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Stella [2.4K]
3 years ago
6

Samantha is riding a raft down a stream that is moving at a rate of 65 feet per minute. How far downstream does she travel in 5

minutes?
Mathematics
2 answers:
Murrr4er [49]3 years ago
4 0

Answer: 325 feet per minute

Step-by-step explanation: If 65 feet is one minute, all you have to do is multiply 65 by 5.

EastWind [94]3 years ago
3 0

Answer:

325 feet

Step-by-step explanation:

65 x 5 = 325

for every minute, she travels 65ft

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What is the next term in the arithmetic sequence? 9,17,25,33,...
lions [1.4K]

<u>Answer:</u>

<u><em>41</em></u>

<u />

<u>Explanation:</u>

To solve this problem we must first understand what the pattern is in the arithmetic sequence. Once we understand the pattern, we can then apply it to the final known term to find the next term.

Take a look at the arithmetic sequence given:

<em>9, 17, 25, 33,...</em>

<em />

Let's start by figuring out how they got the second term in the sequence. To do that, subtract the second term by the first term. This will reveal the pattern.

<em>9 - first term</em>

<em>17 - second term</em>

<em />

<em>17 - 9 = 8</em>

<em />

So, this means they added eight to get the next term. Therefore, the pattern should be 'add eight' to get the next term. Just to be sure the pattern we found is correct, apply it to the given arithmetic sequence.

<em>9, 17, 25, 33,...</em>

<em>9 </em><em>+ 8 = </em><em>17</em>

<em>17  </em><em>+ 8 = </em><em>25</em>

<em>25 </em><em>+ 8 = </em><em>33</em>

<em />

So, since 'adding eight' every time gives us the next term, the pattern is correct.

Finally, let's continue the pattern to find the next term.

<em>9, 17, 25, 33,...</em>

<em />

<em>33 </em><em>+ 8 = </em><em>41</em>

<em />

<em>9, 17, 25, 33, 41,...</em>

<em />

Therefore, the next term in the arithmetic sequence is <u><em>41</em></u>.

3 0
2 years ago
Which of these are coordinates for parts of the Ranger Station​
anastassius [24]

ANSWER

F (2,3)

EXPLANATION

The coordinates are ordered pairs.

So the x-coordinate comes first and the y-coordinate second.

In other words the coordinate on the horizontal axis comes first and that of the vertical axis comes second.

The coordinates of the ranger station are:

(2,3),(2,4),(3,3),(3,4)

The correct choice is F.

6 0
3 years ago
Read 2 more answers
Match each of the parametric equations 1-5 with the curve it represents from the list A through E below. 1. r=3 2. r=2sinθ 3. θ=
ira [324]

Answer:

Step-by-step explanation:

1. r=3

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

When r =3,

Then we have

r=3,

x²+y²=3

All points with r = 3 are at

distance 3 from the origin, so r = 3 describes the circle of radius 3, with center at the origin (0,0).

Option C

2. r=2sinθ

When r=2sinθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2sinθ

Since Sinθ=y/r

r=2y/r

Cross multiply

r²=2y

x²+y²=2y

x²+y²-2y =0

x²+ (y-1)² -1 =0

x²+(y-1)²=1²

Then,

It is a circle with center (0,1) and radius 1.

Because the sine is periodic, we know that we will get the entire curve for values of θ in [0, 2π). As θ runs from 0 to π/2, r increases

from 0 to 2. Then as θ continues to π, r decreases again to 0. When θ runs from π to

2π, r is negative, and it is not hard to see that the first part of the curve is simply traced

out again, so in fact we get the whole curve for values of θ in [0, π). Thus, check attachment for curve, Now, this suggests that the curve could possibly be a circle,

and if it is, it would have to be the circle x² + (y − 1)² = 1. Having made this guess, we can easily check it. First we substitute for x and y to get (r cos θ)² + (r sin θ − 1)² = 1;

expanding and simplifying does indeed turn this into r = 2 sin θ.

Option E

A circle of radius 1 with center on the x-axis

3. θ=π/4

This is a point on the circle

p=(r, θ)

So, r=0

x = rCosπ/4=rCos45

x=r√2 /2

and

y = rsin(π/4) = rSin45

y=r√2 /2

This makes it very

easy to convert equations from rectangular to polar coordinates.

x²+y²= (r√2/2)²+(r√2/2)²

x²+y²= 2r²/4 + 2r²/4

x²+y²= r²

Since r=0

x²+y²= 0

x²=y²

Therefore, x=y

Option D

The straight line y=x

4. r=4θ

Here the distance from the origin

exactly matches the angle, so a bit of thought makes it clear that when θ ≥ 0 we get the spiral of Archimedes ( check attachment ) When θ < 0, r is also negative, and so the full graph is the right hand picture in the figure. Check attachment

The correct option is B

None of the above

5. r=2Cosθ

To convert from polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following equations

x=rCosθ

Cosθ=x/r

y=rSinθ

Sinθ=y/r

Also, r²=x²+y²

Now, apply the given information

r=2cosθ

Since cosθ=x/r

r=2x/r

Cross multiply

r²=2x

x²+y²=2x

x²+y²-2x=0

(x-1)² + y² -1 =0

(x-1)² + y² = 1²

Then,

It is a circle with center (1,0) and radius 1.

A circle of radius 1 with center on the y-axis

Option A is correct

7 0
3 years ago
What is 531 x 321 x 345???
earnstyle [38]
The answer to that is 58,805,595 . hope this helps !!!
7 0
3 years ago
Read 2 more answers
13) Ayla's lunch bill was $8.70 and Harley's was $10.30. The girls' uncle paid
Otrada [13]

Answer:

$2.85

Step-by-step explanation:

First, add the bill up ($8.70 + $10.30 = 19). So now you need to find what 15% of $19 is...To find the percentage of something you need to turn it into a decimal, 0. (whatever the percentage number is). So in this case, 19 times 0.15, which is a tip of $2.85.

5 0
2 years ago
Read 2 more answers
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