± 72) / 8

x = 72 / 8 or 0

Since the width of the floor strip cannot be negative, x = 9 feet. So, the dimensions of the rug should be 18 - 2 * 9 = 0 ft by 26 - 2 * 9 = 8 ft.

Step-by-step explanation:

The values of x are 18 and 4

We have the area of a rectangle

A = L* B

The l and the b would get increased by 2x

180 = (18 - 2x) (26 - 2x)

We have to open the bracket

468 - 36x - 52x + 4x² = 180

468 - 180 - 88x +  4x² = 0

rearrange the equation

4x² - 88x  + 288 = 0

Solve using the quadratic formula equation

This would give us x = 144 / 8 and 32 / 8

x = 18 and x = 4

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The value of the expression is 284 5/ 9

A fraction can be defined as the part of a whole.

Some types of fractions are;

Given the fraction;

-13(21 4/9)

First, we convert the mixed fraction in the bracket to a proper fraction

- 13( 197/ 9)

Now, let's expand the bracket

-2561/ 9

Find the quotient

284 5/ 9

Thus, the value of the expression is 284 5/ 9

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Answer:

b and d (they are the same thing)

Step-by-step explanation:

Answer: The domain would be (0 hours, 2.5 hours) and the range would be (0 feet, 30,000 feet) in this graph.

Step-by-step explanation:

The domain refers to the set of possible input values. The domain of a graph consists of all the input values shown on the x-axis.

The range is the set of possible output values, which are shown on the y-axis.

An x-axis on a graph is the horizontal line and a y-axis on a graph is the vertical line. The x-axis in this graph would be the height in feet and the y-axis in this graph would be the time in hours.

To better understand your question, it is important to identify the key terms and concepts that are being used.

Title: Understanding Terms in a Question

1. . Look for specific words or phrases that relate to the topic at hand, and try to understand their meaning within the context of the question.

2. It can also be helpful to break the question down into smaller parts or sub-questions, and focus on each one individually.

3. If you are unsure about the meaning of a particular term, do some research or consult a dictionary or other reference source.

4. By taking the time to understand the terms and concepts in a question, you can improve your ability to answer it accurately and effectively.

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The value of x in the triangle is 2√13.

We have,

There are two similar triangles.

So,

The ratio of the corresponding sides is equal.

Now,

4/x = x/(9 + 4)

4/x = x / 13

4 x 13 = x²

x² = 4 x 13

x = √(4 x 13)

x = 2√13

Thus,

The value of x in the triangle is 2√13.

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Frequency distributions, count the number of times each value or range of values appears in a dataset, while percentage distributions show the proportion or percentage of times each value or range of values appears in the dataset.

Frequency distributions are useful for summarizing and describing the distribution of a variable in a data set, while percentage distributions are useful for comparing different variables or subgroups within the data set.

For example, a frequency distribution could be used to show the number of hours of sleep each participant in a study gets per night, while a percentage distribution could be used to compare the number of hours of sleep between males and females in the study.

Frequency distributions and percentage distributions provide different perspectives on the same data set and can be used together to gain a more complete understanding of the data.

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The corret option is C. About 36% of all pizzas ordered from Grizzly's Pizza are cheese.

To estimate this percentage we just need to do:

P = 100%(number of cheese pizzas)/(total number)

We know taht there are 56 in total, and 20 of these are cheese, replacing these values in the formula above we will get:

P = 100%*(20/56)

P = 100%*0.36 = 36%

The corret option is C.

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Answer:c=3200

Step-by-step explanation:

2800+c<=6000

2800-2800+c<=6000-2800

c=3200

To stay within budget, all other costs  must be no more than $3200

Calculation

⇒ B ≤ $6000

⇒ C ≤ Budget - the cost of transportation

⇒ C ≤ $6,000 - $2,800

⇒ C ≤ $3,200

Hence, to stay within the budget, all other costs must be below $3,200

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