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sertanlavr [38]

3 years ago

14

The Cat is a high-speed catamaran auto ferry that operates between city A and city B. The Cat can make the 144-mile trip in ab

out 2 and one half hours. Find the catamaran speed for this trip.

2 answers:

AnnZ [28]3 years ago

8 0

Answer:

41.14 mph

Step-by-step explanation:

We are given that Cat is a high speed catamaran auto feery that operates between city A and city B.

Cat travel distance in trip =144 miles

Time taken by Cat in trip=2 and one half hours= $2+1\frac{1}{2}=2+\frac{3}{2}=2+1.5=3.5 hours$

We know that speed= $\frac{Total\;distance}{time\;taken}$

Substitute the value in the given formula

Then, we get speed of Cat= $\frac{144}{3.5}=41.14 mph$

Hence, the speed of Cat=41.14 mph

Arturiano [62]3 years ago

5 0

The catamaran speed for this trip is $\boxed{57.6{\text{ miles/hour}}}.$

Further explanation:

The relationship between speed, distance and time can be expressed as follows,

$\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}$

Given:

The distance covered by the catamaran is $144{\text{ miles}}.$

The time taken to travel is 2 and one half hours.

Explanation:

Consider the speed of catamaran for this trip as $S{\text{ miles/hours}}.$

The distance between the city A and city B is $144{\text{ miles}}.$

The time taken to travel is 2 and one half hours.

The time taken by the Cat can be expressed as follows,

$\begin{aligned}{\text{Time}} &= 2 + \frac{1}{2}\\&= 2 + 0.5\\&= 2.5\\\end{aligned}$

The speed can be obtained as follows,

$\begin{aligned}{\text{Speed}} &= \frac{{144}}{{2.5}}\\&= \frac{{1440}}{{25}}\\&= 57.6{\text{ miles/hour}}\\\end{aligned}$

The catamaran speed for this trip is $\boxed{57.6{\text{ miles/hour}}}.$

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed

Keywords: Cat, high-speed, catamaran, auto ferry, operations, city A, city B, operates, 144 miles, trip, 2 hours, one half hours, catamaran, speed, distance, time, trip, speed for trip.

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Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

$6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) $\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}$

( 2 ) $\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}$

These two identities makes sin(π / 10) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and cos(π / 10) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ .

Therefore cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ . Substitute,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$

And now simplify this expression to receive our answer,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$ = $-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i$ ,

$-\frac{3\sqrt{5+\sqrt{5}}}{4}$ = $-2.01749\dots$ and $\:\frac{3\sqrt{3-\sqrt{5}}}{4}$ = $0.65552\dots$

= $-2.01749+0.65552i$

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

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$6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}$

We know that $6\sqrt{5+\sqrt{5}} = 16.13996\dots$ and $-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots$ . Therefore,

Solution : $16.13996 - 5.24419i$

Which rounds to about option b.

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