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Alexandra [31]
3 years ago
15

Find the distance traveled by a particle with position (x, y as t varies in the given time interval. x = 3?sin2 t, y = 3?cos2 t,

0 ? t ? 4?
Mathematics
1 answer:
ANTONII [103]3 years ago
5 0
Assuming the particle's position is given by

\begin{cases}x(t)=3-\sin2t\\y(t)=3-\cos2t\\0\le t\le4\end{cases}

then the distance traveled over the interval is

\displaystyle\int_{t=0}^{t=4}\sqrt{\left(\dfrac{\mathrm dx(t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy(t)}{\mathrm dt}\right)^2}\,\mathrm dt
=\displaystyle\int_0^4\sqrt{(-2\cos2t)^2+(2\sin2t)^2}\,\mathrm dt
=\displaystyle\int_0^4\sqrt{4\cos^22t+4\sin^22t}\,\mathrm dt
=\displaystyle2\int_0^4\mathrm dt
=2(4-0)=8
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Mark is planning to run in a 10-km race he will have to run 1 4/5 km uphill, 2 7/10 km downhill, and the rest of the race on lev
777dan777 [17]
<span>Uphill distance = 1 4/5 = 9/5 = 18/10 km Downhill Distance = 2 7/10 = 27/10 km Total Uphill and Downhill = 18/10 + 27/10 = 45/10 = 4.5 km Hence total level ground = Total race km - (Uphill + Downhill) =10 - 4.5 = 5.5 km Hence the answer is 5.5 km.</span>
7 0
3 years ago
a store is offering a 20% discount on all sales over $50. If you purchase a shirt and a pair of leans for $62.50, what is the am
vodomira [7]

Answer:

you would receive 12.5% of the discount

Step-by-step explanation:

20% off of 62.50 is 50; so you would pay $50

7 0
3 years ago
This is important please help
Leya [2.2K]

Answer: C

<u>Step-by-step explanation:</u>

∑ 8(\frac{7}{3})⁽ⁿ⁻¹⁾ from n = 1 to n = 5

n = 1 → 8(\frac{7}{3})⁽¹⁻¹⁾

        = 8                                         = \frac{648}{81}

n = 2 → 8(\frac{7}{3})⁽²⁻¹⁾

         = \frac{56}{3}                                         = \frac{1512}{81}    

n = 3 → 8(\frac{7}{3})⁽³⁻¹⁾

          = \frac{392}{9}                                     = \frac{3528}{81}

n = 4 → 8(\frac{7}{3})⁽⁴⁻¹⁾

          = \frac{2744}{27}                                 = \frac{8232}{81}

n = 5 → 8(\frac{7}{3})⁽⁵⁻¹⁾

          = \frac{19208}{81}                                = \frac{19208}{81}

                                                                            Sum = \frac{33128}{81}

                                                                                    = 408.99

     

6 0
2 years ago
I only need to know question b, if anyone can help
kicyunya [14]

243 liters represents 7/10 - 1/4 of the water.

v=243 / (7/10 - 1/4) = 243 / (14/20-5/20) = 243(20)/9 = 540 liters.

Answer: 540 liters

Check:

(7/10)(540) = 7(54) = 378

(1/4)540 = 135

difference = 378 - 135 = 243  good

5 0
3 years ago
Sumalee won 40 super bouncy balls playing horseshoes at her school's game
anzhelika [568]

let x represent how many friends Sumalee has.

40-2(x)=8

40 original balls - 2 to each friend = 8 balls left

3 0
2 years ago
Read 2 more answers
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