11(n – 1) + 35 = 3n

n = –6
n = –3
n = 3
n = 6

Answer:

75 - 25π.

Step-by-step explanation:

To find the work done by a force field on a particle moving along a curve, we use the line integral of the force field over that curve.

In this case, the curve is a circle of radius 5 centered at (0, 0, 3) lying on the plane z = 3. We can parameterize this curve using polar coordinates as:

r(t) = (5cos(t), 5sin(t), 3), where t goes from 0 to 2π.

The differential of the curve, dr(t), is given by:

dr(t) = (-5sin(t), 5cos(t), 0) dt

Now we need to calculate the work done by the force field F along this curve. The line integral of F over the curve is given by:

W = ∫ F · dr = ∫ (2x +y²Z)dx + (2x-4y+Z)dy + (x-2y-Z²)dz

Substituting x = 5cos(t), y = 5sin(t), and z = 3, we get:

W = ∫ (10cos(t) + 25sin²(t)·3) (-5sin(t))dt

∫ (10cos(t) - 20sin(t) + 3) (5cos(t))dt

∫ (5cos(t) - 10sin(t) - 9) (0)dt

Simplifying, we get:

W = -75∫sin(t)cos(t)dt + 50∫cos²(t)dt + 0

Using the trigonometric identities sin(2t) = 2sin(t)cos(t) and cos²(t) = (1 + cos(2t))/2, we can simplify this further:

W = -75∫(1/2)sin(2t)dt + 25∫(1 + cos(2t))dt

= -75·(1/2)·(-cos(2t))∣₀^(2π) + 25·(t + (1/2)sin(2t))∣₀^(2π)

= 75 - 25π

Therefore, the work done by the force field F on the particle moving along the circle of radius 5 centered at (0, 0, 3) lying on the plane z = 3 is 75 - 25π.

Answer:

Coffee Shop, pharmacy, furniture

Step-by-step explanation:

Coffee Shop and Furniture are both Alternate Interior Angles to the Storage, and Pharmacy is a Alternate Interior angle to the previous two

Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

Learn more on linear equation here: https://brainly.com/question/2030026

#SPJ1

Step-by-step explanation:

In order to multiply fractions and mixed numbers, you must first transform the mixed number into a single fraction (will most likely turn into an improper fraction).  An improper fraction is a fraction where the numerator is greater than the denominator.

Suppose that you were given the following fractions to multiply:

\(\large\mathsf{\frac{5}{7}\:\times\:2\frac{3}{5}}\)

The first step is to transform the mixed fraction, \(\large\mathsf{2\:\frac{3}{5}}\), into a single fraction.

You will have to multiply the denominator with the whole number, then add the numerator. The denominator does not change when you do this transformation processs.

The mixed fraction will now turn into the following improper fraction:

\(\large\mathsf{2\:\frac{3}{5}}\)   ⇒  \(\large\mathsf{\frac{13}{5}}\)  

Now, you will be able to multiply \(\large\mathsf{\frac{5}{7}}\) and \(\large\mathsf{\frac{13}{5}}\)  together by multiplying the numerator, 5 and 13 and the denominator, 7 and 5.

\(\large\mathsf{\frac{5}{7}\:\times\:\frac{13}{5}\:=\:\frac{5\:\times\:13}{7\:\times\:5}\:=\:\frac{65}{35}}\)

Since the product of the two fractions is an improper fraction, it is often customary to express the fraction into its lowest terms. Given the improper fraction, \(\large\mathsf{\frac{65}{35}}\), the greatest common factor between 65 and 35 is 5.

Hence, we could simply divide the numerator and the denominator by \(\large\mathsf{\frac{5}{5}}\) to simplify the fraction.

\(\large\mathsf{\frac{65}{35}\:\div\:\frac{5}{5}\:=\:\frac{13}{7}}\)

Therefore, the final answer is: \(\large\mathsf{\frac{13}{7}}\) .  To transform this improper fraction into a mixed number,  simply divide its numerator by the denominator, thereby resulting into the following mixed number:  \(\large\mathsf{1\:\frac{6}{7}}\).

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

Learn more about workers in: https://brainly.com/question/30203906

#SPJ1

Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

For such more question on package

https://brainly.com/question/12251427

#SPJ8

Answer:

public donations

to promote animal welfare

Step-by-step explanation:

Answer:

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

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

For more question on height visit:

https://brainly.com/question/28990670

#SPJ8

Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

For such more questions on histogram

https://brainly.com/question/32761368

#SPJ8

Using Trigonometry, the value of x in the right triangle is 17.1

Since we have a right angle triangle ; The angle L can be obtained thus ;

L = 180 - (90+67)

L = 23

Using Trigonometry:

Sin23° = opposite/ hypotenuse

Opposite= 6.7

hypotenuse= x

Sin23° = 6.7/x

x = 6.7/sin(23°)

x = 17.14

Therefore, the value of x to the nearest tenth is 17.1

Learn more on trigonometry:https://brainly.com/question/24349828

#SPJ1

Answer:

0.225 mm

Step-by-step explanation:

0.025*9 and that gets you 0.225

Answer:

according to desmos scientific calculator, the answer is 13/40

Answer:

length of the hypotenuse = 12.45.

