a) See the file below, b) $s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx$ , c) $s \approx 9.715$

Step-by-step explanation:

a) Points moves clockwise as t increases. See the curve in the file attached below. The parametric equations describe an ellipse.

b) The arc length formula is:

$s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx$

c) The perimeter of that arc is approximately:

$s \approx (\frac{1}{4} + \frac{1}{8})\cdot 2 \pi\cdot \sqrt{\frac{3^{2}+5^{2}}{2} }$

$s \approx 9.715$

5 0

4 years ago

Seven hamburgers and four sodas cost $27.35. Four hamburgers and five sodas cost $18.75

Doss [256]

Answer:

equations:

7x + 4y = 27.35

4x + 5y = 18.75

Step-by-step explanation:

x = burgers

y = sodas

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

7x + 4y = 27.35

4x + 5y = 18.75

5 0

3 years ago

Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times. Round your answer to the neares

grigory [225]

Answer:

0.0728177272

Step-by-step explanation:

Given :

Number of flips = 80

Probability of landing on tail at most 33 times ;

Probability of landing on tail on any given flip = 1 / 2 = 0.5

This a binomial probability problem:

Hence ;

P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)

Using a binomial probability calculator :

P(x ≤ 33) = 0.0728177272

7 0

3 years ago

You start at (2, 4). You move up 6 units and left 1 unit. Where do you end?

mylen [45]

Answer:

(1,10)

Step-by-step explanation:

2-1=1

4+6=10

4 0

2 years ago

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Find the value of x