8. When is a/b equal to an integer?
B=0

B<1

B>1

B=1 or -1



50 pointa for person who answers

Answer:

C

Step-by-step explanation:

It has to represent 2 inches and 60 miles which means the number 2 has to hit 60 miles which is why c is the answer.

By using the independence of path theorem we get the value of ∫(2xy + z)dx + x²dy + x dz is 13.

What is a definite integral?

When the lower and upper bounds are constants, a definite integral represents a number. An extended family of functions, whose derivatives are f, is represented by the indefinite integral. Any two family functions will always differ from one another.

Here, we have

Given:  (2xy + z)Dx + x²Dy + x Dz,  where Y Is a curve from (1,-1,2) To (2,2,3).

We have to evaluate using the independence of the path theorem.

F = (2xy + z)i + x²j + xk

The curl of the given function is 0.

So, F is conservative.

To find Φ such that F = ΔΦ =  (2xy + z)i + x²j + xk = idΦ/dx+ jdΦ/dy + kdΦ/dz

dΦ/dx = 2xy + z ,   Φ = x² y + xz + c

dΦ/dy = x²,     Φ = x²y + c

dΦ/dz = x,     Φ = xz + c

∴ Φ = x² y + xz

dΦ = d(x² y + xz ) =  (2xy + z)dx + x²dy + x dz

Now,

∫(2xy + z)dx + x²dy + x dz = ∫d(x² y + xz)

= {x² y + xz} When, a = (2,2,3) , b = (1,-1,2)

= 13

∫(2xy + z)dx + x²dy + x dz = 13

Hence, by using the independence of path theorem we get the value of ∫(2xy + z)dx + x²dy + x dz is 13.

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So, the probability of ending up with a three-digit number that is divisible by 4 is 1/24.

To find the probability of ending up with a three-digit number that is divisible by 4 when spinning the spinner three times, we need to consider the possible outcomes that satisfy this condition and divide it by the total number of possible outcomes. Let's analyze the given spinner and its possible outcomes:

Spinner: [1, 2, 3, 4, 5, 6]

To form a three-digit number, the hundreds digit will be determined by the first spin, the tens digit by the second spin, and the units digit by the third spin. A number is divisible by 4 if the last two digits (tens and units digits together) form a number divisible by 4. Therefore, we need to find the number of possible outcomes for the tens and units digits that satisfy this condition.

Possible outcomes for the tens digit: [2, 4, 6]

Possible outcomes for the units digit: [2, 4, 6]

Combining the possible outcomes for the tens and units digits, we have a total of 9 (3 possibilities for the tens digit multiplied by 3 possibilities for the units digit) favorable outcomes. The total number of possible outcomes for each spin is 6 (since there are 6 numbers on the spinner). Since we are spinning the spinner three times independently, the total number of possible outcomes for spinning it three times is 6^3 = 216. Therefore, the probability of ending up with a three-digit number divisible by 4 is:

Probability = favorable outcomes / total outcomes

Probability = 9 / 216

Probability = 1 / 24

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a) The volume is (π/27)y³

b) the  volume is π -(π/27)(3 -h)³.

c) the rate at which the  sand in the lower cone is increasing  is  0.0116 inches per second

a) since we  know The volume of a cone is: V = 1/3πr²h, for the problem here we have h = y and r = y/3, so the volume is : (1/3)π(y/3)²(y) = (π/27)y³

b) Now, we know The empty volume of the lower cone is the same as the volume of the upper cone with y=3, so V = (π/27)(3³) = π , as the sand height is h in the lower cone, so the height of the empty space is (3-h), the volume of the empty space is : (π/27)(3-h)³ and the volume will be the difference between that and the cone volume: π -(π/27)(3 -h)³. c) since the ratio of rates of change in height will be inversely proportional to the surface areas of the sand in each section of the cone, the ratio will be proportional to the square of the distance from the sand surface to the cone tip. For the height of the sand in the lower cone of 1   inch high, its volume is: π -(π/27)(3 -1)³ = π -(8π/27) = 19π/27,  then the volume of the sand in the upper cone is: 3π/4 -19π/27 = 5π/108, the height of the sand in the upper cone is then