Explanation

A right triangle consists of the hypotenuse (longest side), the opposite(length of the leg) and the adjacent.

The angle at the corner is 90degrees

Given the following

Length of the leg = 8

angle opposite the side = 40 degrees

To get the hypotenuse, we will use the SOH CAH TOA trigonometry identity;

sin theta = opposite/hypotenuse

sin 40 = 8/hypotenuse

hypotenuse = 8/sin40

hypotenuse = 8/0.6428

hypotenuse = 12.45

Hence the length of the hypotenuse is 12.45.

See the diagram attached

Tn = a + d * (n-1)

T8 = -12 + 2*7

= -12 +14

= 2

The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

Answer:

35.2 ft

Step-by-step explanation:

Multiply the scale factor and the height.

Answer:

1/6

Step-by-step explanation:

We have a favourable possibilty in a total of six possibility

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

For similar question on probability.

https://brainly.com/question/7965468  

#SPJ8

Step-by-step explanation:

Out of the given options, only √196 is a rational number.

A rational number is a number that can be expressed as the ratio of two integers. In other words, it can be written in the form of p/q where p and q are integers and q is not equal to zero.

√56 cannot be simplified further and has no integer factors that can be canceled out to express it as a ratio of two integers. Therefore, it is an irrational number.

Similarly, √63 and √240 cannot be simplified further and do not have any integer factors that can be canceled out to express them as a ratio of two integers. Therefore, they are also irrational numbers.

On the other hand, √196 simplifies to 14 which is a ratio of two integers (14/1). Hence, it is a rational number.

In summary, only √196 is a rational number out of the given options.

Answer:

It's unfactorable

Step-by-step explanation:

x² - 8x - 16 is already in its simplest form. You cannot take GCF or x out. Also, nothing multiplies to -16 and adds up to -8.

Answer: unfactorable

Step-by-step explanation: To factor x² - 8x - 16, we set up our two binomials with x and x as the first position in each binomial.

To fill the second position, we want to

look for factors of -16 that add to -8.

Factors of -16

+16 · -1

-16 · +1

+8 · -2

-8 · + 2

+4 · -4

So what pair of factors add to -16.

Well, none of them do.

When that happens, we say that the original

trinomial is unfactorable and that's your answer.

Answer:

im pretty sure its 152, im sorry if im wrong, i took 180 and subtracted 180 - 16 - 12 and got that soooo

Step-by-step explanation:

Answer:

-6i

Step-by-step explanation:

Complex roots have to come in conjugate pairs

So if we have 6i as a root, we must have -6i as a root

Answer:

-6i

Step-by-step explanation:

Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.

The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.

Thank you

Answer:

A linear equation is a fancy term for a straight line, which can be created by joining 2 points.

A point can be defined by (x, y), where x and y are the horizontal distance and the vertical distance respectively from point (0,0) (called the origin).

There are 3 ways to define a line:

(1) The slope-intercept form

y = mx + b, in which m is the slope, b is the y-intercept, where the line crosses the vertical axis at (0, b). If values of m and b are given, you can substitute and write the equation right away.

The slope, m, is calculated by rise (vertical difference between 2 points on the line) divided by run (horizontal difference between the 2 points on the line)

Step-by-step explanation:

or example, if 2 points on the line are

(x1, y1) and (x2, y2)

Then slope = (y1– y2)/(x1 — x2)

If m > 0, then the line rises to the right.

If m = 0, then the line is horizontal.

If m < 0, then the line rises to the left.

If the line is in the form x = c, where c is a constant, then the line is vertical.

(2) Point slope form

m = (y — y1)/(x — x1), when (x1, y1) and m are given.

In other words,

m(x — x1) = y — y1

mx — m(x1) = y — y1

y = mx — m(x1) + (y1)

Note that b = -m(x1) + (y1)

(3) linear form

ax + by + c = 0, where a, b, and c are constants.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

for such more question on linear function

https://brainly.com/question/9753782

#SPJ8

Answer:

2 and 5 are correct

Step-by-step explanation:

hope this helps

We notice that:

Therefore, we can factor the given equation as follows