A blacksmith has been studying vector calculus and wants to calculate the total mass of a curved metal fitting. Given that the metal fitting has a helix shape parameterized by C:[0,π] → IR3 C(t) = (cos (t), sin(t), t) And the density of the metal material is given by the function:f(x,y,z) = 22 How can the black smith calculate the total mass of the fitting and what is this mass?

Answer:

286 students attended

148 non students attended

Step-by-step explanation:

Given

[tex]Tickets = 434[/tex]

[tex]Students = \$4.00[/tex]

[tex]Non-Students = \$6.00[/tex]

[tex]Total = \$2032.00[/tex]

Solving (a): Number of students

Represent students with S and non students with N

So:

[tex]S + N = 434[/tex] --- (1)

[tex]4S + 6N = 2032[/tex] --- (2)

Make N the subject of formula in (1)

[tex]N = 434 - S[/tex]

Substitute 434 - S for N in (2)

[tex]4S +6(434 - S) = 2032[/tex]

Open Bracket

[tex]4S + 2604 - 6S = 2032[/tex]

Collect Like Terms

[tex]4S - 6S = 2032 - 2604[/tex]

[tex]-2S = -572[/tex]

Divide through by -2

[tex]S = 286[/tex]

Hence; 286 students attended

Solving (b):

Recall that

[tex]N = 434 - S[/tex]

[tex]N = 434 - 286[/tex]

[tex]N = 148[/tex]

148 non students attended

Answer: the answer is A. point

Answer: -4/10

Step-by-step explanation:

Since we are finding the slope, we have to do the rise over run strategy. In this case, rise (y) are the numbers  -3 and 1 and the run (x) is the numbers -6 and 4. After that, we subtract them. So, -3 - 1 and -6 - 4. We get -4 over -10 (or - 4/10) which is your slope.

Answer:

2/7 or 2 over 7

Step-by-step explanation:

4/14 can be simplified. We know this because both 4 and 14 can be divided by 2. 4 divided by 2 = 2 and 1 divided by 2 = 7, thus the answer is 2 over 7.

Answer:The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 0 .

Step-by-step explanation:

Answer:

The slope of y=-3 is 0.

y=-3 is a horizontal line.

Let me know if this helps :)

Answer:

65 or 60

Step-by-step explanation:

I am not really positive about my answers so please take this into consideration.

Answer:

A sinusoidal model would be used

The kind of function that have consistency in the periodic rate of change is the Average rate of changes

Step-by-step explanation:

The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )

For percentage rate of changes :

starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%

For Average rate of changes:

starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2

This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions

The kind of function that have consistency in the period rate of change is the Average rate of changes

Answer:

-5

Step-by-step explanation:

15-20

Answer:

-5

Step-by-step explanation:

15-20=-5

integer means whole number

Answer:

9 is correct answer

Step-by-step explanation:

[tex] {x}^{2} - 6x - 27 \\ = {x}^{2} - 9x + 3x - 27 \\ = x(x - 9) + 3(x - 9) \\ = (x + 3)(x - 9)[/tex]

x=9

Answer:

(x - 9)(x + 3)

Step-by-step explanation:

Given

x² - 6x - 27

Consider the factors of the constant term (- 27) which sum to give the coefficient of the x- term (- 6)

The factors are - 9 and + 3, since

- 9 × 3 = - 27 and - 9 + 3 = - 6, thus

x² - 6x - 27 = (x - 9)(x + 3)

Answer:

i think it's b

Step-by-step explanation:

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Answer: 0.03538944

Step-by-step explanation:

Given, The accuracy of missile = 96%

i.e. The probability that it will hit the shot = 0.96

Probability of missing the shot = 1-0.96= 0.04

Now, each missile is independent of other.

Therefore, the probability only the second one misses = (probability that first will hit the shot) x (probability that second one misses ) x (probability that third will hit the shot)x (probability that fourth will hit the shot)

Thus, the probability only the second one misses is [tex](0.96)(0.04)(0.96)(0.96)=0.03538944[/tex]

Hence, the required probability = 0.03538944

Steps to solve:

8x - 7x + 6 = 6

~Combine like terms

x + 6 = 6

~Subtract 6 to both sides

x = 0

Best of Luck!

Answer:

0

8x0=0 7x0=0

6+0=6

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

So we have the function:

[tex]h(x)=-3x-4[/tex]

To find h(0), substitute 0 for x. Thus:

[tex]h(0)=-3(0)-4[/tex]

Multiply:

[tex]h(0)=0-4[/tex]

Subtract:

[tex]h(0)=-4[/tex]

And we're done!