(π/27)h³ = π(5/108)

h³ = 5/4 ,h = ∛(5/4), the ratio of the  surface areas in the two cones are  The ratio of surface areas : (2 / ∛(5/4))²,  the rate of decrease is 4/100, rate of increase of sand in lower cone is  (4/100)/((2 / ∛(5/4))²)  =(∛12.5)/200 ≈ 0.0116

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Answer:

The value of x is \( - \frac{4}{3} \)

Step-by-step explanation:

☆Combine like terms and solve!

\( \frac{1}{4} x + \frac{4}{3} x - \frac{5}{6} x + 1 = 0 \\ \\ \frac{3}{4} x + 1 = 0 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: - 1 = - 1}{ \frac{ \frac{3}{4}x }{ \frac{3}{4} } = \frac{ - 1}{ \frac{3}{4} } } \\ \\ x = - \frac{4}{3} \)

☆Happy to help!

Answer:

\(5.\overline{55}\) or  \(5\frac{5}{9}\)

Step-by-step explanation:

\(\frac{5}{r} =\frac{9}{10}\)

We multiply the cross values of 5 and 10

5 × 10 = 50

Now we divide by the remaining number, 9

\(50 \div 9 = 5.555555...\)

So, r = \(5.\overline{55}\)

As a fraction, this is \(5\frac{5}{9}\)

Hope this helped!

Answer:

5 5/9 = r

Step-by-step explanation:

5/r = 9/10​

Using cross products

5 * 10 = 9 * r

50 = 9r

Divide by 9

50/9 = r

5 5/9 = r

3 / 0.8 = z / 5.6

To find z, we need to isolate z. How can we do this? Right now, we know z / 5.6 is equal to 3 / 0.8.

This will cancel the divide by 5.6 or the 1/5.6 on the right side to isolate z!

(3 × 5.6) / 0.8 = z

16.8 / 0.8 = z

All we have to is simplify!

z = 21

1125 is the answer to the question

You see they say 32 so they mean multiply 3×3=9.

Nad then they say 53 so multiply 5×5×5=125.

so 125 ×9=1125.

Answer:

The length = 192 feet squared

The diagonal = 16 feet

Step-by-step explanation:

Over here, we can use the Pythagorean theorem which states that in a right triangle, a^2+b^2=c^2

The width measures 12 and the diagonal measures 20, so we have a and c, so 144+b^2=400 which simplifies to b^2=256. The square root of 256 is 16 so that's our length

Then we just plug in the formula to find the area of a rectangle which is l*w, so 12*16=192

The area of the rectangular rug is 192 square feet.

Let, the length of the rectangular rug is L feet.

We know the width of the rug is 12 feet, and the diagonal (D) measures 20 feet.

The diagonal, width, and length of a rectangle form a right triangle.

Using the Pythagorean theorem, we can relate these values:

(Diagonal)² = (Length)² + (Width)²

putting the values we get,

(20)² = L² + (12)²

400 = L² + 144

Now, isolate L²:

L² = 400 - 144

L² = 256

Now, find the square root of both sides to get the length (L):

L = √256

L = 16 feet

So, the length of the rectangular rug is 16 feet.

To find the area (A) of the rug, simply multiply the length and width:

Area = Length * Width

Area = 16 feet * 12 feet

Area = 192 square feet

Therefore, the area of the rectangular rug is 192 square feet.

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The number of hours it will take the airplane to fly the given distance would be = 4.5 hours

To calculate the number of hours that can be used for the distance, the following needs to be done. That is;

The number of hours it take to complete 3600 miles = 3 hours

Therefore the number of hours it will take to complete 5400miles = X hours.

