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brilliants [131]
2 years ago
11

Real quick please. At a carnival it costs $6.54 for 3 tickets. Write an equation that can be used to express the relationship be

tween the total cost (t) and the number of tickets(n) you buy.
Mathematics
1 answer:
BlackZzzverrR [31]2 years ago
3 0

Answer:

t=2.18n

Step-by-step explanation:

Total cost is 6.54 for 3 tickets so divide 6.54 by 3 and you get price per ticket which is 2.18. Multiply that by how many tickets you want and you get your final price.

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Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

<h3>How to find the mass?</h3>

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \int_a^b \delta\left|r^{\prime}(t)\right| d t

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}

Further simplifying;

\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}

Now, use integration to find the mass of the wire;

       \begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

brainly.com/question/27846146

#SPJ4

The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

5 0
1 year ago
Kala got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store
irina [24]

Answer:

31 yards of ribbon

Step-by-step explanation:

Of after purchasing the ribbon in bulk she has $21.28 left from her initial $25 it would mean that she spent $3.72 in total.

25 - 21.28 = 3.72

So in spending $3.72 on ribbons we can find how much yards she bought by seeing how many times 12 cents can go into the $3.72 (the amount of money she spent).

0.12 \sqrt{3.72}  = 31

8 0
2 years ago
There are 156 people taking a boating safety course. The ratio of adults to students is 9 to 4. How many adults are taking the c
iren [92.7K]
108 adults and 48 students.
4 0
3 years ago
The rain caused the River to raise a total of 6 2/3 inches. The river was rising at an average of 2/3 of an inch each hour. How
Gnesinka [82]
It rained for approximately 10.09 hours.
6 2/3 divided by 2/3 = 10.09
3 0
3 years ago
Draw a model to represent the problem 6/12 divided by 1/4
Sloan [31]
0.5/0.25?

Not really sure what ur asking
5 0
3 years ago
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