Answer:

60 × 66,666

60 × 666,666

Step-by-step explanation:

If you look at the pattern on the top numbers, you can see that there is one six that keeps on getting added. I'm not sure of my answer, but that is what I would put.

Answer: 4 2/3

Step-by-step explanation:

Because I said so

Answer:

1-0 = 0 ( This is not the rule of binary) As in binary addition 1-0 = 1

Answer:

x=2

Step-by-step explanation:

2x+5(3x-4)=14

Distribute

2x + 15x -20 = 14

Combine like terms

17x -20 = 14

Add 20 to each side

17x-20+20 =14+20

17x = 34

Divide by 17

17x/17 = 34/17

x=2

Answer:

5

Step-by-step explanation:

o+5=y=5

1+5=y=6

2+5=y=7

.:y=x+5

Answer:

I'm guessing you mean 10^4 = ?

Well, that equals 10 * 10 * 10 * 10

which equals 10,000

Step-by-step explanation:

Answer:

Its D

Step-by-step explanation:

29/1000= 0.029

Answer:

C.

Step-by-step explanation:

29/999 is 0.02929292929292929

Answer:

Step-by-step explanation:

3x - 4 = -2x + 11

5x - 4 = 11

5x = 15

x = 3

3(3) - 4 = 9 - 4 = 5 = y

(3, 5)

Answer:

1.)y=3x-4=5

2.)y=4x-1=7

The image of the graph is missing, so i have attached it.

Answer:

g(x) = 5/3 * f(x)

Step-by-step explanation:

We want to find the equation represents g(x) as a translation of f(x).

From the graph, the y = f(x) function curve has the following observations,

- At x = 0, y = f(0) = 30

- At x = 10, y = f(10) = 36

Similarly, from the graph, the y = g(x) function curve has the following observations,

- At x = 0, y = g(0) = 50

- At x = 10, y = g(10) = 60

From those coordinates on the graph, we can see that;

f(0) = 30 and g(0) = 50

It means that for us to make g(x) as a translation of f(x), g(0) = fraction * f(0)

Fraction = g(0)/f(0) = 50/30 = 5/3

Thus;

g(x) = 5/3 * f(x)

Let's confirm with the second coordinate;

Thus;

g(10) = 5/3 * f(10)

g(10) = 5/3 * 36

g(10) = 60

This value is same as what is on graph, thus we can conclude that;

The equation represents g(x) as a translation of f(x) is; g(x) = 5/3 * f(x)

Answer:

10x+15y≥150

Step-by-step explanation:

Graph y≤13−x (shading down)

graph y≥10− 3/2x (shading up)

Answer:

2q

Step-by-step explanation:

Product is the answer to a multiplication equation or expression. So you could put it like 2 x q but it would be easier and more understanding to do 2q...Or even 2(q).

Answer:

[tex]S(r)=4\pi r^2[/tex].

Step-by-step explanation:

It is given that, the surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell.  

We need to express S as a function of r.

Let r be the radius of the cell and S(r) be the surface area of single-celled organism when radius is r.

According to the question,

[tex]S(r)=4\pi \times r^2[/tex]

[tex]S(r)=4\pi r^2[/tex]

Therefore, the required function is [tex]S(r)=4\pi r^2[/tex].

Answer:

[tex]Second = \$213876[/tex]

Step-by-step explanation:

Given

Highest Winning = $262,743

Second Highest Winning = 81.4012% of the first

Required

Determine the value of the second highest winning

Recall that

[tex]Second\ Highest\ Winning = 81.4012\%\ of\ the\ first[/tex]

Substitute $262,743 for the first highest winning

[tex]Second = 81.4012\%\ of\ \$262,743[/tex]

[tex]Second = 81.4012\%\ * \$262,743[/tex]

[tex]Second = \$213875.954916[/tex]

Approximate

[tex]Second = \$213876[/tex]

Hence, the second highest winning is approximately $213876

Answer: There are 100 boys at the concert

Step-by-step explanation:

If the the ratio of  boys to girls is 2:5 and and there are 250 girls  then a number was multiplied by 5 to get 250  and that number needs to be multiply by 2  to find the number of boys.

So to find that number we will divide 250 by 5.

250/ 5 = 50  

50 * 2 = 100

Moving the slider to 9 inches shows that 9 inches is equivalent to 22.86 centimeters. 1 inch is 2.54 times bigger than a centimeter.

Hi

3/4 = 1/3X

3/4 = X/3

3/4 *3 = X

9/4 = X

2.25 = X