That is;

3600 miles = 3 hours

5400 miles = X hours

make X the subject of formula;

X = 5400×3/3600

= 16,200/3600

= 4.5 hours.

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Answer:

Step-by-step explanation:

Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:

\(tan(70)=\frac{?}{3}\) and

3tan(70) = ? so

? = 8.24

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer: look at the images for the answer and the solution

Step-by-step explanation:

We can see here that in order to find the median of the lower half of data, one will have to sort out the data in an ascending order. Then take the  lower half of the data (i.e., the first half of the sorted data) and find its median.

The median, which is used to measure central tendency in statistics, is the point at which a dataset may be divided into two equal parts. If a dataset has an even number of values, it is the average of the two middle values or the middle value in a sorted dataset.

The values in the dataset must first be arranged from lowest to highest in order to determine the median. The median is the middle value if the dataset has an odd number of values.

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The solution to the given question is given below:(a) f(x) = 3x^2+4/x^2+2To differentiate the given function, we will use the quotient rule of differentiation.

which is given by,(f(x)/g(x))'=[f'(x)g(x)-f(x)g'(x)]/[g(x)]2Now, putting the given values into the formula, we get,f(x) = 3x2+4/x2+2Let f(x) = 3x2+4 and g(x) = x2+2Now,f'(x) = d/dx[3x2+4] = 6xg'(x) = d/dx[x2+2] = 2xAfter substituting all the values in the quotient rule, we get,(f(x)/g(x))'=(6x(x2+2)-2x(3x2+4))/(x2+2)2=(-6x^3-8x+12x^3+16x)/[x^4+4x^2+4] = (6x^3+8x)/[x^4+4x^2+4]Hence, f'(x) = (6x^3+8x)/[x^4+4x^2+4].Therefore, the required derivative of the given function is (6x^3+8x)/[x^4+4x^2+4].(b) f(x) = (x2 - 7x)12To differentiate the given function, we will use the chain rule of differentiation which is given by, d/dx[f(g(x))] = f'(g(x)).g'(x)Now, putting the given values into the formula, we get,Let f(x) = x^12 and g(x) = x2-7xThen,f'(x) = 12x^11g'(x) = d/dx[x2-7x] = 2x-7After substituting all the values in the chain rule, we get,d/dx[f(g(x))] = f'(g(x)).g'(x) = 12(x2-7x)11.(2x-7)Therefore, the required derivative of the given function is 12(x2-7x)11.(2x-7).(c) f(x) = x^4√6x+5To differentiate the given function, we will use the product rule of differentiation which is given by, (fg)' = f'g + fg'Now, putting the given values into the formula, we get,Let f(x) = x^4 and g(x) = √6x+5Then,f'(x) = d/dx[x4] = 4x3g'(x) = d/dx[√6x+5] = 3/√6x+5After substituting all the values in the product rule, we get,(fg)' = f'g + fg' = (4x3).(√6x+5) + (x^4).(3/√6x+5)Hence, f'(x) = (4x3).(√6x+5) + (x^4).(3/√6x+5).Therefore, the required derivative of the given function is (4x3).(√6x+5) + (x^4).(3/√6x+5).

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The derivatives of the functions of the differentiation of the given functions has been calculated.

(a) The rule of differentiation applied to

f(x) = 3x²+4/x²+2 is as follows:

f'(x) = [12x(x²+2)-(6x)(4)] / [(x²+2)²]

=> f'(x) = [12x³-24x] / [(x²+2)²]

=> f'(x) = 12x(1-x²)/[(x²+2)²].

(b) The rule of differentiation applied to f(x) = (x² - 7x)^12 is as follows:

f'(x) = 12(x²-7x)^11(2x-7).

We apply the chain rule, which is the following:

[f(g(x))]' = f'(g(x)) * g'(x).(c)

The rule of differentiation applied to f(x) = x⁴√(6x+5) is as follows:

f'(x) = 4x³ * (6x+5)¹∕² + x⁴ * 1/2(6x+5)^-1/2 * 6

=> f'(x) = [24x³(6x+5) + 3x⁴(6)]/[2(6x+5)¹∕²]

=> f'(x) = [3x³(8x²+15)]/[(6x+5)¹∕²].

Thus, the differentiation of the given functions has been calculated.

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Answer:

15.6=c

Step-by-step explanation:

(12)^2+(10)^2=c^2

144+100=c^2

244=c^2

square root of both sides=244= square root c^2

15.620499=c

15.6=c

The distance of the straight line from starting to end based on the forming triangle will be 18.50 miles.

The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.

As per the given situation is making a right angle triangle.

By Pythagoras theorem,

x = √(12² + 10²)

x = 18.50 miles

Hence "Based on the forming triangle, the length of the straight line from beginning to end will be 18.50 miles".

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Answer:

For x there is no distance since they are both for. For y, they are -6 apart.

Step-by-step explanation:

Answer:

Fox x Diya is no distance since they are both for they are six apart

Step-by-step explanation:

(4-10)

and= just opposite size (10- 4) .

10 -4 = 6 answer 6

and (4-4)

answer is

0

the answer is six apart

understand

We can easily see this by noting that if we multiply this matrix with \underset{x}{\rightarrow}= (x1,x2,x3), we get

|x1 + 2x2 + 3x3|

|4x1 + 5x2 + 6x3|

|7x1 + 8x2 + 9x3|

which to the equation 3x1 + 2x2 + x3 = 0.

A 3x3 matrix for which the kernel is the set of all vectors \underset{x}{\rightarrow}∈ R3 satisfying 3x1 + 2x2 + x3 = 0 is

|1  2  3|

|4  5  6|

|7  8  9|

This matrix has a kernel consisting of all vectors \underset{x}{\rightarrow}= (x1,x2,x3) that satisfy the equation 3x1 + 2x2 + x3 = 0.

We can easily see this by noting that if we multiply this matrix with \underset{x}{\rightarrow}= (x1,x2,x3), we get

|x1 + 2x2 + 3x3|

|4x1 + 5x2 + 6x3|

|7x1 + 8x2 + 9x3|

which to the equation 3x1 + 2x2 + x3 = 0.

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Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.

Any way of moving all the points in the plane such that

a) the relative distance between points stays the same and

b) the relative position of the points stays the same.

There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.

In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance. See Image-1.

A rotation fixes one point (the roto center) and everything rotates by the same amount around that point. Every rotation has a roto center and an angle. See Image-2.

A reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every reflection has a mirror line. See Image-3.

A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance. See Image-4.

Therefore,

Simply put, rigid motions are transformations that preserve the side lengths and angles in a shape. You can see any of these transformations by moving an object you may have around you right now. Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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inequality will not be use in the given expression.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

The given information,

24+6k<-6(-4-k)

24+6k < 24+6k

It's can be seen that both expressions are equal, but in the question, it is given that the inequality which is not valid.

Hence, inequality will not be use in the given expression.

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Answer:

Your answer is 32.9 or 33

Hope that this is helpful. Vote and likhe it

Answer:

4075 squares centimeters

Step-by-step explanation:

V=4/3pi(r^3)

V=4/3pi(9^3)

V=3,054 inches^3

Answer:

5≥17

Step-by-step explanation:

Answer:

it not clear maybe you can take an other pohto

sorry

Step-by-step explanation:

The equation in the slope-intercept form is:

y = 8 + (3/2)x

Herewe have the linear equation:

3x - 2y = -16

And we want to write it in the slope-intercept form.

To do that, we need to isolate the variable y.

We will get:

3x - 2y = - 16

-2y = -16 - 3x

y = (-16/-2) + (-3/-2)x

y = 8 + (3/2)x

That is the equation written in the slope-intercept form.

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